Optimal stabilization of stochastic systems
The paper deals with optimal stabilization of stochastic systems which are solutions of Ito-equations using performance criteria of the type \(E(\int^{\infty}_{t_ 0}g(x,u,t,)\quad dt).\) Assume that the state vector is known for all t, and the system is completely controllable. Then a Lyapunov function that ensures stochastic (asymptotic) stability (in the large) and fulfills the steady state Bellman equation yields optimal stability (in one of the senses above). This result is specialized for systems that are linear in the control with performance criterion quadratic in the control. For linear systems, i.e. linear in state and control with quadratic performance criterion in x and u, the Lyapunov function can be made specific, which for time-invariant systems under the condition of complete controllability entails optimal stability in the sense of stochastic asymptotic stability in the large.
stochastic asymptotic stability in the large
scientific article; zbMATH DE number 3854944