Sum of Squares based Convex Approach for Optimal Control Synthesis

We consider an optimal control synthesis problem for a class of control-affine nonlinear systems. We propose Sum-of-Square based computational framework for optimal control synthesis. The proposed computation framework relies on the convex formulation of the optimal control problem in the dual space of densities. The convex formulation to the optimal control problem is based on the duality results in dynamical systems’ stability theory. We used the Sum-of-Square based computational framework for the finite-dimensional approximation of the convex optimization problem. The efficacy of the developed framework is demonstrated using simulation results.