This article investigates prescribed performance neural autonomous control of discrete-time nonlinear systems subject to actuator saturation. Unlike existing sliding-mode-control (SMC) driven structure, we aim to construct a more general and user-friendly framework that achieves prescribed behaviors by indirectly stabilizing transformed errors in the discrete-time domain. We propose two new approaches to accomplish such objective. The first one is to compensate actuator saturation by developing a modification system, the state of which is further applied to design flexible terms that endow an ability to resiliently adjust prescribed envelopes according to saturation condition, which constitutes the second approach. In comparison with current discrete-time prescribed performance control (PPC), the proposed method avoids the singularity problem and consequently remedies the fragility defect. In addition, an adaptive neural back-stepping procedure is used to devise discrete-time PPC protocols that limit tracking errors inside the developed flexible prescribed envelopes to satisfy both transient and steady-state properties. Finally, the efficiency of design is illustrated via Lyapunov synthesis, and is further verified by numerical simulation.Note to Practitioners—The motivation arises from the requirement for autonomous tracking control of discrete-time nonlinear systems with actuator saturation and fragility relaxation. Unfortunately, existing SMC-driven discrete-time PPC isn’t able to achieve expected prescribed behaviors in the presence of actuator saturation. To break through this bottleneck, we firstly develop a new design framework, being different from existing SMC-based ones, to impose prescribed performance on tracking errors by indirectly stabilizing transformed errors, and then we define a new modification system which effectively compensates the actuator saturation so that the fragility defect can be remedied. On this basis, a novel discrete-time tracking control approach with flexible prescribed performance is addressed for constrained systems while relaxing the fragility. The obtained results in this study are of great significance for providing a more general and user-friendly framework for discrete-time PPC synthesis.

This paper explores a novel fuzzy fault-tolerant control scheme for hypersonic flight vehicles (HFVs) that accounts for parameter perturbations and system disturbances, thereby achieving flexible prescribed properties and designated-time convergence. In contrast to existing studies, this framework incorporates the more detrimental elevator stuck fault within the context of prescribed performance control (PPC). To mitigate the fragility issues associated with PPC in fault-tolerant control, we propose an innovative approach that integrates a fault sensing system along with a readjustment prescribed envelope. This is accomplished by transforming the original HFVs model into an imprecise pure feedback model, allowing for the design of low-complexity fuzzy controllers with minimal model dependence through the utilization of higher-order error functions and fuzzy logic systems. Finally, numerical simulations validate both the effectiveness and superiority of the proposed method.

Notwithstanding the successful design of state-of-the-art cooperative control protocols to accomplish formation tracking for multiple unmanned aerial vehicles (UAVs), the assurance of performance optimality cannot be guaranteed in the face of complex disturbances affecting these multi-UAV systems. In order to surmount this challenge, this research endeavor aims to establish a feedforward-feedback learning-based optimal control methodology to facilitate cooperative UAV formation tracking in the presence of intricate disturbances. To be more precise, by leveraging backstepping-based feedback control, the problem of UAV formation tracking is transformed into an equivalent optimal regulation problem. Consequently, a learning-based feedforward control scheme is devised, wherein the cooperative policy iteration algorithm is formulated based on a two-player zero-sum game. The critic-only echo state network (ESN) is employed to approximate the optimal feedforward control policies, with the inclusion of an online adaptive tuning law and compensation terms to alleviate the persistence of excitation condition and eliminate the need for an initial admissible control. As a result, the closed-loop stability is guaranteed in terms of uniformly ultimately boundedness for tracking errors and ESN weights.Note to Practitioners—In real-world scenarios, the flight of multiple UAVs is invariably affected by intricate disturbances, resulting in compromised tracking precision. There is an urgent need to enhance resistance to disturbances and ensure optimal performance for cooperative formation tracking of multiple UAVs. Beyond the capabilities of model-based controllers, the integration of reinforcement learning has shown promise in achieving robust control actions. By introducing the cooperative policy iteration algorithm based on a two-player zero-sum game, the tracking performances of UAV formation can be further optimized. In order to facilitate the practical application of reinforcement learning in UAV systems, our proposed algorithm addresses the persistency of excitation condition by incorporating innovative compensation terms into the ESN tuning law. Furthermore, we resolve the requirement for initial admissible control by introducing a novel piecewise compensation term into the ESN tuning law, which is based on a newly proposed Lyapunov function.

