Effects of the control bounds in the stochastic optimal control problem

This paper proposes a method to solve the stochastic optimal control problem with fixed state terminal conditions and control bounds. Being applicable to strongly nonlinear stochastic systems under parametric and external excitations, the method makes use of Bellman's principle of optimality an...

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Bibliographic Details
Main Authors: Crespo, L.G., Sun, J.Q.
Format: Conference Proceeding
Language:English
Subjects:
Applied sciences
Computer science
control theory
systems
Control systems
Control theory. Systems
Cost function
Exact sciences and technology
Gaussian approximation
Mechanical engineering
Nonlinear control systems
Optimal control
State-space methods
Stochastic processes
Stochastic systems
Sun
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Summary:This paper proposes a method to solve the stochastic optimal control problem with fixed state terminal conditions and control bounds. Being applicable to strongly nonlinear stochastic systems under parametric and external excitations, the method makes use of Bellman's principle of optimality and the short-time Gaussian approximation. The solution found is global in the sense that optimal controls for all the initial conditions in a bounded region of the state space are obtained. A Markov chain with a control dependent transition probability matrix is built using the generalized cell mapping method. This allow us to study the transient and stationary effects of the control on the system response in the probability sense. The method is applied to a few systems resulting in excellent control performances. The dependence of the response on the control bounds is studied for a 1D-state nonlinear system and the Van der Pol oscillator.
ISSN:0743-1619
2378-5861
DOI:10.1109/ACC.2002.1024597