2012/11/14 by Mohamed Abdalmoaty, M. Rasheed Abdalmoaty, Didier Henrion +5
Computer Science · Engineering · Mathematics · #Adaptive Dynamic Programming Control #FOS: Mathematics #Optimization and Control (math.OC) #Spacecraft Dynamics and Control #Stability and Control of Uncertain Systems #math.OC
paper · pdf · doi:10.48550/arxiv.1211.3318
arxiv created 2012/11/14 · openalex publication_date 2012/11/14 · arxiv updated 2012/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper considers the class of deterministic continuous-time optimal control problems (OCPs) with piecewise-affine (PWA) vector field, polynomial Lagrangian and semialgebraic input and state constraints. The OCP is first relaxed as an infinite-dimensional linear program (LP) over a space of occupation measures. This LP, a particular instance of the generalized moment problem, is then approached by an asymptotically converging hierarchy of linear matrix inequality (LMI) relaxations. The relaxed dual of the original LP returns a polynomial approximation of the value function that solves the Hamilton-Jacobi-Bellman (HJB) equation of the OCP. Based on this polynomial approximation, a 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.