The multi-objective dynamic optimization of time-delay switched systems (TDSS) presents considerable challenges, stemming from the complex interplay among time-delay-induced dynamic lag, discrete switching logic, and conflicting performance objectives. To address these difficulties, a multi-objective hybrid intelligent optimization method is proposed, aimed at generating a well-distributed and comprehensive Pareto solution set. First, an improved Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) is developed, which adopts uniformly distributed weight vectors to ensure comprehensive Pareto front coverage and integrates neighborhood-based collaboration to improve computational efficiency. The algorithm also incorporates a constraint-handling mechanism to maintain solution feasibility throughout the search process, thereby enabling effective global exploration within the feasible domain. Then, Hamiltonian-based costate analysis is employed to derive exact gradients of the scalarized objective function with respect to switching times and control parameters, providing a theoretical basis for precise local refinement of candidate solutions. Finally, numerical simulations on a nonlinear TDSS validate the effectiveness of the multi-objective hybrid intelligent optimization method, as it generates a more uniform Pareto front, delivers better objective performance than the MOEA/D and ϵ-constrained method.

In this paper, a hybrid intelligent optimization method based on multi-objective enhanced particle swarm optimization-genetic algorithm (MOEPSO-GA) is proposed for solving multi-objective dynamic optimization problem. This method innovatively combines the global search capability of heuristic algorithms with the high precision and guaranteed optimality of deterministic algorithms, ensuring an evenly distributed Pareto front. Firstly, a global dual optimal selection mechanism is introduced, utilizing a genetic algorithm to balance the diversity and convergence of non-dominated solutions. Secondly, an adaptive flight parameter adjustment mechanism is designed to assist particles in adaptively selecting learning modes, thereby balancing the global exploration and local development capabilities. Thirdly, the optimal replacement mechanism significantly enhances population diversity, enabling MOEPSO-GA to rapidly explore non-dominated regions. Fourthly, the adaptive ε-constraint method is combined with sequential quadratic programming to optimize the non-dominated set explored by MOEPSO-GA, promoting rapid convergence to the true Pareto front and thereby reducing computational costs. Finally, the effectiveness and superiority of the proposed algorithm are validated through numerical simulations and comparisons with state-of-the-art algorithms.

In microseismic monitoring systems (MMS), efficiently and accurately recognizing fracture waveforms and picking their arrival times of P-wave and S-wave are two crucial signal processing tasks for timely rockburst warnings. Previous studies have overlooked the potential relationship between these two tasks and have processed them independently, leading to redundant computations and performance bottlenecks. An intuitive solution is to integrate the two tasks into a multitask learning (MTL) framework. However, due to their competing optimization objectives, where recognition primarily focuses on global shape features and picking relies on local detail features, conventional parallel MTL structures often suffer from conflicting gradients. This conflict leads to a severe seesaw phenomenon that results in significant performance degeneration in picking task. To address this issue, we proposeMSNet, a cascade MTL framework forMicroseismicSignal processing. In this framework, a self-supervised fracture-perception module and a dual-scale fusion module are proposed to model the hierarchical dependence between recognition and picking tasks. Specifically, these modules enable a forward cascaded feature refinement from recognition to picking, as well as an information supplement from picking to recognition. Thus, MSNet transforms the two tasks from parallel competing learning into a mutually cooperative process that effectively mitigates the seesaw phenomenon. Finally, MSNet is validated on two datasets collected from different tunnel boring machine excavation projects. The results demonstrate its superiority over state-of-the-art methods in terms of accuracy that achieves an approximate 2% improvement under laboratory conditions. Furthermore, the practical applicability of MSNet is further validated through its deployment in a real-world tunnelling project, where it successfully detects rockburst events and provides real-time warnings.

In this article, a hybrid intelligent optimization method is proposed for the dynamic optimization of path-constrained switched systems with free switching sequences. This method combines improved particle swarm optimization and differential evolution (IPSO-DE) method with a gradient-based dynamic optimization method, which can simultaneously obtain the global optimal solution, i.e., optimal control input, optimal switching instants, and optimal switching sequences. First, control vector parameterization (CVP), switching time parameterization (STP), and switching sequence smoothing techniques are employed to transform the original problem into a continuous finite-dimensional dynamic one. Second, the path constraints are discretized into a finite number of point constraints, and the IPSO-DE algorithm is proposed to search for the global optimal solution of the continuous dynamic problem with discretized constraints. Then, the obtained optimal solution serves as the initial point to calculate the gradients of the objective function with respect to control input, switching instants, and switching sequences. Third, the gradient-based deterministic method is applied to obtain the global optimal solution that satisfies the first-order optimality condition. Fourth, the finite termination of the hybrid intelligent optimization method is proven. Finally, the effectiveness of the proposed method is verified through three numerical examples.

An efficient dynamic optimization approach for internally forced switching systems is provided in this work. The distinguishing characteristic of the internally forced switching systems is that once the trajectory of the state of a mode hits a switching surface in the state space, the current mode stops operating immediately and then the next mode is activated automatically. To effectively address the optimal control of such systems, first, the continuous control input is approximated by piecewise constant functions utilizing the control vector parametrization (CVP) technique. Sensitivity analysis is subsequently used to derive the gradient of the cost function with respect to (w.r.t.) parameterized control input, while the state transition matrix is introduced for determining the gradients of the objective function w.r.t. switching instants. Second, a dynamic optimization method with the aid of gradient information is presented to locate the optimal solution for internally forced switching systems with a guarantee of rigorously satisfying the path constraints. Third, it is demonstrated that the designed algorithm terminates finitely to generate a feasible solution satisfying the Karush-Kuhn-Tucker (KKT) conditions of the dynamic optimization of internally forced switching systems to a specified tolerance. Finally, the proposed optimization approach is applied to the fed-batch fermentation process to obtain a high concentration of 1,3-propanediol production, while ensuring that the glycerol concentration rigorously satisfies the required boundary during the whole feed process. Note to Practitioners—The motivation of this work is to develop an efficient optimization method for path-constrained internally forced switching systems, which have a wide range of applications in practice, e.g., obstacle avoidance robots, chemical batch feed fermentation, etc. Although research methods for dynamic optimization of switched systems have been well-established, to the best of the author’s knowledge, there is almost no research directly dealing with internally forced switching systems. Since the switching instant of such systems is strongly dependent on the inputs and the state of the system, which makes it difficult to analyze the gradient of the objective function w.r.t. the switching instant. Moreover, it is necessary to consider the inequality path constraints that guarantee the requirements such as system safety and product quality. Therefore, this work aims at the dynamic optimization of the path-constrained internal forced switching system, considering the two important requirements of rigorous satisfaction of path constraints and a finite number of iterations of the algorithm. An efficient dynamic optimization approach is proposed based on the variational method, semi-infinite program technique, and right-handed constraint method, which can simultaneously obtain the optimal switching instants and optimal control inputs while guaranteeing that the path constraints are rigorously satisfied.

