Optimal control for stochastic linear quadratic singular Takagi–Sugeno fuzzy delay system using genetic programming

• Published in: Applied soft computing 2012-08, Vol.12 (8), p.2085-2090
• Main Authors: Nallasamy, Kumaresan, Ratnavelu, Kuru
• Format: Article
• Language: English
• Subjects: Differential algebraic equation; Genetic programming; Matrix Riccati differential equation; Optimal control; Runge Kutta method; Stochastic linear singular Takagi–Sugeno fuzzy delay system
• ISSN: 1568-4946; 1872-9681
• DOI: 10.1016/j.asoc.2012.03.017

[Display omitted] ► Genetic Programming (GP) generates mathematical expressions using grammar. ► If required number of expressions satisfy the fitness function, then the expressions are the solution of matrix Riccati differential equation(MRDE). ► Solution of MRDE is used to find the optimal control for stochastic linear quadratic singular Takagi-Sugeno fuzzy delay system. ► GP solution is better than the solution of Runge Kutta method. In this paper, optimal control for stochastic linear singular Takagi–Sugeno (T–S) fuzzy delay system with quadratic performance is obtained using genetic programming (GP). To obtain the optimal control, the solution of matrix Riccati differential equation (MRDE) is computed by solving differential algebraic equation (DAE) using a novel and nontraditional GP approach. The GP solution is equivalent or very close to the exact solution of the problem. Accuracy of the GP solution to the problem is qualitatively better. The solution of this novel method is compared with the traditional Runge Kutta (RK) method. An illustrative numerical example is presented for the proposed method.