Sequential Quadratic Sum-of-squares Programming for Nonlinear Control Systems

Abstract: Many problems in nonlinear systems analysis and control design, such as local region-of-attraction estimation, inner-approximations of reachable sets or control design under state and control constraints can be formulated as nonconvex sum-of-squares programs. Yet tractable and efficient solution methods are still lacking, limiting their application in control engineering. To address this gap, we propose a filter line-search algorithm that solves a sequence of quadratic subproblems. Numerical benchmarks demonstrate that the algorithm can significantly reduce the number of iterations, resulting in a substantial decrease in computation time compared to established methods for nonconvex sum-of-squares programs. An open-source implementation of the algorithm along with the numerical benchmarks is provided