Abstract
Dynamic optimization theory is established for nonlinear complementarity systems, a class of highly nonlinear and nonsmooth dynamical systems, which find widespread use in engineering. In particular, optimal control problems involving complementarity systems are solved using a direct approach, allowing for gradient-based sequential methods (e.g., single or multiple shooting) to update a parametrically discretized control. This is accomplished via lexicographic directional differentiation, a recently developed tool in nonsmooth analysis. The computationally relevant theory is specialized to optimization-constrained ODEs and parameter estimation problems, with motivating applications.
Published Version
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