This article is devoted to the exploration of a novel design process for synthesizing fuzzy prescribed performance control (PPC), with a specific emphasis on achieving preselected behaviors in discrete-time. To overcome the limitations of existing studies that solely rely on a fixed and inflexible sliding mode control framework, we put forward an innovative indirect stabilization method that offers a practical and readily implementable design process in discrete-time. Different from current approaches, our method ensures enhanced prescribed performance by guaranteeing finite-time convergence and avoiding high frequency chattering. To achieve this, we directly develop discrete-time PPC protocols using a low-computational fuzzy approximation strategy based on completely unknown system dynamics, thus eliminating the need for complex model equivalent reconstruction as demanded by previous studies. Finally, we verify the effectiveness and superiority of our proposed design.

This study focuses on a low-computational neural discrete-time attitude controller for the seeker stabilized platform, with the aim of ensuring fixed-time prescribed behaviors in tracking errors through an event-triggered approach. In contrast to existing reaching-law- based discrete-time prescribed performance control (DPPC) methodologies that rely on fully/partially accurate model plants, our approach establishes discrete-time protocols that accommodate unknown system dynamics while guaranteeing fixed convergence time and minimizing steady-state error to its utmost extent. This is achieved through a newly constructed design framework that completely deviates from current DPPC practices. Our framework incorporates fixed-time performance functions, the back-stepping procedure, and innovative accumulation terms, all of which synergistically enhance steady-state accuracy while obviating the need to calculate virtual controller differences. Furthermore, we utilize neural networks to approximate unknown system dynamics and devise an event-triggered mechanism instead of a time-based one for intermittently updating neural approximators, thereby effectively reducing computational costs. Finally, comparative validation results demonstrate that the proposed control precision has been enhanced by 27% to one or more orders of magnitude and the simulation run time has been reduced by more than 26% under identical conditions compared with existing strategies.

This article is dedicated to safety flight control of hypersonic vehicles that serve as long-range strategic transport aircraft, with the aim of alleviating the inherent fragility defect in existing prescribed performance control (PPC) schemes. In pursuit of this goal, we first establish a safety boundary that offers early warnings for fluctuations in hypersonic tracking errors and serves as a crucial mechanism for envelope adjustment. Building on this groundwork, we further develop a universal sensing-adjustment system with dynamically activated states triggered by the defined safety boundary, enabling active readjustment of the prescribed envelope boundaries. This results in a new PPC scheme capable of promptly detecting error fluctuations and smoothly readjusting prescribed envelopes, effectively addressing the fragility defect associated with existing protocols while ensuring hypersonic flight safety. Moreover, our proposed hypersonic controller does not necessitate approximators or learning parameters required for current fuzzy/neural control approaches, showcasing a low-computational design framework. Finally, we assess the efficiency of our approach by conducting comparative simulations.

The control performance of permanent magnet brush (PMB) DC motors, which are essential components in electric vehicles, is crucial for ensuring the seamless and secure operation of these vehicles. This study investigates discrete-time fuzzy-neural intelligent control with fixed-time prescribed performance for the electromechanical dynamics of PMB DC motors. Unlike existing prescribed performance control (PPC) schemes designed for continuous-time systems, our approach introduces a more practical discrete-time version of PPC that guarantees system outputs with fixed-time preselected behaviors. This advancement addresses the technical limitations faced by current discrete-time PPC methods when managing dynamic systems with time-varying sampling intervals. To achieve this objective, we integrate an enhanced fuzzy-neural approximation technique with the back-stepping design to develop a low-computational discrete-time control protocol. Our method minimizes online learning parameters while circumventing the issue known as “explosion of terms”. Finally, we compare our proposed controller against several existing alternatives to demonstrate its effectiveness and superiority.

