# Dp 493 en

# Measures and LMIs for Optimal Control of Piecewise-Affine Dynamical Systems[edit]

**Author**: Hilmy Abdalmoaty Mohamed Rasheed

The project considers the class of deterministic continuous-time optimal control problems (OCPs) with piecewise-affine (PWA) vector fields and polynomial data. The OCP is relaxed as an infinite-dimensional linear program (LP) over space of occupation measures. The LP is then written as a particular instance of the generalized moment problem (GMP) which is then approached by an asymptotically converging hierarchy of linear matrix inequality (LMI) relaxations. The relaxed dual of the original LP gives a polynomial approximation of the value function of the OCP along optimal trajectories. Based on this polynomial approximation, a novel suboptimal policy is developed to construct a state feedback in a sample-and-hold manner.
The results show that the suboptimal policy succeeds in providing a stabilizing suboptimal state feedback law that drives the system relatively close to the optimal trajectories and respects the given constraints.

**Hilmy Abdalmoaty Mohamed Rasheed**, mailto:rasheed@ieee.org