This study proposes a novel adaptive funnel-based approach for optimal formation control in second-order nonlinear multi-agent systems (MASs). The nonlinear system considered includes unknown dynamics, with only one measurable output variable. The states, not directly measurable, are reconstructed using fuzzy state observers. In the context of an actor-critic framework, a novel funnel optimal predefined-time formation controller is developed. The primary objective is to achieve practical predefined-time stability in the closed-loop system, confining formation errors within a specified funnel while minimizing the cost of maintaining formation patterns between the leader and followers. Comparative simulations further confirm the advantages of the proposed method.Note to Practitioners—Cooperative control of multi-agent systems (MASs) has garnered considerable interest in diverse applications, including multi-motor synchronization and spacecraft formation flying. Managing complex engineering systems is challenging with a solitary component, prompting a focus on MASs. Formation control, a key aspect of MASs, has become a prominent research area. In practical applications, certain states are challenging to measure, and performance behaviors, such as convergence rate, maximum overshoot, and maximum steady-state error, often require predefined specifications. Simultaneously, achieving control tasks must be balanced with minimizing resource consumption. This study explores funnel-based output-feedback optimal leader-following control for MASs, emphasizing predefined-time convergence.

Dyadic control is a new control frontier, which is to address two (often conflicting) objectives simultaneously. We consider rendering bothcompact formationandcollision avoidancein uncertain cooperative road transportation systems. These two tasks, however, present conflicting objectives, where excessive stress on formation tightness may lead to an increased risk of collisions. The tasks are creatively formulated as equality constraints and inequality constraints. Based on the generalized Udwadia-Kalaba (GUK) equation, two independent controllers are developed to handle these constraints, with orthogonality between the control components ensuring no mutual interference. The proposed method guarantees the uniform boundedness and uniform ultimate boundedness of the system, even in the presence of unknown uncertainties. The effectiveness of the control strategy is demonstrated through simulations of a four-vehicle fleet system.

Deep neural networks (DNNs) have shown significant progress in many application fields. However, overfitting remains a significant challenge in their development. While existing data-augmentation techniques such as MixUp have been successful in preventing overfitting, they often fail to generate hard mixed samples near the decision boundary, impeding model optimization. In this article, we present adversarial MixUp (AdvMixUp), a novel sample-dependent method for regularizing DNNs. AdvMixUp addresses this issue by incorporating adversarial training (AT) to create sample-dependent and feature-level interpolation masks, generating more challenging mixed samples. These virtual samples enable DNNs to learn more robust features, ultimately reducing overfitting. Empirical evaluations on CIFAR-10, CIFAR-100, Tiny-ImageNet, and ImageNet demonstrate that AdvMixUp outperforms existing MixUp variants.

Aiming to address the time-varying formation control problem of uncertain and networked multiagent systems, this article develops a novel robust constraint-following control approach, which is implemented in two steps. First, a kinematic model (i.e., kinematic constraint) for each agent is constructed by employing local tracking errors; this constraint mainly ensures formation maintenance and trajectory following. Second, based on the kinematic model, and to attenuate time-varying uncertainties, a robust constraint-following controller is meticulously designed. This controller not only ensures the strict satisfaction of kinematic constraints but also sufficiently suppresses time-varying uncertainties. Ultimately, an application to quadrotor swarm is provided to illustrate the proposed control scheme.

This article concerns nonlinear model predictive control (MPC) with guaranteed feasibility of inequality path constraints (PCs). For MPC with PCs, the existing methods, such as direct multiple shooting, cannot guarantee feasibility of PCs because the PCs are enforced at finitely many time points only. Therefore, this article presents a novel MPC framework that is capable of not only achieving stability control but also guaranteeing feasibility of PCs during the rolling optimization stages of MPC. Under the above MPC framework, an algorithm is first proposed by applying the semi-infinite programming technique to the rolling optimization of MPC. However, it takes heavy computational time to achieve guaranteed feasibility of PCs. Therefore, to guarantee feasibility of PCs meanwhile effectively reducing the computation burden of the closed-loop system, an event-triggered sampling mechanism is constructed in the above path-constrained MPC algorithm. Moreover, sufficient conditions are given for asymptotic convergence of the closed-loop systems. Finally, the effectiveness of the proposed results is illustrated via a cart-damper-spring system.

In this article, we develop two invariance principles for nonlinear discrete-time switched systems based on multiple Lyapunov functions and multiple weak Lyapunov functions, respectively, which allow the first differences of multiple weak Lyapunov functions to be positive on certain sets. It is shown that the solution of the system is attracted to the largest weakly invariant set in a certain specific region. Then, based on the invariance principle developed and geometrical dissipativity, we obtain the generalized output synchronization for discrete-time dynamical networks with nonidentical nodes by an appropriate switching among several communication topologies. Finally, two examples are provided to demonstrate the effectiveness of the main results.

A new type of containment maneuvering protocols for multiple marine surface vehicles (MSVs) is developed to follow a parameterized path in this work, where the tracking errors are constrained within finite time and the information needed to be transmitted is quantized during coordination. To achieve containment maneuvering of multiple MSVs, a two-objective coordinated control framework is proposed. For the geometric objective, by developing tan-type barrier Lyapunov functions (BLFs) and extended Lyapunov condition-based finite-time guidance laws, the performance of the parameterized line-of-sight guidance framework, including convergence speed and tracking error constraints, is improved. For the dynamic objective, based on quantized control strategy and smooth saturation functions, novel bounded containment maneuvering protocols are proposed to dramatically alleviate the burden of communications among MSVs and ensure more faster dynamic behavior on tracking the path updating speed. Both theoretical analysis and experimental tests with comparative studies illustrate the validity of the proposed containment maneuvering strategy.

