Modeling and solving problems of optimal control of hybrid systems with autonomous switches using particle swarm optimization and direct transcription methods

Document Type : Original Paper


1 Department of Industrial and Applied Mathematics, Shahid Beheshti University, Tehran, Iran

2 Department of Applied Mathematics, Amirkabir University of Technology, Tehran, Iran

3 Department of Industrial and Applied Mathematics, Shahid Beheshti University, Tehran, IRAN


In this paper, it is focused on a specific category of hybrid optimal control problems with autonomous systems. Because of existence of continuous and discrete dynamic, the numerical solutions of hybrid optimal control are not simple. The numerical direct and indirect methods presented for solving optimal control of hybrid systems have drawbacks due to sensitivity to initial guess and the inability of finding a global minimum solution. Meta-heuristic methods have been proposed. In this method, Meta-heuristic methods (e.g. using PSO) is used to determine the mode sequence, and by the attention to the prescribed the mode sequence, a problem with a determinate mode sequence is obtained, and then the switching times, the optimal value of the target function and the state and control are estimated by using the direct approach. Actually, using the proposed model, we will eliminate basic challenges of solving optimal control of hybrid autonomous systems problems, in which the number of switches and mood sequence are unknown .Finally, numerical results for solving an example presented.


Main Subjects

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Volume 9, Issue 1
March 2019
Pages 120-142
  • Receive Date: 25 February 2018
  • Revise Date: 23 December 2018
  • Accept Date: 21 March 2019
  • First Publish Date: 21 March 2019