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A probabilistic framework is proposed for the optimization of efficientswitched control strategies for physical systems dominated by stochasticexcitation. In this framework, the equation for the state trajectory isreplaced with an equivalent equation for its probability distribution functionin the constrained optimization setting. This allows for a large class ofcontrol rules to be considered, including hysteresis and a mix of continuousand discrete random variables. The problem of steering atmospheric balloonswithin a stratified flowfield is a motivating application; the same approachcan be extended to a variety of mixed-variable stochastic systems and to newclasses of control rules.

A probabilistic framework for the control of systems with discrete states and stochastic excitation