A First-Order Approach for Optimal Control of Nonlinear Dynamical Systems

초록

This paper introduces an efficient first-order optimization approach for optimal control of nonlinear dynamical systems. The primary challenges in these systems include nonlinearity in dynamics and nonconvexity in the constraints on state and control variables. Traditional sequential convex programming (SCP) methods, while commonly employed to address these challenges, are computationally demanding and rely heavily on initial conditions. Our proposed method reformulates nonlinear optimal control problems into linear control problems with nonconvex constraints, utilizing a first-order approach that projects onto nonconvex sets. This approach significantly reduces computational complexity, aligning it with that of solving a single convex problem. Numerical experiments on spacecraft orbit transfer with complex constraints validate the effectiveness of our algorithm in managing nonlinear optimal control problems with nonconvex constraints.