Optimal control of a linear system subjected to external sinusoidal and white noise excitations
Periodic Control Systems, Volume # 3 | Part# 1
Daniil V. Iourtchenko
Digital Object Identifier (DOI)
optimal control,stochastic control,dynamic programming
The paper discusses a problem of stochastic optimal control of a linear single-degree-of-freedom system subjected to external sinusoidal and white noise excitations. An external, bounded in magnitude control force is introduced into the system to reduce mean system response energy. The dynamic programming approach is used to derive the corresponding Hamilton-Jacobi-Bellman equation. Hybrid solution method is used to derive a solution to this equation, thereby found an optimal control policy.
 Chernousko F.L., Kolmanovskii V.B. (1978). Optimal control with stochastic excitation. Nauka (in Russian).  Fleming W.H., Soner H.M. (1992). Controlled Markov Processes and Viscosity Solutions. Springer-Verlag, New York.  Bratus A.S, Iourtchenko D.V., Menaldi J.-L. (2006). Local solutions to the Hamilton Jacobi Bellman equation in stochastic problems of optimal control. Doklady Mathematics. 74, N 1, pp. 610-613.  Iourtchenko D.V. (2000). Stochastic optimal bounded control for a system with the Boltz cost function. Journal od Vibration and Control., N. 6. pp. 1195-1204.  Dimentberg M.F., Iourtchenko D.V., Bratus A.S. (2000). Optimal bounded control of steady-state random vibrations. Probabilistic Engineering Mechanics . 15, pp. 381-386.