Impulsively-controlled systems and reverse dwell time: A linear programming approach |
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| Institution: | 1. School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, People’s Republic of China;2. Department of Engineering, Faculty of Engineering and Science, University of Agder, N-4898 Grimstad, Norway;1. Department of Electronics Engineering, College of Engineering, Ewha Womans University, 52 Ewhayeodae-gil, Seodaemun, Seoul 120-750, South Korea;2. Control and Power Group, Electrical and Electronic Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom;3. Dipartimento di Ingegneria dell''Informazione University of Florence, via S. Marta, 3 50139 Firenze, Italy;1. State Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Yuquan Campus, Hangzhou, 310027, P. R. China;2. School of Electrical and Electronic Engineering, University of Adelaide, Adelaide, SA 5005, Australia;3. College of Engineering and Science, Victoria University, Melbourne, Vic. 8001, Australia;4. Institute of Information and Control, Hangzhou Dianzi University, Hangzhou, 310018, P. R. China |
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| Abstract: | We present a receding horizon algorithm that converges to the exact solution in polynomial time for a class of optimal impulse control problems with uniformly distributed impulse instants and governed by so-called reverse dwell time conditions. The cost has two separate terms, one depending on time and the second monotonically decreasing on the state norm. The obtained results have both theoretical and practical relevance. From a theoretical perspective we prove certain geometrical properties of the discrete set of feasible solutions. From a practical standpoint, such properties reduce the computational burden and speed up the search for the optimum thus making the algorithm suitable for the on-line implementation in real-time problems. Our approach consists in approximating the optimal impulse control problem via a binary linear programming problem with a totally unimodular constraint matrix. Hence, solving the binary linear programming problem is equivalent to solving its linear relaxation. Then, given the feasible solution from the linear relaxation, we find the optimal solution via receding horizon and local search. Numerical illustrations of a queueing system are performed. |
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| Keywords: | Impulse control Hybrid systems Reverse dwell time |
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