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DOE OSTI · 2572556

On optimal control of hybrid dynamical systems using complementarity constraints

Kazi, Saif Rahaman [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000341146893)·Wang, Kexin [Zhejiang Univ., Hangzhou (China)]·Biegler, Lorenz T. [Carnegie Mellon Univ., Pittsburgh, PA (United States)] (ORCID:0000000338754441)
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Abstract

Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate them using non-smooth and non-convex complementarity constraints as a mathematical program with complementarity constraints (MPCC). We utilize a moving finite element based strategy to discretize the differential equation system to accurately locate the unknown switching points at the finite element boundary and achieve high-order accuracy at intermediate non-collocation points. We propose a globalization approach to solve the discretized MPCC problem using a mixed NLP/MILP-based strategy to converge to a non-spurious first-order optimal solution. The method is tested on three dynamic optimization examples, including a gas–liquid tank model and an optimal control problem with a sliding mode solution.

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97 MATHEMATICS AND COMPUTINGComplementarity constraintsDifferential complementarity systemsHybrid dynamical systems

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Kazi, Saif Rahaman [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000341146893), Wang, Kexin [Zhejiang Univ., Hangzhou (China)], Biegler, Lorenz T. [Carnegie Mellon Univ., Pittsburgh, PA (United States)] (ORCID:0000000338754441). 2025-07-08. On optimal control of hybrid dynamical systems using complementarity constraints. https://doi.org/10.1016/j.jprocont.2025.103492

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