Discrete-Time Neural Control With Flexible Prescribed Performance for Constrained Systems With Fragility Relaxation

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.