This article investigates the fault-tolerant coordinated tracking control problem for networked fixed-wing unmanned aerial vehicles (UAVs) against faults and communication delays. By supplementing the commonly used Gaussian functions in the fuzzy neural networks (FNNs) with sine-cosine functions and constructing two kinds of recurrent loops within the FNN architecture, double recurrent perturbation FNNs are cleverly designed to learn the unknown terms containing faults and uncertainties. Then, adaptive laws are designed for double recurrent perturbation FNNs. Moreover, by assimilating fractional-order calculus into the sliding-mode surfaces and the control signals, refined transient-state and steady-state adjustment performances can be obtained. It is shown by Lyapunov stability analysis that all fixed-wing UAVs can coordinately track their desired trajectories and the tracking errors are uniformly ultimately bounded. Comparative simulation results are provided to show the effectiveness of the proposed control strategy.

This article presents an adaptive fuzzy fixed-time output feedback control approach for achieving an optimal time-varying formation (TVF) of multiple omnidirectional robot systems (MORSs) with uncertain external disturbances. Given that only output variables of the system are measurable, the method employs fuzzy state observers to reconstruct other unmeasured states. Novel performance index functions that incorporate exponential power terms are developed to achieve the optimization of a formation control system's performance. This function is utilized to design a fixed-time optimal scheme based on an identifier–actor–critic structure, which is a well-established control framework. Through rigorous analysis, it is proved that the proposed scheme guarantees fixed-time boundedness of all signals in the system and achieves formation control at a minimum cost. The comparative simulations and data analyses verify the effectiveness and superiority of the proposed control algorithm.

This article proposes a novel predefined-time optimal formation control approach for second-order heterogeneous multiagent systems with nonlinear dynamics and external disturbances. Fuzzy logic systems are used to identify unknown nonlinearities. To enhance the system's robustness against external disturbances, an$H_\infty$control strategy is implemented. The predefined-time optimal formation control method is developed by leveraging backstepping technology and actor–critic framework. This approach is designed to guarantee that the closed-loop system is practical predefined-time stable and$L_{2}$-gain is less than or equal to a positive real number$\nu$, and all system signals are predefined-time bounded while minimizing the cost of maintaining a formation pattern between the leader and followers. Simulation results validate the effectiveness and superiority of this control strategy.

Agile formation (AF) is a new frontier for intelligent swarm system formation. The AF pertains to perform various tasks in short phases of work and frequent reassessment and adaptation of plans. This greatly increases the applicability of swarm systems. There are however two major challenges for the control design: smooth task transitions and guaranteed collision avoidance. We adopt the constraint-following approach to address these. First, for agile formation, a plateau activation function is proposed to generate a sequence of consecutive and disjoint formations. For collision avoidance, a distance-gauge function is proposed. Second, by taking the objectives of agile formation control and collision avoidance as desirable constraints, the agile formation together with collision avoidance are both cast into a constraint following control problem. Third, to evaluate the constraint-following error, a performance measure$\beta $is introduced and then an agile formation control is designed to render the$\beta $-measure to be asymptotically convergent to zero. By this, the swarm system can follow the agile formation constraint and collision avoidance constraint. Therefore, agile formation and collision avoidance are both accomplished.

In this article, a dynamic event-triggered adaptive antidisturbance (ETAAD) switching control strategy is proposed for switched systems subject to multisource disturbances. The disturbances are divided into two categories: the available unmodeled disturbance and the unavailable dynamic neural network modeled disturbance. First, a dynamic ET criterion is set based on the system state. Then, a novel dynamic ETA disturbance estimator is introduced to observe the modeled disturbance. Furthermore, according to the ET rule and adaptive disturbance observer, a switched controller is designed. Next, under the controller and switching criterion with the average dwell time limitation, sufficient conditions are given to force the switched systems to realize multisource disturbance suppression (DS), trajectory tracking, and communication resource (CR) saving simultaneously. Meanwhile, the Zeno phenomenon may be caused by the ET rule being excluded. In addition, the presented ETAAD approach is also applicable to the nonswitched systems case. Finally, a simulation case is given to validate the effectiveness of the dynamic ETAAD switching control method.

Cyber–physical systems (CPSs) driven by a local controller and a remote controller have been gaining significant research interest in recent years due to its application scenarios in practice, such as unmanned aerial vehicles (UAVs). In this article, we consider the security issue in the remote control system with a local controller under stealthy attacks. Under this framework, one controller is designed locally based on the limited measurements collected by a local sensor, and the other controller is designed remotely and is transmitted to the actuator through a wireless communication channel, which may suffer malicious attacks due to its openness. To defend attacks on remote control signal, the K–L divergence-based detector or$\chi ^{2}$detector is often adopted. However, there may be attackers adopting stealthy attacks, which can bypass such detectors. Therefore, we analyze the existence of such attacks, and analytically characterize the worst-estimation performance degradation induced by the remote control signal attack. Further, we construct the optimal attack signal to achieve the upper bound on the estimation performance degradation. In addition, we also give countermeasures against such stealthy attacks. Simulations are provided to illustrate the proposed results.

This article focuses on the event-triggered consensus control (ETCC) issue of the time-varying delayed leader-following nonlinear multiagent systems (TVDLFNMASs). In order to minimize the influence on uncertain factors of the information transmission and the data information loss, the switching topologies are constructed as the generally uncertain Markovian jumping forms whose transition rates include completely unknown elements and estimate values of uncertain elements. In addition, the event-triggered (ET) transmission strategy is given based on the threshold parameter and the ET matrix to relieve the communication burden of TVDLFNMASs. The new leader-following (LF) consensus conditions and control gains are obtained based on ET strategy. Finally, the effectiveness of the ET consensus criteria is demonstrated in the simulation section.

In this article, the event-triggered output regulation problem (EORP) under the denial-of-service (DoS) attacks is considered for networked switched systems (NSSs) with unstable switching dynamics (USDs). The USDs here refer to the unsolvable output regulation of each subsystem and the destabilization at partial switching instants, which indicates that the Lyapunov function does not decrease monotonically in activation intervals of each subsystem and increases at partial switching instants. First, long-duration DoS attacks (LDDAs) are considered, where LDDAs imply that their duration may be longer than the total dwell time (DT) of several adjacent activated subsystems. By imposing constraints at switching instants, consecutive asynchronous subsystem switching caused by LDDAs and USDs is allowed, that is, the subsystem switches several times but the controller switching is blocked by LDDAs and controllers fail to switch correspondingly. Second, mixed event-triggered mechanisms (ETMs), combining event-triggered conditions and periodic sampling conditions, are designed to reduce network burden under LDDAs and improve system performance subject to destabilizing switching. Then, an improved DT for switching signal permits irregular arrangement of destabilizing and stabilizing switching and is more suitable for NSSs subject to LDDAs. Moreover, sufficient conditions ensure the solvability of EORP for NSSs with USDs under LDDAs, network-induced delays, random packet losses, and packet disorders. Finally, a switched RLC circuit shows the feasibility of the proposed method.

