The recursive algorithm for the optimal static output feedback control problem of linear singularly perturbed systems. (English) Zbl 0666.93031
Given a linear time-invariant control system with a quadratic performance criterion and output \(y=Cx\), it is known that the gain matrix of the optimal static feedback \(u=Fy\) can be obtained by solving a system of nonlinear matrix algebraic equations. A known iterative algorithm for solving this system requires at every step the solution of two Lyapunov- type matrix equations. The paper is devoted to a solution procedure for the latter equations, in the case where the original control system is singularly perturbed (a small parameter \(\epsilon\) multiplies a part of the derivatives). A complete slow-fast decomposition is achieved so that only low-order systems are involved in the computations at every step. The accuracy after k steps is proved to be \(O(\epsilon^ k)\).
Reviewer: V.Veliov
MSC:
93B40 | Computational methods in systems theory (MSC2010) |
34E15 | Singular perturbations for ordinary differential equations |
15A24 | Matrix equations and identities |
93C05 | Linear systems in control theory |
49M27 | Decomposition methods |