Asymmetric prescribed performance‐barrier Lyapunov function for the adaptive dynamic surface control of unknown pure‐feedback nonlinear switched systems with output constraints

Abstract

An adaptive dynamic surface control scheme for a class of pure-feedback nonlinear switched systems possessing completely unknown nonlinearities and output constraints is proposed in this paper. By enabling the barriers to vary with prescribed performance functions in time, an asymmetric prescribed performance-barrier Lyapunov function (APP-BLF) is developed to guarantee the prescribed tracking performance simultaneously with constraint satisfaction under arbitrary switching, while the initial conditional requirements are relaxed. To handle the nonaffine problem, an affine variable is constructed to transform pure-feedback systems into a strict-feedback form with the nonaffine and switching properties existing in time-varying bounded parameters by utilizing the mean value theorem at each step of the backstepping design procedure. Next, by incorporating the supremum norm theory, dynamic surface control, and the Nussbaum gain technique, a novel adaptive approach is presented to overcome unknown nonlinearities, unknown control coefficients, and the explosion of complexity. At last, by using the common Lyapunov function approach in combination with the decoupled backstepping method, a common approximation-free adaptive controller is constructed to guarantee that all the signals in the closed-loop system are semiglobally uniformly bounded.Moreover, the proposed controller alleviates the problems of overparameterization and the computational burden. Two simulation studies are conducted to demonstrate the effectiveness, robustness, and applicability of the proposed approach. KEYWORDS adaptive dynamic surface control, asymmetric barrier Lyapunov function (ABLF), common Lyapunov function (CLF), prescribed performance control (PPC), pure-feedback nonlinear switched systems Int

Adaptive anti-disturbance control for a class of unknown pure feedback switched nonlinear systems

“…Without loss of generality, we assume that the sign of , 1 1 ( , ) Remark 2: Note that Assumptions 1 and 2 are standard assumptions for the back-stepping design of nonlinear systems. However, Assumption 2 possesses less conservativeness than in the preexisting literature [1,2,[23][24][25], which assumes that the d y and its time derivatives up to the 2 nd or th n order are bounded and continuous. Furthermore, the system energy is always finite from a practical point of view.…”

“…Switched systems consist of a family of subsystems and a switching rule that orchestrates the switching among them; a large number of practical systems belong to this category due to changing environmental factors and various jumping parameters [1,2], such as circuit and power systems [3], hypersonic flight vehicles [4], and chemical processes [5]. Since their vital engineering applications and the development of intelligent control theories, for instance, neural networks (NNs) and fuzzy logical systems (FLSs), significant results have been obtained for nonlinear switched systems in the literature [1,[6][7][8][9][10][11][12].…”

“…On the other hand, a switched system does not inherit the characteristics of the subsystems, which makes stability analysis very complicated. Fortunately, in recent decades, some important approaches have been proposed to analyse the stability of nonlinear switched systems, such as the average dwell time (ADT) [1,5,6,13], the common Lyapunov function [2,7,8,10] and the multiple Lyapunov function [14]. Among these methods, the ADT is regarded as a popular and effective technique for carrying out the stability analysis of switched systems.…”

“…2) The developed control approach can not only overcome the "explosion of complexity" problem by adopting command filter technology but also compensate for the filter error, achieving better control performance than that in the previous literature [1,2,[23][24][25].…”

Adaptive controller design with prescribed performance for switched nonstrict feedback nonlinear systems with actuator failures

“…An output‐feedback control method with prescribed performance is proposed in the work of Li et al 20 for SISO switched nonstrict feedback nonlinear systems, which has only one tuning parameter in controller design. An adaptive prescribed performance control for a class of pure feedback nonlinear switched systems possessing completely unknown nonlinearities and output constraints is proposed in the work of Chen 21 . In the work of Kamali et al, 22 the tracking problem for a class of uncertain switched nonlinear delayed systems with nonstrict feedback structure under state‐dependent switching law is investigated, and the transient and steady‐state tracking performance is guaranteed by the prescribed performance bounds.…”