This article focuses on the dissipativity-based consensus tracking control (DBCTC) problems of time-varying delayed leader-following nonlinear multiagent systems (LFNMASs) with the event-triggered transmission strategy. The switching topologies of the LFNMASs are subject to the uncertain and partially unknown generally Markovian jumping process. The control inputs of the following agents are updated according to the proposed event-triggered transmission strategy, which could reduce the communication burden. Based on the event-triggered transmission condition and distributed consensus protocol, some dissipativity-based criteria obtained by adopting the delay-product-term Lyapunov-Krasovskii functional (DPTLKF) and higher order polynomial-based relaxed inequality (HOPRII) are proposed to guarantee the LFNMAS consensus. The validity of the main results is verified by two simulation examples.

This article concerns the finite-time performance analysis for switched Takagi–Sugeno fuzzy (STSF) systems subject to time-varying delay. Since the existing relevant results for finite-time synthesis of general switched systems require the finite-time stability property of the individual subsystem, a more general situation that the STSF systems comprised fully of finite-time unstable delayed subsystems are considered in the investigation. For surmounting this situation, a novel time-dependent multiple Lyapunov–Krasovskii functional approach is developed by integrating a ranged dwell time switching mechanism. Then, the corresponding (input–output) finite-time stability criteria with less conservativeness are simultaneously derived for the (perturbed) STSF delayed systems to be (input–output) finite-time stable over the concerned finite-time interval. Finally, two illustrative examples are provided to demonstrate the accuracy and superiority of the developed (input–output) finite-time analysis framework.

Aeroengine performance optimization rem- ains significant for both efficiency and safety during specific operating conditions. Previous works usually solve this optimization problem under a single-objective optimization framework, while multiple objectives need to be optimized simultaneously. Besides, the underlying optimization process requires a variety of function evaluations, and the evaluation cost for an aeroengine is expensive. In reality, the aeroengine model has multiple information sources with different costs and accuracy. The different costs and accuracy of the multiple information sources should be traded off to guide the search for the optimal in a cost-efficient way. Therefore, we propose a multi-information-source framework for enabling efficient multiobjective Bayesian optimization. We construct the surrogate model with a multifidelity Gaussian process and choose the location–source pair with a modified acquisition function. Finally, we apply the proposed method to improve the performance indexes of the aeroengine, which confirms the efficiency of the proposed algorithm.

Recently, dynamic memristor (DM)-cellular neural networks (CNNs) have received widespread attention due to their advantage of low power consumption. The previous works showed that DM-CNNs have at most 318 equilibrium points (EPs) with$n=16$cells. Since time delay is unavoidable during the process of information transmission, the goal of this article is to research the multistability of DM-CNNs with time delay, and, meanwhile, to increase the storage capacity of DM-delay (D)CNNs. Depending on the different constitutive relations of memristors, two cases of the multistability for DM-DCNNs are discussed. After determining the constitutive relations, the number of EPs of DM-DCNNs is increased to$3^{n}$with$n$cells by means of the appropriate state-space decomposition and the Brouwer’s fixed point theorem. Furthermore, the enlarged attraction domains of EPs can be obtained, and$2^{n}$of these EPs are locally exponentially stable in two cases. Compared with standard CNNs, the dynamic behavior of DM-DCNNs shows an outstanding merit. That is, the value of voltage and current approach to zero when the system becomes stable, and the memristor provides a nonvolatile memory to store the computation results. Finally, two numerical simulations are presented to illustrate the effectiveness of the theoretical results, and the applications of associative memories are shown at the end of this article.

Dynamic optimization problems are pervasive in various fields, ranging from chemical process control to aerospace, autonomous driving, physics, robotics, and beyond. These problems involve optimizing a dynamic system considering inputs, parameters, constraints, and a cost function. For dynamic optimization, two broad classes of strategies emerge: deterministic and heuristic methods. Deterministic optimization methods leverage the analytical properties of the problem, generating a sequence of points that converge to the optimal solution. These techniques are suitable when explicit models and constraints are available and easy to evaluate. On the other hand, heuristic approaches treat the problem as a black box, relying on iterative improvements to a fitness function. They are employed for complex problems with challenging system models or significant uncertainty.

Dynamic optimization is one of the model-based adaptive reinforcement learning methods, which has been widely used in industrial systems with switching mechanisms. This article presents an efficient dynamic optimization strategy to locate an optimal input and switch times for switched systems with guaranteed satisfaction for path constraints during the whole time period. In this article, we propose a single-level algorithm where, at each iteration, gradients of the objective function with respect to switch times and the system input are evaluated by solving adjoint systems and sensitivity equations, respectively. Then the optimization of the input is performed at the same iteration with that of the switch time vector, which greatly reduces the number of nonlinear programs (NLPs) and computational burden compared with multistage algorithms. The feasibility of the optimal solution is guaranteed by adapting a new policy iteration method proposed to switched systems. It is proven that the proposed algorithm terminates finitely, and converges to a solution which satisfies the Karush-Kuhn-Tucker (KKT) conditions to specified tolerances. Numerical case studies are provided to illustrate that the proposed algorithm has less expensive computational time than the bi-level algorithm.

This article investigates the problem of path following for the underactuated unmanned surface vehicles (USVs) subject to state constraints. A useful control algorithm is proposed by combining the backstepping technique, adaptive dynamic programming (ADP), and the event-triggered mechanism. The presented approach consists of three modules: guidance law, dynamic controller, and event triggering. First, to deal with the "singularity" problem, the guidance-based path-following (GBPF) principle is introduced in the guidance law loop. In contrast to the traditional barrier Lyapunov function (BLF) method, this article converts the USV's constraint model to a class of nonlinear systems without state constraints by introducing a nonlinear mapping. The control signal generated by the dynamic controller module consists of a backstepping-based feedforward control signal and an ADP-based approximate optimal feedback control signal. Therefore, the presented scheme can guarantee the approximate optimal performance. To approximate the cost function and its partial derivative, a critic neural network (NN) is constructed. By considering the event-triggered condition, the dynamic controller is further improved. Compared with traditional time-triggered control methods, the proposed approach can greatly reduce communication and computational burdens. This article proves that the closed-loop system is stable, and the simulation results and experimental validation are given to illustrate the effectiveness of the proposed approach.

