This paper is concerned with the problem of prescribed performance tracking control for strict-feedback systems with parametric uncertainties and unmatched disturbances. An adaptive command-filtered control approach with performance guarantees is put forward to address the problem. By means of a new-type self-adjustable performance function and a barrier function, it is capable of achieving the practical prescribed time tracking and enhancing the reliability of control implementation simultaneously, without yet the requirement for the specific initial condition. In the control design, a class of finite-time command filters is adopted to solve the “explosion of complexity” problem, and the error compensation mechanism with practical finite-time stability is introduced to remove the impact of filtered errors. Moreover, considering that the overshoot of the tracking error fails to be quantified by the majority of performance functions with infinite initial values, a pair of asymmetric performance functions is constructed such that the trajectory tracking with the predefined overshoot, settling time, and accuracy is achieved, while preserving the capability of relaxing the initial condition. It turns out that the proposed approach warrants the performance-related constraint satisfaction and the boundedness of all the closed-loop signals. Three simulation studies are carried out to demonstrate the theoretical findings.Note to Practitioners—This paper is motivated by the potential fragility problem exhibited in the traditional constraint-handling methods in the presence of paroxysmal factors such as suddenly strong disturbances or highly fluctuating target trajectories. For practical applications (e.g., satellite docking, automobile production, target interception, and network congestion control) suffering from the above scenario, it might be favorable to widen prescribed performance boundaries in a proactive way from the perspective of the safe and reliable operation of the controlled system. On this basis, a novel command filter-based adaptive tracking control solution with self-adjustable performance guarantees is proposed. It not only achieves trajectory tracking with the preassigned overshoot, settling time, and accuracy in the context of raising the reliability of control implementation but also possesses the attributes of inexpensive computation burden and easy acceptability in practical applications.

This article proposes a resilient performance-based funnel control approach for transmission control protocol (TCP)/active window management (AWM) networks subject to sudden external disturbances, enabling effective congestion control within a prescribed time. The proposed scheme utilizes an error transformation mechanism with a fixed-time convergence performance function, which not only enhances the flexibility in handling initial conditions but also ensures tight performance guarantees. Additionally, a novel self-adjustable funnel boundary is constructed to mitigate the reliability degradation of control schemes caused by bursty factors such as strong disturbances and highly fluctuating reference signals. These techniques are then integrated into a command-filtered backstepping framework to ensure predefined tracking performance and the boundedness of all closed-loop signals. Finally, simulations demonstrate the feasibility and superiority of the proposed theoretical approach.

This article is concerned with the prescribed performance tracking control problem for the strict-feedback systems with unknown nonlinearities and unmatched disturbances. The challenge lies in the realization of a complete performance specification for trajectory tracking in the sense of quantitatively regulating the peak value, overshoot, settling time, and accuracy while ensuring that the initial condition holds naturally. To this end, an error transformation, equipped with a shifting function, is introduced and incorporated with a new-type barrier function. Then, a class of performance functions is exploited to quantify the settling times and steady-state bounds of the intermediate errors. Moreover, to improve the flexibility of formulating performance specifications for the tracking error, a pair of asymmetric performance boundaries are further designed. With their combination, a novel robust prescribed performance control (PPC) approach is proposed in this article. It not only achieves the quantitative performance guarantees but also preserves the unique simplicity of PPC, evading the needs for function approximation, parameter identification, disturbance estimation, derivative calculation, or command filtering. The above theoretical findings are confirmed via three simulation studies.

This work addresses a finite-time tracking control issue for a class of nonlinear systems with asymmetric time-varying output constraints and input nonlinearities. To guarantee the finite-time convergence of tracking errors, a novel finite-time command filtered backstepping approach is presented by using the command filtered backstepping technique, finite-time theory, and barrier Lyapunov functions. The newly proposed method can not only reduce the complexity of computation of the conventional backstepping control and compensate filtered errors caused by dynamic surface control but also can ensure that the output variables are restricted in compact bounding sets. Moreover, the proposed controller is applied to robot manipulator systems, which guarantees the practical boundedness of all the signals in the closed-loop system. Finally, the effectiveness and practicability of the developed control strategy are validated by a simulation example.

