Title: Controller Synthesis for Discrete-time Hybrid Polynomial Systems via Occupation Measures,
Abstract: We present a novel controller synthesis approach for discrete-time hybrid
polynomial systems, a class of systems that can model a wide variety of
interactions between robots and their environment. The approach is rooted in
recently developed techniques that use occupation measures to formulate the
controller synthesis problem as an infinite-dimensional linear program. The
relaxation of the linear program as a finite-dimensional semidefinite program
can be solved to generate a control law. The approach has several advantages
including that the formulation is convex, that the formulation and the
extracted controllers are simple, and that the computational complexity is
polynomial in the state and control input dimensions. We illustrate our
approach on some robotics examples.