In this article, two algorithms are proposed to solve multiobjective path-constrained dynamic optimization problems. In each algorithm, an adaptive$\varepsilon $-constraint method is employed to solve the multiobjective dynamic optimization problems (MODOPs) with path constraints in two iterative loops. In the outer loop, the adaptive$\varepsilon $-constraint method adaptively adjusts the choice of the parameters$\varepsilon $, which transfers MODOP into a sequence of single-objective dynamic optimization problems (SODOPs) with extra inequality constraints. In the inner loop, two different algorithms are used to solve the single-objective optimization problems. The first algorithm guarantees that the path constraints can be satisfied with any finite prescribed tolerance by replacing path constraints with a finite number of point constraints. Furthermore, the second algorithm guarantees that the path constraints are rigorously satisfied by enforcing the path constraints at a limited number of time points and by restricting the right-hand side of the path constraints. The proposed algorithms are proven to converge within finite iterations. The effectiveness of the algorithms is verified via numerical studies, along with a comparison to a state-of-the-art algorithm.

Stochastic model predictive control (SMPC) with probabilistic path constraints remains an open and challenging issue due to the intractability of probabilistic path constraints, let alone guarantee rigorous satisfaction. For the SMPC problem, the greatest difficulty lies in how to solve a finite time domain optimal control problem in the corresponding sampling step while ensuring that the probabilistic path constraints are rigorously satisfied. Aiming at the above problem, this article presents a new method for SMPC with guaranteed rigorous satisfaction of probabilistic path constraints. Specifically, first, to convert thorny probabilistic path constraints into computationally solvable and equivalent deterministic constraints, a transformation technique is proposed by utilizing a designed ancillary feedback controller and the information on the probabilistic distribution of disturbances. Then, a probabilistic path-constrained dynamic event-triggered SMPC (DETSMPC) algorithm is further designed where not only control input can be obtained but also the probabilistic path constraints can be rigorously satisfied over the entire time domain. In addition, to mitigate redundant computation consumption, a novel event-triggering sampling scheme with two dynamic thresholds is proposed by the virtue of prediction horizon, real-time sampled data, and previous predicted and triggered states. Furthermore, it is proved that the proposed algorithm is feasible for the overall probabilistic path-constrained closed-loop DETSMPC system. Moreover, the convergence in probability of the closed-loop system is presented. Finally, a numerical example is provided to illustrate the effectiveness of the proposed methods.

This letter investigates the positivization with the stability of switched linear systems by logic-based switchings without requiring the positivity conditions of each subsystem. First, the definitions on row submatrix and nonzero-row submatrix are introduced to characterize the structure of subsystems. Second, a logic-based switching law is designed based on the structural characteristics. Third, the sufficient conditions on the positivization together with stability for switched linear systems are derived in the framework of the logic switching law. Thus, based on the logic switching law, the sufficient conditions are presented for that of 3-D switched systems by further presenting a more concrete case. Finally, a numerical example is given to illustrate the validity of the proposed methods.

This work proposes a command filter-based adaptive practical prescribed-time (PPT) asymptotic tracking control scheme for autonomous underwater vehicles (AUVs) under dynamic uncertainties. Considering that the followers have limited communication angles in the leader–follower formation structure, where a novel controller is proposed to ensure communication angles to achieve preassignable precision within a predefined time. First, we present a PPT control for handling the limited communication angles and, thus, they are allowed to be limited, turnable, and controllable. Then, to achieve the asymptotic convergence of output tracking errors, the proposed adaptive controllers can effectively insure the trajectory tracking errors of AUVs asymptotically converge to zero under the influence of dynamic uncertainties. Furthermore, the derived asymptotically tracking command filter technique for AUVs not only deduce an acceleration-free strategy for followers but also achieve the asymptotic convergence of output tracking errors for the command filters themselves. In the end, the effectiveness of the proposed control strategy is demonstrated through stability analysis and simulation test.

This article addresses an adaptive backstepping finite-time optimal formation control problem for second-order multiagent systems (MASs) with unknown nonlinear dynamics. Neural networks (NNs) are used to identify the unknown uncertain terms in the controlled system. Then, the finite-time optimal formation control is designed by constructing a novel optimal performance index function containing exponential power terms based on the framework of identifier–actor–critic. It is proved that all signals in the system are bounded in finite time, and the formation control is simultaneously achieved at minimum cost. The effectiveness and superiority of the proposed control algorithm are verified by simulation comparisons and data analyses.

The automatic control of blast furnace (BF) ironmaking process has always been an important yet arduous task in metallurgic engineering and automation. In this article, a novel Kalman filter-based robust model-free adaptive predictive control (MFAPC) method is proposed for the direct data-driven control of molten iron quality in BF ironmaking. First, a compact-form dynamic linearization-based extended MFAPC method for multivariable molten iron quality control is proposed by generalizing the existing single-variable MFAPC method to multivariable systems. Based on it, a Kalman filter-based robust MFAPC is further proposed considering the problems of data loss and measurement noise in quality detection. Specifically, the robust mechanism in the robust MFAPC combines a novel dynamic linearization method with a concept termed Pseudo-Jacobian matrix to predict the missing data during data loss. After that, a Kalman filter is constructed based on a prediction model to filter the measurement noise. The stability of the proposed control method is analyzed, and various data experiments using actual industrial data are performed to verify the effectiveness of the proposed methods.Note to Practitioners—The extremely complicated dynamics of blast furnace ironmaking process make the model-based controllers difficult to realize in practice. In this article, a novel robust model-free adaptive predictive control method is proposed for direct data-driven control of multivariate molten iron quality in the ironmaking process. This method directly uses the process input and output data to design the multivariable quality controller online by the compact-form dynamic linearization technology and the internal multilayer prediction mechanism, thus avoids the drawback of model-based controllers in troublesome process modeling. Moreover, the proposed method can effectively avoid the influence of data loss and measurement noise on the controller performance with the designed Kalman filter-based robust mechanism. The superiority and practicability of the proposed method are verified using various experiments against actual industrial data.

