  A probabilistic framework is proposed for the optimization of efficient
switched control strategies for physical systems dominated by stochastic
excitation. In this framework, the equation for the state trajectory is
replaced with an equivalent equation for its probability distribution function
in the constrained optimization setting. This allows for a large class of
control rules to be considered, including hysteresis and a mix of continuous
and discrete random variables. The problem of steering atmospheric balloons
within a stratified flowfield is a motivating application; the same approach
can be extended to a variety of mixed-variable stochastic systems and to new
classes of control rules.
