On optimal control of hybrid dynamical systems using complementarity constraints

Kazi, Saif Rahaman; Wang, Kexin; Biegler, Lorenz T.

doi:10.1016/j.jprocont.2025.103492

On optimal control of hybrid dynamical systems using complementarity constraints

Journal Article · Tue Jul 08 00:00:00 EDT 2025 · Journal of Process Control

DOI:https://doi.org/10.1016/j.jprocont.2025.103492· OSTI ID:2572556

^[1]; Wang, Kexin ^[2]; ^[3]

Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Zhejiang Univ., Hangzhou (China)
Carnegie Mellon Univ., Pittsburgh, PA (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 2572556

Report Number(s):: LA-UR--25-21926; 10.1016/j.jprocont.2025.103492

Journal Information:: Journal of Process Control, Journal Name: Journal of Process Control Vol. 153; ISSN 0959-1524

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (20)

A high accuracy method for solving ODEs with discontinuous right-hand side Stewart, David Numerische Mathematik, Vol. 58, Issue 1 https://doi.org/10.1007/BF01385627	journal	December 1990
Optimal control of systems with discontinuous differential equations Stewart, David E.; Anitescu, Mihai Numerische Mathematik, Vol. 114, Issue 4 https://doi.org/10.1007/s00211-009-0262-2	journal	September 2009
Finite Elements with Switch Detection for direct optimal control of nonsmooth systems Nurkanović, Armin; Sperl, Mario; Albrecht, Sebastian Numerische Mathematik, Vol. 156, Issue 3 https://doi.org/10.1007/s00211-024-01412-z	journal	May 2024
Solving Mathematical Programs with Equilibrium Constraints Guo, Lei; Lin, Gui-Hua; Ye, Jane J. Journal of Optimization Theory and Applications, Vol. 166, Issue 1 https://doi.org/10.1007/s10957-014-0699-z	journal	January 2015
Control of systems integrating logic, dynamics, and constraints Bemporad, Alberto; Morari, Manfred Automatica, Vol. 35, Issue 3 https://doi.org/10.1016/S0005-1098(98)00178-2	journal	March 1999
A class of discontinuous dynamical systems I. An ideal gas–liquid system Moudgalya, Kannan M.; Ryali, Venkatarao Chemical Engineering Science, Vol. 56, Issue 11 https://doi.org/10.1016/S0009-2509(01)00043-4	journal	June 2001
A class of discontinuous dynamical systems II. An industrial slurry high density polyethylene reactor Moudgalya, Kannan M.; Jaguste, Shubhangi Chemical Engineering Science, Vol. 56, Issue 11 https://doi.org/10.1016/S0009-2509(01)00044-6	journal	June 2001
Some applications of Filippov’s dynamical systems Biák, Martin; Hanus, Tomáš; Janovská, Drahoslava Journal of Computational and Applied Mathematics, Vol. 254 https://doi.org/10.1016/j.cam.2013.03.034	journal	December 2013
An MPEC formulation for dynamic optimization of distillation operations Raghunathan, Arvind U.; Soledad Diaz, M.; Biegler, Lorenz T. Computers & Chemical Engineering, Vol. 28, Issue 10 https://doi.org/10.1016/j.compchemeng.2004.03.015	journal	September 2004
Globally Convergent Method for Optimal Control of Hybrid Dynamical Systems Kazi, Saif R.; Thombre, Mandar; Biegler, Lorenz IFAC-PapersOnLine, Vol. 58, Issue 14 https://doi.org/10.1016/j.ifacol.2024.08.446	journal	January 2024
MPEC strategies for optimization of a class of hybrid dynamic systems Baumrucker, B. T.; Biegler, L. T. Journal of Process Control, Vol. 19, Issue 8 https://doi.org/10.1016/j.jprocont.2009.02.006	journal	September 2009
Pseudonormality and a Lagrange Multiplier Theory for Constrained Optimization Bertsekas, D. P.; Ozdaglar, A. E. Journal of Optimization Theory and Applications, Vol. 114, Issue 2 https://doi.org/10.1023/A:1016083601322	journal	August 2002
Optimal control of a class of hybrid systems Cassandras, C. G.; Pepyne, D. L.; Wardi, Y. IEEE Transactions on Automatic Control, Vol. 46, Issue 3 https://doi.org/10.1109/9.911417	journal	March 2001
NOSNOC: A Software Package for Numerical Optimal Control of Nonsmooth Systems Nurkanovic, Armin; Diehl, Moritz IEEE Control Systems Letters, Vol. 6 https://doi.org/10.1109/LCSYS.2022.3181800	journal	January 2022
Contact-Implicit Trajectory Optimization Using Orthogonal Collocation Patel, Amir; Shield, Stacey Leigh; Kazi, Saif IEEE Robotics and Automation Letters, Vol. 4, Issue 2 https://doi.org/10.1109/LRA.2019.2900840	journal	April 2019
Optimal Control of Switched Systems Based on Parameterization of the Switching Instants Xu, X.; Antsaklis, P. J. IEEE Transactions on Automatic Control, Vol. 49, Issue 1 https://doi.org/10.1109/TAC.2003.821417	journal	January 2004
Local Convergence of SQP Methods for Mathematical Programs with Equilibrium Constraints Fletcher, Roger; Leyffer, Sven; Ralph, Danny SIAM Journal on Optimization, Vol. 17, Issue 1 https://doi.org/10.1137/S1052623402407382	journal	January 2006
Convergence Properties of a Regularization Scheme for Mathematical Programs with Complementarity Constraints Scholtes, Stefan SIAM Journal on Optimization, Vol. 11, Issue 4 https://doi.org/10.1137/S1052623499361233	journal	January 2001
Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity Scheel, Holger; Scholtes, Stefan Mathematics of Operations Research, Vol. 25, Issue 1 https://doi.org/10.1287/moor.25.1.1.15213	journal	February 2000
An Optimal Control Approach for Hybrid Systems Riedinger, P.; lung, C.; Kratz, F. European Journal of Control, Vol. 9, Issue 5 https://doi.org/10.3166/ejc.9.449-458	journal	January 2003

Similar Records

Convex Relaxation of Grid-Connected Energy Storage System Models With Complementarity Constraints in DC OPF

Journal Article · Wed Apr 29 20:00:00 EDT 2020 · IEEE Transactions on Smart Grid · OSTI ID:1660118

A complementarity constraint formulation of convex multiobjective optimization problems.

Journal Article · Wed Apr 01 00:00:00 EDT 2009 · Inform J. Computing · OSTI ID:952918

Penalty interior-point method fails to converge.

Journal Article · Mon Aug 01 00:00:00 EDT 2005 · Optimization Methods Software · OSTI ID:961473

Related Subjects

97 MATHEMATICS AND COMPUTING
Complementarity constraints
Differential complementarity systems
Hybrid dynamical systems

On optimal control of hybrid dynamical systems using complementarity constraints

Citation Formats

References (20)

Similar Records

Related Subjects