This article studies the vision-based tracking control problem for a nonholonomic multirobot formation system with uncertain dynamic models and visibility constraints. A fixed onboard vision sensor that provides the relative distance and bearing angle is subject to limited range and angle of view due to limited sensing capability. The constraint resulting from collision avoidance is also taken into account for safe operations of the formation system. Furthermore, the preselected specifications on transient and steady-state performance are provided by considering the time-varying and asymmetric constraint requirements on formation tracking errors for each robot. To address the constraint problems, we incorporate a novel barrier Lyapunov function into controller design and analysis. Based on the recursive adaptive backstepping procedure and neural-network approximation, we develop a vision-based formation tracking control protocol such that formation tracking errors can converge into a small neighborhood of the origin in finite time while meeting the requirements of visibility and performance constraints. The proposed protocol is decentralized in the sense that the control action on each robot only depends on the local relative information, without the need for explicit network communication. Moreover, the control protocol could extend to an unconstrained multirobot system. Both simulation and experimental results show the effectiveness of the control protocol.

In this article, for a class of continuous-time nonlinear nonaffine systems with unknown dynamics, a robust approximate optimal tracking controller (RAOTC) is proposed in the framework of adaptive dynamic programming (ADP). The distinguishing contribution of this article is that a new Lyapunov function is constructed, by using which the derivative information of tracking errors is not required in computing its time derivative along with the solution of the closed-loop system. Thus, the proposed method can make the system states follow nondifferentiable reference signals, which removes the common assumption that the reference signals have to be continuous for tracking control of continuous-time nonlinear systems in the literature. The theoretical analysis, simulation, and application results well illustrate the effectiveness and superiority of the proposed method.

This article investigates a distributed fractional-order fault-tolerant formation-containment control (FOFTFCC) scheme for networked unmanned airships (UAs) to achieve safe observation of a smart city. In the proposed control method, an interval type-2 fuzzy neural network (IT2FNN) is first developed for each UA to approximate the unknown term associated with the loss-of-effectiveness faults in the distributed error dynamics, and then a disturbance observer (DO) is proposed to compensate for the approximation error and bias fault encountered by each UA, such that the composite learning strategy composed of the IT2FNN and the DO is obtained for each UA. Moreover, fractional-order (FO) calculus is incorporated into the control scheme to provide an extra degree of freedom for the parameter adjustments. The salient feature of the proposed control scheme is that the composite learning algorithm and FO calculus are integrated to achieve a satisfactory fault-tolerant formation-containment control performance even when a portion of leader/follower UAs is subjected to the actuator faults in a distributed communication network. Furthermore, it is shown by Lyapunov stability analysis that all leader UAs can track the virtual leader UA with time-varying offset vectors, and all follower UAs can converge into the convex hull spanned by the leader UAs. Finally, comparative hardware-in-the-loop (HIL) experimental results are presented to show the effectiveness and superiority of the proposed method.

This article proposes a fractional-order intelligent fault-tolerant synchronization tracking control (FO-I-FTSTC) scheme for multiple unmanned airships (UAs) against actuator faults. Within the developed control architecture, fixed-time prescribed performance functions (PPFs) are first designed to transform the synchronization tracking errors into a new set of error variables, such that the original errors are strictly confined within the prescribed bounds. Then, fractional calculus and sliding mode surface are sequentially introduced to construct the FO errors. Moreover, to handle the unknown terms and bias faults in the FO sliding-mode error dynamics, fuzzy neural networks with recurrent loops are artfully constructed to act as the intelligent learning units. Furthermore, the norm of the loss-of-effectiveness fault factors is introduced for each UA to reduce the number of adaptive parameters. The distinct feature of the proposed method is that the FO-I-FTSTC performance is significantly enhanced by integrating recurrent fuzzy neural networks, fractional calculus, and fixed-time PPFs into a unified framework, leading to a high-precision control scheme. It is shown by Lyapunov analysis that all UAs can track their desired references in a synchronized manner, and the synchronization tracking errors are bounded and strictly confined within the prescribed error bounds. Comparative hardware-in-the-loop experiments are presented to show the effectiveness of the proposed FO-I-FTSTC scheme.

This article first investigates the issue on dynamic learning from adaptive neural network (NN) control of discrete-time strict-feedback nonlinear systems. To verify the exponential convergence of estimated NN weights, an extended stability result is presented for a class of discrete-time linear time-varying systems with time delays. Subsequently, by combining the n -step-ahead predictor technology and backstepping, an adaptive NN controller is constructed, which integrates the novel weight updating laws with time delays and without the σ modification. After ensuring the convergence of system output to a recurrent reference signal, the radial basis function (RBF) NN is verified to satisfy the partial persistent excitation condition. By the combination of the extended stability result, the estimated NN weights can be verified to exponentially converge to their ideal values. The convergent weight sequences are comprehensively represented and stored by constructing some elegant learning rules with some novel sequences and the mod function. The stored knowledge is used again to develop a neural learning control scheme. Compared with the traditional adaptive NN control, the proposed scheme can not only accomplish the same or similar tracking tasks but also greatly improve the transient control performance and alleviate the online computation. Finally, the validity of the presented scheme is illustrated by numerical and practical examples.

This article investigates the distributed fault-tolerant time-varying formation control problem for multiple unmanned airships (UAs) against limited communication ranges and input saturation to achieve the safe observation of a smart city. To address the strongly nonlinear functions caused by the time-varying formation flight with limited communication ranges and bias faults, intelligent adaptive learning mechanisms are proposed by incorporating fuzzy neural networks. Moreover, Nussbaum functions are introduced to handle the input saturation and loss-of-effectiveness faults. The distinct features of the proposed control scheme are that time-varying formation flight, actuator faults including bias and loss-of-effectiveness faults, limited communication ranges, and input saturation are simultaneously considered. It is proven by Lyapunov stability analysis that all UAs can achieve a safe formation flight for the smart city observation even in the presence of actuator faults. Hardware-in-the-loop experiments with open-source Pixhawk autopilots are conducted to show the effectiveness of the proposed control scheme.

This article investigates stabilization problems of networked event-triggered switched systems under multiasynchronous switching. Different from the existing asynchronous literature, a novel problem is considered in this article, i.e., the event-triggering scheme and controller both have independent switching delays relative to the system, which is called multiasynchronous switching. An adaptive event-triggering scheme with switching structure is utilized to achieve better adjustment in triggering frequency. A systematic framework for analyzing multiasynchronous switching stability and solving controller gains is established. Different Lyapunov functionals are employed, and new tight bound conditions on average dwell time are constructed. Besides, an active packet loss approach for handling packets disorder issues caused by large transmission delays is presented. Since the activation instants of the system, triggering scheme, and controller are mutually staggered with the data updating instants of the actuator, a novel analytical method aiming at the coupling effect is proposed. Finally, the validity of the adopted method in this article is demonstrated.