This article investigates stochastic stability of positive singular Markovian jump systems (PSMJSs) with mode-dependent derivative-term coefficient. Different from the existing results, the condition on stochastic stability of PSMJSs associated with state jumps behavior at switching instants is given by means of linear co-positive Lyapunuov function. On the basis of it, the conditions on stochastic stability under the cases of partially known transition rates and uncertain transition rates have been presented, respectively. All obtained conditions can be solved by linear programming (LP) technique. Finally, an example is introduced to illustrate the effectiveness and the merits of the results proposed in this article.

This article focuses on an annular domain finite-time connectively bounded (ADFTCB) problem for a large-scale system with expanding construction (LSWEC). The LSWEC is built via adding new subsystems into the original system which is operating. Inspired by the notion of finite-time annular domain stability (FTADS), a new concept, ADFTCB, is presented in this article, and it is extended to LSWEC for the first time. First of all, the mathematical models of LSWEC and LSWEC with observer are built, and then the corresponding decentralized state-feedback stabilizers and output-feedback stabilizers with observers are designed with the aid of finite-time Lyapunov theory and linear matrix inequality (LMI) method which can make the closed-loop system ADFTCB. A simulation study is provided to demonstrate the feasibility and effectiveness of the presented strategy.

This paper investigates an adaptive finite-time control (FTC) problem for a class of strict-feedback nonlinear systems with both time-delays and quantized input from a new point of view. First, a new concept, called preassigned finite-time performance function (PFTF), is defined. Then, another novel notion, called practically preassigned finite-time stability (PPFTS), is introduced. With PFTF and PPFTS in hand, a novel sufficient condition of the FTC is given by using the neural network (NN) control and direct adaptive backstepping technique, which is different from the existing results. In addition, a modified barrier function is first introduced in this work. Moreover, this work is first to focus on the FTC for the situation that the time-delay and quantized input simultaneously exist in the nonlinear systems. Finally, simulation results are carried out to illustrate the effectiveness of the proposed scheme.

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 work investigates a finite-time adaptive fuzzy tracking control problem for a class of nonstrict feedback nonlinear systems from a new point of view. A new concept, named finite-time performance function (FTPF), is defined in this paper for the first time. Moreover, a finite-time adaptive state feedback fuzzy tracking controller is derived based on fuzzy approximation, backstepping technique and prescribed performance control (PPC), which guarantees that all the signals of the closed-loop system are bounded, the output tracking error converges to a prescribed arbitrarily small region within a finite-time interval, and maximum overshoot is not more than a predefined level. In addition, a controller design process is given which is less complex than the existing finite-time control design methods. Three simulation studies are provided to verify the feasibility and effectiveness of the theoretical finding in this study.

The estimation of the domain of attraction of a class of susceptible-infectious-removed-susceptible immigration is investigated. On assumption the disease-free equilibrium and the endemic equilibrium existences, hence a Lyapunov function too, the domain of attraction of the epidemic model is estimated by means of LF-LMI-moment and SOS optimization approaches. An invariant subset of the domain of attraction, along with certain enlargement, has been achieved. Simulation results, given in a comparison presentation, demonstrate feasibility and validity of the proposed technique as well as reveal that this algorithm outperforms other ones in applications to epidemic models.

A decentralized connective stabilization control problem employing reduced-order observers is solved for complexity large-scale systems with expanding construction. Without changing the original decentralized control laws, a decentralized controller is designed for the resulting expanded system so that the new subsystem added to the original one and the expanding system are robustly connective stable. Furthermore the sufficient condition is derived by using Lyapunov theory and LMI approach. Finally, the proposed method is applied to the AGC design of an expanding power system. The simulation results show both the feasibility and the effectiveness of the proposed decentralized control design.

An active queue management controller based on Hamiltonian energy theory for a class of nonlinear TCP network congestion system in the p resence of uncertain parameters and unknown external disturbances is derived. The restriction of inequality assumption is eliminated by introducing the MiniMax methods into dissipation Hamilton system. Sufficient conditions for the existence of MiniMax controller under circumstances the network system is attacked with maximum impact disturbance has been derived via Lyapunov stability theory. Furthermore, the nonlinear uncertainties presence i.s successfully ameliorated by employing a parameter projection mechanism. Simulation experiments have demonstrated this energy based control strategy ameliorates the pertinent control complexity and is considerably more effective in improving both transient stability and robustness.

