Fuzzy State Observer‐Based Adaptive Dynamic Surface Control of Nonlinear Systems with Time‐Varying Output Constraints

Abstract

In this paper, a new fuzzy dynamic surface control approach based on a state observer is proposed for uncertain nonlinear systems with time-varying output constraints and external disturbances. An adaptive fuzzy state observer is used to estimate the states that cannot be measured in the systems. In our method, a time-varying Barrier Lyapunov Function (BLF) is used to ensure that the output does not violate time-varying constraints. In addition, dynamic surface control (DSC) technology is applied to overcome the problem of “explosion of complexity” in a backstepping control. Finally, the stability and signal boundedness of the system are confirmed by the Lyapunov method. The simulation results show the effectiveness and correctness of the proposed method.

Adaptive output feedback control for a class of uncertain non-strict feedback systems with asymmetric time-varying output constraints

“…where the unknown functions g(x), f (x), and control input u(t) should be in the same equation of the state space model. The control method in refs [25][26][27] deals with strict feedback system (59):…”

“…, x n T , and f i (x) is the functions of whole state variables. When the controller of the non-strict feedback system is designed by the control methods in refs, 22,[25][26][27][28] the virtual control signal and adaptive law of each subsystem are the functions of whole state variables. Consequently, the algebraic loop problem arises, which makes the controller design of a non-strict feedback system very difficult.…”

“…Therefore, the controller design method of the non-strict feedback system (66) considered in this paper is quite different from that of the controller design methods in refs. 22,[25][26][27][28] (2) Refs 10,11 proposed adaptive control methods for the non-strict feedback system (60), but unknown nonlinear functions in the system are required to satisfy a strict assumption, that there exists a strict increasing smooth function…”

“…Moreover, all states of the system in refs 10,11,22,[25][26][27][28] should be measurable. These strict limitations make control methods difficult to realize in practical applications.…”

“…To deal with asymmetric time-varying constraints, some researchers have proposed asymmetric timevarying BLFs (ABLFs). [25][26][27][28] But all the control methods in those studies were aimed at strict feedback systems and required that all states be measurable. Ref.…”