This article considers the decentralized fractional-order fault-tolerant control problem for unmanned aerial vehicles (UAVs) against wind disturbances and actuator faults in a directed communication network. A new composite adaptive disturbance observer-based decentralized fractional-order fault-tolerant control (CADOB-DFO-FTC) scheme, which incorporates fractional-order (FO) sliding-mode surfaces, nonlinear disturbance observers (NDOs), fuzzy wavelet neural networks (FWNNs), and robust controllers, is developed to achieve the attitude tracking control of networked UAVs in a decentralized way. Based on the FO sliding-mode surfaces, the NDOs are first developed to estimate the lumped uncertainties due to the aerodynamic parameter perturbations, wind disturbances, and actuator faults. Then, adaptive FWNNs with updating weighting matrices, mean vectors, and deviation vectors are constructed to effectively attenuate the adverse effects induced by the NDO estimation errors. Furthermore, to compensate the FWNN approximation errors, robust controllers are integrated into the developed control scheme to enhance the approximation abilities. It is shown that by using Lyapunov methods, all UAVs can track their attitude references. Finally, comparative simulation results are presented to demonstrate the effectiveness of the proposed method.

In mobile systems or the failure detection applications, the output for some input event is state-dependent and nondeterministic after intermittent sensor failures or measurement uncertainties, which does not hold under the conventional observability hypothesis. In this article, such cases can be modeled by a Mealy-based finite-state machine (FSM) with nondeterministic output functions, and we investigate the “initial-state” observability by use of matrix semitensor product (matrix-STP). First, to characterize the nondeterministic output functions, a virtual state set consisting of state–event pairs is introduced to obtain an augmented FSM. By resorting to the matrix-STP, the algebraic expression of augmented FSM is proposed. Subsequently, based on the newly constructed model, the initial-state observability can be verified by checking the distinguishability of state trajectories of the augmented FSM. Meanwhile, the necessary and sufficient condition for such initial-state observability is derived from a discriminant matrix consisting of polynomial elements. Finally, numerical examples show the validity of the proposed method. The current results are further conducive to explore the critical safety of cyber–physical systems in many real-world systems.

This article studies the$H_{\infty }$composite anti-bump switching control problem for switched systems. First, a more general description on the anti-bump switching performance is presented, including the definition on the existing input anti-bump switching performance and that on the rate anti-bump switching performance as special cases. Then, by virtue of determining a group of controllers combined with a switching logic, a control design program is steered for handling the problem of$H_{\infty }$composite anti-bump switching control for the switched systems. Further, a criterion is attained to capture the composite anti-bump switching performance and disturbance restrain performance, conquering the conflicts in the requirements of the input anti-bump switching, rate anti-bump switching, and disturbance attenuation. Also, this condition admits that each of the composite anti-bump switching performance and disturbance restrain performance may not be held by subsystems. In the end, a practical model example is provided to display how the formed control design scheme effectively works.

This article concentrates on finite-time stabilization and energy consumption estimation for nonlinear systems with and without delay. By constructing an appropriate controller and utilizing inequality techniques, sufficient conditions are proposed to guarantee the finite-time stability of the delayed nonlinear system. Furthermore, the energy consumption produced in system controlling is estimated by inequality techniques. Then, we formulate similar results for the delay-free case. Finally, numerical examples are presented to demonstrate the effectiveness of our theoretical results.

Dense medium separation (DMS) is of great significance for coal cleaning. The DMS control system always involves dense medium density adjustment and ash content control that are operating on fast and slow time scales, respectively. The inherent time-varying and strongly nonlinear characteristics of the DMS process give rise to challenges for the design of this multitime scale control system. To address this issue, this article proposes a dual-rate adaptive optimal tracking control approach for the DMS system. For the basic loop process, a nonlinear adaptive PI controller containing a neural network (NN)-based unmodeled dynamics compensator is proposed. Then, a lifting technique is used to unify the time scales of the two loops accompanied by formulating a generalized controlled object, whose dynamics is completely unknown. On this basis, a data-driven operation optimization control method that combines adaptive dynamic programming algorithm and reference control is developed, which is implemented using NNs. Finally, the stability of the proposed method is analyzed. The simulation results indicate its effectiveness.

This article presents an enhanced fault-tolerant synchronization tracking control scheme using fractional-order (FO) calculus and intelligent learning architecture for networked fixed-wing unmanned aerial vehicles (UAVs) against actuator and sensor faults. To increase the flight safety of networked UAVs, a recurrent wavelet fuzzy neural network (RWFNN) learning system with feedback loops is first designed to compensate for the unknown terms induced by the inherent nonlinearities, unexpected actuator, and sensor faults. Then, FO sliding-mode control (FOSMC), involving the adjustable FO operators and the robustness of SMC, are dexterously proposed to further enhance flight safety and reduce synchronization tracking errors. Moreover, the dynamic parameters of the RWFNN learning system embedded in the networked fixed-wing UAVs are updated based on adaptive laws. Furthermore, the Lyapunov analysis ensures that all fixed-wing UAVs can synchronously track their references with bounded tracking errors. Finally, comparative simulations and hardware-in-the-loop experiments are conducted to demonstrate the validity of the proposed control scheme.

In this article, the event-triggered output regulation problem is investigated for a networked flight control system with a switched system approach. By properly scheduling triggered times of periodic sampling associated with continuous event-triggering and switching instants of each subsystem, an alternate event-triggered mechanism based on the subsystem model is proposed to transmit the triggered information to the candidate controller. Since the subsystem may switch between two adjacent events while the corresponding controller does not switch, asynchronous switching may occur. Meanwhile, an event-triggered switching signal caused by asynchronous switching is designed with the mode-dependent average dwell time approach and event-triggered instants. By constructing multiple Lyapunov functions in the framework of the input delay approach and designing an error feedback controller, the sufficient condition for event-triggered asynchronous output regulation problem is solved. Finally, the proposed methods are proved to be effective by the F-18 aircraft model.

