Optimal control of piecewise-deterministic processes.
Zhengdi Shen (Center for Applied Mathematics, Cornell University)
Deterministic optimal control problems lead to first order non-linear Hamilton-Jacobi-Bellman equations (HJB). In contrast, the standard stochastic optimal control formulation leads to the 2nd order (uniformly elliptic) HJB PDE, but has several shortcomings in many applications (including robotic path planning).
One alternative is provided by the so called "piecewise-deterministic" control processes, where the random perturbation is a discrete-time event -- essentially a random switching among several modes of cost and dynamics. This leads to a system of weakly coupled 1st-order HJB equations. In this talk, we investigate the optimal controls resulting from such models and the computational challenges associated with them. (work in progress; joint with A. Vladimirsky.)