LMI optimization for nonstandard Riccati equations arising in stochastic control. (English) Zbl 0863.93087

Ait Rami, Mustapha; El Ghaoui, Laurent

IEEE Trans. Autom. Control 41, No. 11, 1666-1671 (1996).

Quadratic cost optimal control problems for linear systems depending on an underlying, finite state Markov process (jump linear systems) lead to coupled Riccati equations. The authors show that such equations can be solved using convex optimization over linear matrix inequalities, if the system is mean-square stabilizable. Under the additional assumption that each mode (i.e. all subsystems for each state of the Markov process) is observable, the optimal solutions are mean-square stabilizing. The method breaks down for systems with white noise terms multiplying the input matrix. Several examples illustrate the range of applicability of the proposed approach.

Reviewer: W.Kliemann (Ames)

MSC:

93E20	Optimal stochastic control
93B40	Computational methods in systems theory (MSC2010)
15A39	Linear inequalities of matrices

Keywords:

stabilization; jump linear systems; optimal control; Markov process; convex optimization; linear matrix inequalities

Software:

LMITOOL