Path constraints in tychastic and unscented optimal control: Theory, application and experimental results

In recent papers, we have shown that a Lebesgue-Stieltjes optimal control theory forms the foundations for unscented optimal control. In this paper, we further our results by incorporating uncertain mixed state-control constraints in the problem formulation. We show that the integrated Hamiltonian minimization condition resembles a semi-infinite type mathematical programming problem. The resulting computational difficulties are mitigated through the use of the unscented transform; however, the price of this approximation is a solution to a chance-constrained optimal control problem whose risk level is determined a posteriori. Experimental results conducted at Honeywell are presented to demonstrate the success of the theory. An order of magnitude reduction in the failure rate in obtained through the use of an unscented optimal control that steers a spacecraft testbed driven by control-moment gyros.