Waverider vehicles (WVs) have the prominent advantage of long-distance and rapid delivery over traditional vehicles, but meanwhile, it also brings new challenges in control system design. Consequently, it is crucial to develop a reliable controller with good transient performance and steady-state accuracy for WVs. This article introduces a non-fragile prescribed performance control (NPPC) scheme that incorporates a precise flexible term for WVs subject to actuator constraints. The proposed NPPC scheme addresses the fragility issue of traditional PPC through two approaches: firstly, by designing a finite-time anti-saturation compensation system (FACS) with adjustable convergence time to accurately compensate for tracking errors; secondly, by utilizing the FACS as an error sensor and developing a precisely tunable prescribed performance flexible term. Moreover, uncertainty-estimation-free controllers are designed for WVs under actuator constraints based on the NPPC scheme and backstepping design approach. Additionally, the stability of the proposed controllers is proven through Lyapunov analysis while their advantages are further demonstrated and validated through comparative simulations.

This article presents a novel distributed robust fuzzy control scheme to address the global consensus problem of unknown nonlinear multiagent systems (MASs). By replacing the nonlinear dynamic model constrained by the global Lipschitz condition with a more general system model, the proposed approach enhances applicability. A robust fuzzy control scheme based on a smooth switching function is introduced, effectively resolving the global consensus problem for unknown nonlinear systems. Furthermore, time-varying σ-modification terms are incorporated into the adaptive parameter design, replacing constant terms to avoid asymptotically uniform ultimate boundedness and ensuring global asymptotic consensus of the closed-loop systems. The efficacy of the proposed scheme is demonstrated through simulation results.

In this article, we concern on prescribed performance autonomous control of discrete-time non-affine systems subject to unknown nonlinearities and directions. Unlike existing Nussbaum-type function based strategies, the addressed issue is transformed as the unknown direction control of affine systems, and it is further effectively handled without using such Nussbaum-type functions within a novel design framework that is completely different from current sliding-mode-based structure. Inside the newly developed framework, we devise a family of fixed-time performance functions and then define discrete-time nonlinear functions for control synthesis. On this basis, a new indirect stabilization approach is achieved, to pursue desired prescribed performance in the discrete-time domain with sliding-mode-design avoidance. Besides, adaptive neural approximations are employed to reject system unknown nonlinearities, and improved adaptive laws are explored to reduce computational load. Finally, we apply the proposed method to a type of discrete-time systems to verify its effectiveness and improvement.Note to Practitioners—The motivation of this article arises from the need for fixed-time prescribed performance autonomous control of discrete-time systems exhibiting unknown directions. However, existing discrete-time PPC methodologies, constructed within the sliding-mode-based framework, cannot guarantee the fixed convergence time for tracking errors. To address this issue, we firstly propose a new family of discrete-time performance functions which impose fixed convergence time for tracking errors in the discrete-time domain, and then we further develop a new design framework which is completely different from current sliding-mode-based structure. On those bases, we also cleverly handle the unknown direction control problem without utilizing Nussbaum-type functions. The presented results of this paper are of great significance for providing a standard and general procedure for discrete-time PPC development.

This article focuses on fuzzy prescribed performance stabilization of high-order discrete-time systems with multiple unknown nonlinearities. A novel back-steeping framework is employed to devise the unique actual control protocol, while the series of virtual controllers associated with the existing back-stepping are not necessary for the proposed approach. Furthermore, as to the considered high-order system whose subsystems contain unknown dynamics, only one fuzzy approximator is used to directly estimate the final control law. This results in a low-computational model-free design procedure. In particular, a finite-time performance function is developed to sustain the system output within a constraint envelope to satisfy the desired prescribed performance in the discrete-time domain. Finally, the stability of a closed-loop system and the reachability of prescribed performance are proved via Lyapunov synthesis, and the efficiency of the explored method is verified via numerical simulation.

