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Robustness of non-linear stochastic optimal control for quasi-Hamiltonian systems with parametric uncertainty. (English) Zbl 1287.93110
Summary: The robustness of non-linear stochastic optimal control for quasi-Hamiltonian systems with uncertain parameters is studied. Based on the independence of uncertain parameters and stochastic excitations, the non-linear stochastic optimal control for the nominal quasi-Hamiltonian system with average-value parameters is first obtained by using the stochastic averaging method and stochastic dynamical programming principle. Then, the means and standard deviations of root-mean-square responses, control effectiveness and control efficiency for the uncertain quasi-Hamiltonian system are calculated by using the stochastic averaging method and the probabilistic analysis. By introducing the sensitivity of the variation coefficients of controlled root-mean-square responses, control effectiveness and control efficiency to those of uncertain parameters, the robustness of the non-linear stochastic optimal control is evaluated. Two examples are given to illustrate the proposed control procedure and its robustness.

MSC:
93E20 Optimal stochastic control
93B35 Sensitivity (robustness)
49L20 Dynamic programming in optimal control and differential games
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