Research On Decentralized Adaptive PI Tracking Control Scheme For Interconnected Nonlinear Time-delay Systems

Many practical controlled plants are modeled as the interconnected nonlinear systems,which are composed of some interconnected low-dimensional subsystems,such as chemical industrial production system,biometric systems,power systems,and multiple robotic systems.Therefore,the control problem on interconnected nonlinear systems has become an important research topic recently.In interconnected nonlinear systems,time-delay,output constraints and unmodeled dynamics are common and affect the stability of the controlled systems.Hence,it is of great significance to study the control strategy for the interconnected nonlinear systems with time-delay,output constraints and unmodeled dynamics.In this paper,the corresponding decentralized adaptive proportional-integral(PI)control schemes are designed for a class of interconnected nonlinear time-delay systems with the aforementioned problems.The main research contents of this paper are summarized as follows:(1)First of all,for a class of interconnected nonlinear time-delay systems with unstructured uncertainties and unknown interconnection delays,the appropriate Lyapunov-Krasovskii functions are introduced to conquer the difficulties arising from interconnection delays.A decentralized adaptive PI tracking control scheme is designed by utilizing backstepping control technique and adaptive control technique.Through Lyapunov theory,it is proved that all the signals in the closed-loop systems are uniformly ultimately bounded.Finally,simulation results are provided to verify the effectiveness of the proposed scheme.(2)Secondly,the interconnected nonlinear time-delay systems with asymmetric time-varying output constraints,unstructured uncertainties,unknown interconnection delays and uncertain input delays are further studied.The asymmetric time-varying Barrier Lyapunov function is used to deal with the output constraints in the systems.Combined with backstepping control technique and adaptive control technique,an asymmetric time-varying output constraints decentralized adaptive PI control scheme is designed.According to Lyapunov theory,it is proved that the proposed control scheme can ensure the stability of the closed-loop systems.Finally,the effectiveness of the proposed scheme is illustrated by simulation results.(3)Finally,for a class of strong interconnected nonlinear time-delay systems with strong interconnection,unmodeled dynamics,unstructured uncertainties and uncertain input delays are further considered in the system model.The smooth switching function is used to deal with the strong interconnection function and design the novel strong interconnection compensation mechanism.The difficulties generated by unmodeled dynamics are dominated by using a dynamic auxiliary signal.Combined with backstepping control technique and adaptive control technique,a decentralized adaptive PI tracking control scheme with unmodeled dynamics is developed.The proposed scheme can ensure that the tracking errors converge to a small neighborhood near the origin based on the Lyapunov stability theory.Finally,the effectiveness of the proposed scheme is illustrated by simulation results.