The perturbations in model parameters of hypersonic flight vehicles (HFVs) are highly likely to induce fluctuations in control error, which can potentially render the existing prescribed performance control (PPC) singular and pose a threat to flight safety. Therefore, our objective is to propose an adaptive fuzzy safety control protocol for HFVs that aims to achieve adaptable prescribed behaviors in the presence of parameter perturbations. To accomplish this, we initially develop a novel error-sensing system for timely detection and forecasting of error fluctuations. Building upon this foundation, we further define an adjustment mechanism that appropriately adjusts the upper envelope upward and the lower envelope downward at regular intervals. In contrast to existing fixed PPC approaches, the proposed sensing and adjustment mechanism enables both velocity and altitude tracking errors to satisfy a new type of adaptable prescribed qualities, thereby ensuring safe flight control of HFVs. In addition, we explore low-computational-burden fuzzy approximation techniques that minimize the required online adaptive parameters while guaranteeing excellent real-time control performance. Finally, comparative simulations are conducted to validate the proposed method.

This study introduces a novel adaptive fuzzy fault-tolerant controller designed for tailless aircraft's attitude tracking problem, even in the absence of angular velocity measurements. The controller addresses challenges posed by external disturbances, model uncertainties, and actuator faults. Initially, we propose a fixed-time sliding mode differentiator to estimate unmeasured angular velocity. Model uncertainties and external disturbances are approximated using fuzzy logic systems. Subsequently, a nonsingular fixed-time adaptive fuzzy fault-tolerant control scheme is developed based on the backstepping theory, which actively mitigates the impact of actuator faults, resulting in superior attitude tracking performance. The theoretical foundation of the proposed control scheme guarantees the boundedness and convergence of all closed-loop attitude control system states to a confined region around the origin within a fixed time. Notably, this convergence is achieved regardless of initial errors. Finally, simulation examples are presented to verify the effectiveness of the estimator and controller.

The path tracking control problem for autonomous vehicle with uncertain dynamics requires simultaneous consideration of control optimality and safety-based performance constraints. In this paper, an adaptive optimal control method with prescribed performance is proposed to solve this problem, which contains two contributions: 1) by introducing a prescribed performance function (PPF) into adaptive dynamic programming (ADP), the controller can constrain the tracking error of the system within a specified performance boundary while optimizing the control cost; 2) the critic-only ADP is used for the controller design, which simplifies the commonly used actor-critic ADP scheme, and the convergence of the estimation error is guaranteed under FE conditions. On this basis, the neural network identification technique is introduced to deal with the unknown dynamic parameters of the vehicle system. The control scheme is able to strictly guarantee user-defined vehicle performance specifications with approximately optimal control performance. The stability of the closed-loop system is rigorously demonstrated by the Lyapunov method. In addition, the controller also embeds a radial basis function neural network (RBFNN) compensator to approximate the nonlinear external disturbances of the autonomous vehicle. Finally, the efficiency of the controller to achieve autonomous vehicle path tracking is verified by CarSim-Simulink simulation.

A fuzzy-neural-approximation-based pseudo nonaffine control protocol is proposed for waverider vehicles (WVs), which is capable of guaranteeing tracking errors with desired prescribed performance and rejecting the obstacle of fragility inherent to the traditional prescribed performance control (PPC). The pseudo control is defined to approximate the nonaffine dynamics of WVs, while there is no need of model affinization. Furthermore, fuzzy neural approximators are combined with the adaptive compensation strategy to resist both system uncertainties and external disturbances. Especially, a new type of nonfragile prescribed performance, being able to self-adjust its prescribed funnel, is proposed to remedy the fragility defect associated with the existing PPC. Finally, the realizability of the spurred prescribed performance is proved via stability proof, and the superiority of the addressed design is tested by compared simulations.