This paper investigates the problem of delay-dependent stabilization for uncertain T-S fuzzy systems with state and input time time-varying delays. A new method is proposed by defining a novel Lyapunov-Krasovskii functional and making use of novel techniques to achieve delay dependence. Unlike existing works in this topic, this approach developed in this paper employs neither free-weighing matrices nor model transformations, using Jensen's inequality. As a result, simplified yet improved stability conditions for T-S fuzzy systems with norm bounded type uncertainties are obtained. All the conditions are derived in terms of linear matrix inequalities (LMI), which can be solved by using LMI optimization techniques. The benefits and efficiency of the method are demonstrated by the numerical example.

A Metropolis criterion based fuzzy Markov game flow controller (MFMC) is proposed to cope with congestion problems in high-speed networks. Because of uncertainties and highly time-varying time delays, for such networks the complete and accurate information is not easy to obtain in real time The Q-learning, which is independent of mathematic model and prior knowledge and yet enables achieving good performance, is a viable alternative. The fuzzy Markov game offers a promising platform for robust control in the presence of external disturbances and unknown parameter variations that are bounded. The Metropolis criterion can cope with the balance between exploration and exploitation in action selecting. Simulation experiments demonstrate the proposed controller can learn to take the best action in order to regulate source flows. Thus it can guarantee high throughput and low packet loss ratio while efficiently avoiding the congestion.

An active queue management (AQM) scheme employing state observer and sliding mode control (SMO-SMC) is designed in this paper in order to overcome congestion problem in TCP communication networks. First, sliding mode observer is designed for input delay network system; a sufficient condition is given for the existence of such an observer in terms of linear matrix inequality. Then, on the grounds of estimated system state vector, a controller is synthesized by using the sliding-mode control theory combined with the reaching law technique. The reachability condition in such a SMO-SMC AQM scheme is also discussed. The stability and robustness of the proposed control scheme are then validated for different network scenarios using Matlab/Simulink. Simulation results for the single-bottleneck benchmark network confirmed the proposed scheme achieves high-quality performance as well as outperforms the previous observer-based sliding-mode and traditional controllers.

The investigated control problem of nonlinear time-delay discrete-time systems is addressed using Takagi-Sugeno model. Parametric uncertainty and time-delay terms are employed in building the Takagi-Sugeno model for the controlled plant for the purpose of close representation of the original plant system. The integrity and robustness are guaranteed for the closed-loop fuzzy system in sense of Lyapunov stability method via fuzzy state observers. Sufficient conditions for the fuzzy system to possess integrity against actuator failures and sensor failures in the closed-loop are derived in terms of linear matrix inequalities under assumption of known bounds on uncertainties. The results for trailer-truck example are used to illustrate the effectiveness of the method.

A robust tracking fuzzy control technique for nonlinear time-delay systems based on fuzzy T-S model is proposed. The fuzzy T-S system model with parametric uncertainties is employed to represent a nonlinear time-delay plant. The control design synthesis is aimed to reduce to negligible small the tracking error for all bounded reference inputs and to guarantee Hinfinperformance. The advantage of proposed tracking control design is only a simple fuzzy controller designs are employed. By means of the proposed method, the fuzzy tracking control design problem is parameterized in terms of a linear matrix inequality problem, which can be efficiently solved using any convex optimization techniques. The example of trucking control for the benchmark truck-trailer system is given to demonstrate the efficiency as well as the validity of the proposed technique.

The problem of robust connective stabilities is considered in this paper for a class of large-scale uncertain interconnected power systems in the case of uncertain structural reconfigurations. Robust connective stability is defined based on the interconnected matrix and the load normalization factor uncertainties of power systems. A new analysis method with a robust degree is presented to establish a sufficient condition of connective stability for the system and the robustness bound for uncertainty parameters, by using the property of norms, eigenvalues and global parameters of the system matrices. The proposed method is applied to a two-area power system, and it shows the effectiveness of given conditions.