This paper introduces a robust decentralized regulation approach of linear interconnected time-varying systems. If the optimal optimization problems of time-varying systems are considered, the solution of time-varying Riccati differential equation should be involved and pre-calculated. The weighting parameters of the optimal performance index in this paper are all time varying. The optimal solution relies on the initial conditions of the solutions of Riccati differential equations, and these initial conditions are derived by the backward Euler’s method. Then the obtained optimal control gain is modified to accommodate the interactions among the subsystems. The overall system is mathematically proved to be exponentially stable with a prescribed degree of stability. Computer simulations of a time-varying example composed of three subsystems are conducted to demonstrate the feasibility of this approach.
In this paper, a decentralized stabilization scheme of linear time-varying large-scale interconnected systems with unmeasurable states is proposed. These interactions among subsystems are also time-varying and affect each subsystem through its input. First a decentralized observer scheme for time-varying interconnected system is constructed by the dual optimal control solution to obtain good estimations for the unmeasurable states. Based on these observer states, a time-varying decentralized feedback law is introduced to achieve the global system exponential stability. The solutions of time varying Riccati equations are obtained by backward Euler’s method and implemented with the original system dynamics. Computer simulations of the responses of an example are also conducted to show the effectiveness of the proposed approach.
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