Adaptive Output-Feedback Control For Nonlinear Switched Systems With Output Constraint

Recent years,the nonlinear switched systems received a real attention in the field of control.Switched system is a collection of finite subsystems combined by switching logic organically.Many modern industrial processes display the property of switching and hybrid,and exist various uncertain factors such as unmodeled dynamics,input/output/state constraints,unknown control gain sign,external disturbance,and so on.All of these will seriously affect the performance of the system and even lead to system instability.There are more research achievements on non-switched systems with a variety of influence factors.However,the research findings on nonlinear switched systems with uncertainties influence are relatively fewer.Therefore,the investigation on the adaptive control problem for a class of nonlinear switched systems with unmodeled dynamics and output constraints has important theoretical significance.Three adaptive tracking control schemes are proposed in this paper by combining the dynamic surfacc control with the asymmetric barrier Lyapunov function,the K filter and the Nussbaum function.The main studies of this paper are summarized as follows:Firstly,an adaptive dynamic surface control scheme based on the common Lyapunov function is proposed for a class of output feedback nonlinear switched systems with unmedeled dynamic and time-varying constraints.Radial basis function neural networks are utilized to approximate the unknown continuous functions in the controller design process.A K-filter is designed to handle the issue of the unmeasured states,and an available dynamic signal is constructed to solve the unmodeled dynamics.An asymmetric barrier Lyapunov function is introduced to design the adaptive controller and realize the constraints on the output.It is proved in the part of the stability analysis that the designed control strategy can ensure the tracking error converges near the origin.The simulation results are provided to verify the effectiveness of the proposed method.Secondly,an adaptive multiple-Lyapunov-functions-based dynamic surface tracking control strategy for a class of nonlinear switched output feedback systems with output constraints,input and state unmodeled dynamics is proposed in this paper.Based on a one-to-one nonlinear mapping,the complex nonlinear switched system with output constraints is transformed into a system without constraints.The unknown continuous functions produced in the controller design process are approximated by the radial basis function neural networks.A normalization signal is introduced to restrain the input unmodeled dynamic and overcome the input unmodeled dynamics influence in the system.By designing Lyapunov functions for each subsystem respectively and ensuring them monotonically non-increasing based on the dynamic surface control scheme,the whole system can keep stability under switching.The theoretical analysis proved that all the signals in the switched closed-loop system are semi-globally uniformly ultimately bounded.Finally,the numerical example illustrates the effectiveness of the proposed scheme.Thirdly,the adaptive prescribed performance control problem with arbitrary switching signals is investigated for a class of nonlinear switched systems with state unmodeled dynamics.The unmodeled dynamics of different subsystems are solved by the constructed auxiliary dynamic signals.Meanwhile,the neural networks are employed to approximate the unknown terms of each subsystem.The definition and lemma of the Nussbaum function are used to solve the unknown control gain sign problem.The prescribed performance index can be transformed into the steady-state index by introducing the performance function and error transformer.Based on the MLFs,we construct multiple Lyapunov functions and prove that all signals of the closed-loop system are semi-globally uniformly ultimately bounded.Simulation example verifies the effectiveness of the proposed approach.