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 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 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.

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.

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.

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.