Single and Multi-objective Optimal Control Design by Genetic Programming and Comparison with Riccati Equation Solutions

Document Type : Research Article

Authors

1 Faculty of Mechanical Engineering, University of Guilan, Rasht, Iran

2 Department of Mechanical Engineering, Faculty of Mechanical Engineering, University of Guilan, Rasht, Iran

3 Faculty of Mechanical Enginnering, University of Guilan, Rasht, Iran

Abstract

 Gaining the function of control signal that transfer the system states from initial to desired final conditions is one of the main issues related to the optimal control of modern systems. Optimal control signal is usually obtained by numerical solution (such as dynamic programming algorithm) or analytical solution (like Hamilton-Jacobi-Bellman or Riccati equations approaches) of a single-objective performance index which is a weighted combination of control effort and the fitness of system’s states. However, choosing proper weight coefficients in these approaches needs a lot of trial and error in addition to experience. In this papers, such time consuming procedures are eliminated by using Genetic programming in single and multi-objective optimization process to find those closed-form mathematical solutions of optimal control problems. In this way, it would be readily possible to trade-off among the objective functions using the obtained pareto-front of those solutions based on the needs of the control system designer. It will be shown that in the case of same weighting factors, the solution of the Riccati equation would also be obtained using the approach of this paper

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References

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Amirkabir Journal of Mechanical Engineering
Volume 52, Issue 12
March 2021
Pages 3369-3382

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