Applications of numerical optimal control to nonlinear hybrid systems |
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| Institution: | 1. Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, IL, USA;2. School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA;3. Innovation Center, Decision and Control Group, Eaton Corporation, Eden Prairie, MN, USA;1. Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800, Thailand;2. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia;3. Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece;1. South Dakota School of Mines and Technology, USA;2. Missouri University of Science and Technology, USA;1. College of Information Science and Technology, Bohai University, Jinzhou 121013, PR China;2. College of Engineering, Bohai University, Jinzhou 121013, PR China;3. Institute of Intelligent Control and Systems, Harbin Institute of Technology, Harbin 150001, PR China;4. Department of Engineering, Faculty of Engineering and Science, University of Agder, 4879 Grimstad, Norway;5. Department of Informatics, King?s College London, London, WC2R 2LS, UK;1. Dipartimento di Elettronica, Informatica e Bioingegneria, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy;2. IEIIT-CNR, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy;3. School of Electrical and Computer Engineering, University of Newcastle, Callaghan, New South Wales, 2308, Australia;4. Dipartimento di Matematica e Informatica, Università di Udine, 33100 Udine, Italy |
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| Abstract: | This paper develops a technique for numerically solving hybrid optimal control problems. The theoretical foundation of the approach is a recently developed methodology by S.C. Bengea and R.A. DeCarlo Optimal control of switching systems, Automatica. A Journal of IFAC 41 (1) (2005) 11–27] for solving switched optimal control problems through embedding. The methodology is extended to incorporate hybrid behavior stemming from autonomous (uncontrolled) switches that results in plant equations with piecewise smooth vector fields. We demonstrate that when the system has no memory, the embedding technique can be used to reduce the hybrid optimal control problem for such systems to the traditional one. In particular, we show that the solution methodology does not require mixed integer programming (MIP) methods, but rather can utilize traditional nonlinear programming techniques such as sequential quadratic programming (SQP). By dramatically reducing the computational complexity over existing approaches, the proposed techniques make optimal control highly appealing for hybrid systems. This appeal is concretely demonstrated in an exhaustive application to a unicycle model that contains both autonomous and controlled switches; optimal and model predictive control solutions are given for two types of models using both a minimum energy and minimum time performance index. Controller performance is evaluated in the presence of a step frictional disturbance and parameter uncertainties which demonstrates the robustness of the controllers. |
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