Study On Guaranteed Cost Control For Uncertain Nonlinear Systems With Time-Delay

The main systems that are researched in modern control theory are MIMO. For the control system that have optimized-cost index, it requires the cost index of systems minimize. But the optimal cost control is not likely to be realized for the uncertain systems, the robust control of uncertain systems are received wide-regard. Because the guaranteed cost control (GCC) can deal with the precision of control systems and the calculative workload in effectively, in recent year, the GCC for uncertain systems that is regarded as an approach of this class problem is received wide-regard. In 1972, the GCC is firstly proposed in the self-adapt control by Chang & P eng. The research have run through the whole fields of control systems, such as uncertain linear system, uncertain disperse system time-delay system uncertain 2D system and uncertain generalized system.In this paper, first we set forth the GCC and status quo of research, classify the types of GCC, and compare the production of severe kinds. On the base, we research farther in the nonlinear system, extend the GCC to nonlinear system. At last, an approach of GCC with a minimize cost index is derived.In the 2nd chapter, we research a class of nonlinear GCC with time-delay, using Riccati equation as an approach, and receive a minimal cost index upper limit. In the 3rd chapter, a kind of guaranteed cost controller is proposed for uncertain nonlinear systems with time-delay, where the part of nonlinear have a bounded property. Sufficient conditions for the existence of guaranteed cost controllers are given. This control law guarantees the robust stability of the closed-loop system, and an upper bound on the cost function, finally, the designing method for state feedback guaranteed cost controller is proposed by using the LMI approach. For a kind of delay dependent GCC for uncertainnonlinear systems with time-delay, the problem of designing a guaranteed cost state feedback controller is considered in the 4th chapter. Using LMI as a kind means same as the 3rd chapter. At last, we compare the delay independent GCC with the delay dependent GCC, attest to the latter is superior to the former in the small time-delay stale.In the conclusion part of this paper, we summarize the current problem of the control systems, and prospect the study of nonlinear GCC. We point out the problem that should be considered in the future study of the design for the nonlinear systems with time-delay and the direction for the future research work is indicated.