Abstract
This paper proposes a Genetic Programming based algorithm that can be used to design optimal controllers. The proposed algorithm will be named a Multiple Basis Function Genetic Programming (MBFGP). Herein, the main ideas concerning the initial population, the tree structure, genetic operations, and other proposed non-genetic operations are discussed in details. An optimization algorithm called numeric constant mutation is embedded to strengthen the search for the optimal solutions. The results of solving the optimal control for linear as well as nonlinear systems show the feasibility and effectiveness of the proposed MBFGP as compared to the optimal solutions which are based on numerical methods. Furthermore, this algorithm enriches the set of suboptimal state feedback controllers to include controllers that have product time-state terms.
Highlights
Genetic Programming (GP) is a stochastic search method that inspired by the selection and the natural genetics
This paper proposes a Genetic Programming based algorithm that can be used to design optimal controllers
Enhancing the standard tree structure used in the GP algorithm by new thoughts, ideas, and tools represent a road map to get an efficient methodology for controller design for nonlinear dynamic systems
Summary
Genetic Programming (GP) is a stochastic search method that inspired by the selection and the natural genetics. In order to increase the efficiency of GP to deal with optimal control problems, a set of syntactic rules are created to force all tree structures in the population such that the GP will evolve only solutions of desired form. These rules state for each node which terminal node and non-terminal node can be its children nodes while generating new trees and performing genetic operations. The GP is one of the powerful current soft computing algorithms [4,5,6] It can solve different types of problems in control discipline. Enhancing the standard tree structure used in the GP algorithm by new thoughts, ideas, and tools represent a road map to get an efficient methodology for controller design for nonlinear dynamic systems
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