This article investigates the exponentially stabilization problem for a class of switched positive systems with actuator saturation under dwell time switching signal. The state feedback controllers for each subsystem are designed by proposing a new type of multiple time-varying linear co-positive Lyapunov functions (MTVLCLFs), and sufficient conditions for the exponentially stabilization of the studied systems are proposed under dwell-time switching. In order to cope with actuator saturation, the convex hull technique is utilized. Finally, an example of a turbofan engine model is presented to show the effectiveness of our proposed method.

This article concentrates on the synchronization problem of memristive complex-valued neural networks (CVNNs) with time delays via the pinning control method. Different from general control schemes, the pinning control is beneficial to reduce the control cost by pinning the fractional nodes instead of all ones. By separating the complex-valued system into two equivalent real-valued systems and employing the Lyapunov functional as well as some inequality techniques, the asymptotic synchronization criterion is given to guarantee the realization of synchronization of memristive CVNNs. Meanwhile, sufficient conditions for exponential synchronization of the considered systems is also proposed. Finally, the validity of our proposed results is verified by a numerical example.

Motion tracking control design of nonholonomic mobile robot systems considering actuator dynamics is addressed in this paper. A trajectory tracking controller is designed at actuator level, which guarantees that the nonholonomic mobile robot tracks a given trajectory. A numerical example is shown to demonstrate and validate the proposed approach in this paper.

This paper concentrates on the bumpless transfer control problem for a category of switched fuzzy systems with L2-gain property. A description of the bumpless transfer performance for switched fuzzy systems is introduced for the first time. A general multiple Lyapunov functions strategy is exploited to solve the bumpless transfer control problem of the switched fuzzy systems with the L2-gain property. The multiple Lyapunov functions scheme allows the disconnection of the successive Lyapunov functions when a switching happens. A criterion on the bumpless transfer performance with the L2-gain property is established, allowing each subsystem to satisfy neither the bumpless transfer performance nor the L2-gain property. Moreover, when only the L2-gain property is considered, the condition is mildly expressed in terms of matrix inequalities rather than the usual combination of matrix inequalities and matrix equalities. Finally, an example of controlling a mass-spring-damping model is offered to validate the effectiveness of the developed control strategy.

In this paper, a new adaptive approximation-based tracking controller design approach is developed for a class of uncertain nonlinear switched lower-triangular systems with an output constraint using neural networks (NNs). By introducing a novel barrier Lyapunov function (BLF), the constrained switched system is first transformed into a new system without any constraint, which means the control objectives of the both systems are equivalent. Then command filter technique is applied to solve the so-called "explosion of complexity" problem in traditional backstepping procedure, and radial basis function NNs are directly employed to model the unknown nonlinear functions. The designed controller ensures that all the closed-loop variables are ultimately boundedness, while the output limit is not transgressed and the output tracking error can be reduced arbitrarily small. Furthermore, the use of an asymmetric BLF is also explored to handle the case of asymmetric output constraint as a generalization result. Finally, the control performance of the presented control schemes is illustrated via two examples.

In this brief, an online robust adaptive dynamic programming algorithm is proposed for two-player zero-sum games of continuous-time unknown linear systems with matched uncertainties, which are functions of system outputs and states of a completely unknown exosystem. The online algorithm is developed using the policy iteration (PI) scheme with only one iteration loop. A new analytical method is proposed for convergence proof of the PI scheme. The sufficient conditions are given to guarantee globally asymptotic stability and suboptimal property of the closed-loop system. Simulation studies are conducted to illustrate the effectiveness of the proposed method.

In this brief, the utilization of robust model-based predictive control is investigated for the problem of missile interception. Treating the target acceleration as a bounded disturbance, novel guidance law using model predictive control is developed by incorporating missile inside constraints. The combined model predictive approach could be transformed as a constrained quadratic programming (QP) problem, which may be solved using a linear variational inequality-based primal-dual neural network over a finite receding horizon. Online solutions to multiple parametric QP problems are used so that constrained optimal control decisions can be made in real time. Simulation studies are conducted to illustrate the effectiveness and performance of the proposed guidance control law for missile interception.

In this paper, an adaptive generalized predictive control method using adaptive-network-based fuzzy-inference system (ANFIS) and multiple models is proposed for a class of uncertain discrete-time nonlinear systems with unstable zero-dynamics. The proposed controller consists of a linear and robust generalized predictive adaptive controller, a nonlinear generalized predictive adaptive controller based on ANFIS, and a switching mechanism. It has been shown that the linear generalized predictive adaptive controller can ensure the boundedness of the input and output signals, and the nonlinear generalized predictive controller can improve the transient performance of the system. By switching between the two earlier described controllers, the switching mechanism can simultaneously improve the performance and ensure the closed-loop stability. Moreover, the method has relaxed the global boundedness assumption of the higher order nonlinear term and established the analysis of stability and convergence of the closed-loop system. In the proposed controller, ANFIS is adopted to estimate and compensate the unmodeled dynamics, which avoids some possible flaws of a backpropagation (BP) neural network. Simulation results have demonstrated the superiority of the proposed method and verified the theoretical analysis.

In this paper, robust invariance switching control problem for a class of multi-input uncertain nonlinear cascade systems with structural uncertainties is studied. By using methods of passivity and switching control of states of the linear subsystem, both stabilization of the linear subsystem and invariance of the specified region in state space can be guaranteed simultaneously. Hence, a sufficient condition for the robust invariance switching control of this class of systems is derived. Under some additional assumptions, the whole system is semi-global asymptotically stable (Semi-GAS). Input-state stability (ISS) assumptions or linear growth conditions on nonlinearities are not required. Simulation results demonstrate the effectiveness of the proposed design.

By utilizing the controllability of High Voltage Direct Current (HVDC), which means that the power delivered can be modulated, to improve the stability and operation performances of the parallel AC/DC transmission system, a new adaptive back-stepping approach for this system is developed. Compared with the existing controller based on “classical” adaptive back-stepping, the approach does not follow the classical certainty-equivalence principle. We introduce this approach, for the first time, into parallel AC/DC systems containing unknown parameters and present a novel parameter estimator and dynamics feedback controller. Besides the preserving useful nonlinearities and the real-time estimation of uncertainty parameter, the proposed approach possesses better performances with respect to the response of the system and the speed of adaptation. Simulation results demonstrate that the proposed approach is better than the design based on “classical” adaptive back-stepping in terms of properties of stability and parameter estimation and that it recovers the performance of the “full-information” controller, which is obtained by assuming that the parameters are known and apply standard back-stepping, hence it will be an alternative to practice engineering and applications.