On the solution of discrete-time Markovian jump linear quadratic control problems. (English) Zbl 0822.93074

Summary: A necessary and sufficient condition for the existence of a positive- semidefinite solution of the coupled algebraic discrete-time Riccati-like equation occurring in Markovian jump control problems is derived. By verifying a simple matrix inequality, it is shown that such a solution exists and can be obtained as a limit of a monotonic sequence. This leads to a straightforward numerical algorithm for the computation of the solution. An example is given to illustrate the proposed method.


93E20 Optimal stochastic control
93C55 Discrete-time control/observation systems
93B40 Computational methods in systems theory (MSC2010)
49N10 Linear-quadratic optimal control problems
49K45 Optimality conditions for problems involving randomness
60J75 Jump processes (MSC2010)
Full Text: DOI


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