Time-optimal control problem for a linear parameter varying system with nonlinear item |
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| Institution: | 1. School of Mathematical Sciences, Dalian University of Technology, Dalian, China;2. School of Control Science and Engineering, Dalian University of Technology, Dalian, China;3. Liaoning Key Laboratory of Computational Mathematics and Data Intelligence, China;4. Key Laboratory of Intelligent Control and Optimization for Industrial Equipment, Dalian University of Technology, Ministry of Education;1. Department of Electrical Engineering, University of Technology of Paraná – UTFPR Cornélio Procópio 86300-000, PR, Brazil;2. Federal Institute of São Paulo – IFSP, Campus Avaré, Avaré 18707-150, SP, Brazil;1. Federal University of São João del-Rei, 170 Frei Orlando, São João del-Rei;1. Department of Electrical and Computer Engineering, University of Alberta, Edmonton T6G 2W3, Canada;2. Department of Electrical Engineering, Sahand University of Technology, Tabriz, Iran;1. Universidad de Monterrey, Av. I. Morones Prieto 4500 Pte., 66238, San Pedro Garza García N.L., México;2. Universidad Autónoma de Nuevo León, Av. Universidad s/n, 66450, San Nicolás de los Garza N.L., México;3. Université Grenoble Alpes, GIPSA-lab, F-3800 Grenoble, France;1. Department of Electronics Engineering, Universidade Federal de Minas Gerais – UFMG, Belo Horizonte, MG, Brazil;2. Dynamic Systems Research Group, Technological Sciences Institute (ICT), Universidade Federal de Itajubá – Unifei, Itabira, MG, Brazil;3. Dept. of Mechatronics, Universidad Politécnica de Pachuca, Zempoala, 43830, Mexico;4. Department of Electrical Engineering, Exact and Applied Sciences Institute (ICEA), Universidade Federal de Ouro Preto – UFOP, João Monlevade, MG, Brazil |
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| Abstract: | In this paper, we considered a time-optimal control problem for a new type of linear parameter varying (LPV) system which is obtained through data identification in the process of dealing with actual problems. The addition of non-linear terms is compensation for the method that does not require linear expansion at the equilibrium point. Since the objective function is the terminal time which is an implicit function concerning decision variables, it is a non-standard optimal control problem with uncertain terminal time. To find the global optimal solution to this problem, firstly, the control parameterization method is used to transform it into a nonlinear optimization problem of parameter selection, and then the modifed particle swarm optimization (PSO) algorithm is combined to solve the equivalent nonlinear programming problem. Numerical examples are used to illustrate the effectiveness of the proposed algorithm. |
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