(165a) Globally Convergent Mpcc Based Algorithm to Solve Hybrid Dynamical Optimization Problems

Hybrid Dynamical Systems are an important way to model multiple physical processes like contact based mechanical systems and vapor liquid equilibrium systems. Optimal control of hybrid dynamical systems requires modeling and solving the non-smooth dynamics with kinks using complementarity constraints. Unfortunately, higher order numerical integration methods fail to achieve desired accuracy with uniform discretization grid.Adaptive discretization methods which can detect these non-smooth points accurately are required to solve these optimal control problems (OCP) accurately. Recently, Nurkanovic et al. (arXiv:2205.05337) developed a finite elements with switch detection (FESD) method for solving the non-smooth OCP. The method builds on a previous idea (Baumrucker et al.(DOI:10.1016/j.jprocont.2009.02.006)) of using variable step sizes and additional constraints with cross-complementarities to enforce the non-smooth points to be at the boundary of the nite elements. Since the complementarity problem is solved using the penalty formulation, the approach is not suitable for highly nonlinear dynamical systems. Moreover, the algorithm can converge to spurious solutions which are not local optimum of the original OCP. We propose a hybrid strategy based on constraint relaxation and sequential linearization for solving the dynamic complementarity system which overcomes the drawbacks of the penalty approach. We present examples which show the efficacy of the proposed method.