The Study Of H₂, H₂/H_∞ Control For Stochastic Systems

Linear quadratic (LQ) optimal control was pioneered by Kalman in 1960 for deterministic systems [ 1 ]. which has been playing a central role in modern control theory. Up to now. LQ problem has been investigated extensively in both theory and application. From the practical backgrounds of engineering, all the above we has studied are the standard LQ problems, i.e.Q≥0, R>0. Until 1998 [5] has found the essential difference between the deterministic LQ problems and the stochastic LQ. i.e. for stochastic LQ problems, when D ≠ 0 the control weighting matrices R may be indefinite or even negative definite, however the cost functional is still well posed. This finding motivated a series of research later and established the important theory of indefinite stochastic LQ problems, in which the work of X. Y. Zhou et al is most excellent. But as we know, for the optimal problems of a physical system in practice, all kinds of constraints are indispensable, such as the state or control satisfies some kinds of conditions. [12] studied the indefinite stochastic LQR problems in which the state and control satisfied integral quadratic constraints.In chapter 1, we investigate the following indefinite stochastic LQ problems with the terminal state satisfying the linear constraints.Problem 1:...