Adaptive Dynamic Surface Control Based on Observer for Switched Non-Strict Feedback Systems With Full State Constraints

Abstract

As we all know, it is very difficult to design the controller and prove the stability for switched nonlinear systems. Therefore, the engineering application of switching system and the development of switching control theory are limited. In order to solve the control problem for constrained switched system, an adaptive output feedback control scheme based on backstepping technology is studied in this paper for switched non-strict feedback nonlinear systems with asymmetric time-varying full state constraints and unknown external disturbances. A switched state observer based on fuzzy logic system is designed to estimate the unmeasurable states of the uncertain switched system. Asymmetric time-varying barrier Lyapunov functions are adopted to keep the full states of the system satisfying their asymmetric timevarying constraints. A variable separation approach is used to address the algebraic loop problem of nonstrict feedback structure. The stability of the closed-loop system and the semi-globally uniformly ultimately bounds of the signals are proved by the Lyapunov method and average dwell time theory. Finally, simulation results are given to show the effectiveness of the proposed control scheme. Different from the existing results, this paper is the first to investigate adaptive control for switched non-strict feedback systems with full state time-varying constraints, unmeasurable states and unknown disturbances, which is a more general case in real systems.

Adaptive Finite-Time Tracking Control for Nonlinear Time-Varying Delay Systems With Full State Constraints and Input Saturation

“…In the past pears, notable constraint-handling methods such as barrier Lyapunov functions (BLFs) [1], set invariance [25], reference governors [26], and model predictive control [27] have been well studied. Among these methods, the BLFs-based control has received increasing attention [3,[28][29][30][31]. With the help of BLFs and command filter method, the adaptive output feedback control problem of full-state constrained nonlinear systems was addressed in [3].…”

“…The adaptive DSC design of a class of stochastic nonlinear systems with full state constraints was proposed by employing the BLFs in [28]. For the nonlinear constrained switched system, an adaptive output feedback control scheme based on BLFs was proposed in [29]. Moreover, adaptive finite-time tracking control has been investigated for nonlinear time-varying full state constrained systems in strict-feedback [30] and pure-feedback [31] form, respectively.…”

Global exponential stabilization for a class of nonlinear systems by output feedback control with three gain‐scaling factors

“…Output feedback control problems have received much attention in the control field and several related results for nonlinear systems have been reported, for example, References 1‐20. In these regards, most reported results on the output feedback control for a class of nonlinear systems have certain conditions on the perturbed nonlinearities such as lower triangular conditions, 1‐3,21 upper triangular (feedforward) conditions, 4‐6,21 and nontriangular conditions 1,3,7 .…”

“…However, since the results of References 4‐6,18 are limited to the upper triangular conditions, their results are not applicable to either the lower triangular conditions or nontriangular conditions. Under nontriangular conditions, the global stabilization problem of the sampled‐data output feedback for stochastic nonlinear systems is considered in Reference 1, the sampled‐data output feedback controller with scaling‐gain for uncertain nonlinear systems is proposed in Reference 3 where their proposed controllers with scaling‐gain can only be high‐gain controllers, and the adaptive control scheme based on backstepping technique for nonstrict feedback nonlinear systems is studied in Reference 20. However, the result of Reference 20 does not consider the input term in the nonlinearity, though it can deal with nontriangular nonlinearity.…”

“…Under nontriangular conditions, the global stabilization problem of the sampled‐data output feedback for stochastic nonlinear systems is considered in Reference 1, the sampled‐data output feedback controller with scaling‐gain for uncertain nonlinear systems is proposed in Reference 3 where their proposed controllers with scaling‐gain can only be high‐gain controllers, and the adaptive control scheme based on backstepping technique for nonstrict feedback nonlinear systems is studied in Reference 20. However, the result of Reference 20 does not consider the input term in the nonlinearity, though it can deal with nontriangular nonlinearity. Although in Reference 7, the proposed controller for dealing with the nontriangular nonlinearity can be either a high‐gain controller or a low‐gain controller, the method of Reference 7 often shows some conservativeness regarding the control parameter selection and allowed growth rate of nonlinearity because of the controller structure with a single gain‐scaling factor.…”