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Discrete-time optimal control with control-dependent noise and generalized Riccati difference equations. (English) Zbl 0944.93032
The optimal control law is derived for discrete-time linear stochastic systems with quadratic performance criterion and control-dependent noise. The linear operator used for determining the stability of the second moments equation is different from the one used for showing the convergence of the generalized Riccati difference equation. This is a consequence of having explicitly modelled the noise dependence on the control. It is shown how this treatment leads to explicit conditions for solvability of the control problem. Moreover, the control law derived in this way leads to a system theoretic interpretation as a compromise between stability and optimality.
MSC:
93E20Optimal stochastic control (systems)
93C55Discrete-time control systems
49N10Linear-quadratic optimal control problems