A new algorithm for suboptimal stochastic control

Abstract

An apparently new stochastic control algorithm, called <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> -measurement-optimal feedback control, is described for discrete-time systems. This scheme incorporates <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> future measurements into the control computations: when <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> is zero,it reduces to the well-known open-loop-optimal feedback control; when <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> is the actual number of measurements remaining in the problem, it becomes the truly optimal stochastic control. This new algorithm may also be used to simplify computations when the plant is nonlinear, when the controls are constrained, or when the cost is nonquadratic. Simulation results are presented which show the superiority of the new algorithm over the open-loop-optimal feedback control.