In this article, we propose a concise fuzzy neural control framework for waverider vehicles with input constraints, while the spurred prescribed performance can be guaranteed, and the challenging fragility problem associated with the existing prescribed performance control (PPC) is avoided. Unlike the existing control protocols without considering computational costs, in this study, the low-complexity fuzzy neural approximation is combined with simple performance functions, which reduces the complexity burden and improves the practicability. Then, in order to handle the adverse effect of the actuator saturation on the control performance, bounded-input-bounded-state stable systems are developed to stabilize the closed-loop control system based on bounded compensations. Specially, flexible adjustment terms are exploited to modify the developed simple performance functions, while fragility-free prescribed performance is achieved for tracking errors, and moreover the fragility defect of the existing PPC is remedied. Finally, the efficiency and superiority of the design are verified via compared simulations.

In this article, a specified-time event-triggered fuzzy adaptive control algorithm is developed to solve the consensus tracking control problem for stochastic high-order nonlinear multiagent networks, which is intrinsically challenging due to the existence of stochasticity and high-order (positive odd integers greater than one) terms. More precisely, a novel specified-time performance function is incorporated into the time-varying high-order tan-type barrier Lyapunov function to guarantee that the tracking errors remain under time-varying constraints within specified time. Combining fuzzy logic systems with the adding on power integrator technique, an adaptive approximation policy is introduced to handle the system uncertainties. Moreover, a new switching threshold event-triggered mechanism is devised to determine the control signals updating instants, which reduces the transmission and computation burden, while resizing the triggering threshold in real time. The Zeno phenomenon is excluded by guaranteeing that the triggering intervals is lower bounded by a positive constant. Two simulation examples are provided to demonstrate the effectiveness of the designed algorithm.

Waverider Vehicles (WVs) show great potential in air and space transportation. This article aims at exploring finite-time prescribed performance control (FPPC) for WVs, being able to guarantee the spurred performance. Firstly, the dynamics of WVs is decomposed as the velocity subsystem and the altitude subsystem of non-affine formulations. Then, a new type of back-stepping controller without any approximation/estimation is devised based on FPPC, such that all tracking errors satisfy spurred finite-time prescribed performance. Moreover, the closed-loop stability and the guarantee of prescribed performance are proved via Lyapunov synthesis. The special contribution is that no fuzzy/neural approximation/estimation is required for the resistance of unknown dynamics, yielding a low computation and complexity design. Finally, compared simulation results with practical examples are presented to validate the superiority.

Optimal performance is extremely important for hypersonic flight control. Different from most existing methodologies, which only consider basic control performance including stability, robustness, and transient performance, this article deals with the design of nearly optimal tracking controllers for hypersonic flight vehicles (HFVs). First, main controllers are developed for the velocity subsystem and the altitude subsystem of HFVs via concise fuzzy approximations. Then, optimal controllers are nearly implemented utilizing single-network adaptive critic design. Moreover, the stability of closed-loop systems and the convergence of optimal controllers are theoretically proved. Finally, compared simulation results are given to verify the superiority. The special contribution is the application of a low-complex control structure owing to the critic-only network and advanced learning laws developed for fuzzy approximations, which is expected to guarantee satisfied real-time performance.

This article addresses a finite-time prescribed performance controller within the concise fuzzy-neural framework with application to a waverider aircraft. First, new finite-time performance functions are developed to construct a constraint funnel, which accomplishes that tracking errors converge to their steady-state values in a given time (i.e., finite-time convergence), being expected to guarantee tracking errors with small overshoots. Then, the equivalent transformation approach is introduced to unify unknown dynamics such that the control complexity is reduced. Moreover, to further reduce computational costs, a single-learning-parameter-based regulation scheme is developed for fuzzy-neural approximation. Finally, the proposed method is applied to a waverider aircraft to test its effectiveness and superiority.