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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.

Amplitude constraints of waverider vehicles (WVs) will yield error fluctuations and further result in the singular problem of prescribed performance control (PPC), threatening flight safety. It is the purpose of this study to propose a fuzzy-neural-approximation-based intelligent safety control method for WVs with actuator saturation. The saturation compensation is adopted by developing compensation systems to deal with the divergence of the transformed error, which guarantees the realizability of prescribed performance. Moreover, performance functions are devised to construct a type of variable-prescribed funnels, which are actively readjusted based on actuator saturation. While the fragile problem associated with existing PPC is handled, and moreover, quantitative prescribed performance indices are guaranteed for velocity tracking and altitude tracking errors of WVs. Besides, the addressed fuzzy-neural control does not require a recursive design procedure of back-stepping and also avoids high computational burden. Finally, the superiority of the design is validated via compared simulations.

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.