Simulation of Optimal Stochastic Control Strategies by Maximum Principle

J. Štecha and J. Rathouský (Czech Republic)


Maximum principle, stochastic systems, LQG control, ARX model, Lyapunov and Riccati equations.


The Pontrjagin maximum principle solves the problem of optimal control of a continuous deterministic system. The discrete maximum principle solves the problem of optimal control of a discrete-time deterministic system. The max imum principle changes the problem of optimal control to a two point boundary value problem which can be com pletely solved only in special tasks. Optimal control of stochastic systems or even sys tems with probabilistic parameters is usually derived us ing stochastic dynamic programming. In the paper an al ternative approach based on a stochastic modification of the maximum principle is presented, both for continuous and discrete-time systems. Cautious and certainty equiv alent optimal control strategies are then derived using this method and the results are consistent with those achieved by stochastic dynamic programming. Finally, simulations of these optimal control strategies are presented and com pared in terms of control quality.

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