N. Kumaresan

Solution of matrix Riccati differential equation for the linear quadratic singular system using neural networks

Abstract In this paper, the solution of the matrix Riccati differential equation (MRDE) for the linear quadratic singular system is obtained using neural networks. The goal is to provide optimal control with reduced calculus effort by comparing the solutions of the MRDE obtained from well-known traditional methods like Runge–Kutta, Runge–Kutta Butcher and non-traditional method neural network. The neural training is performed using Levenberg–Marquardt algorithm. Accuracy of the solution of the neural network approach to the problem is qualitatively better. The advantage of the proposed approach is that, once the network is trained, it allows instantaneous evaluation of solution at any desired number of points spending negligible computing time and memory. An illustrative numerical example for the proposed method is given.

Optimal control for nonlinear singular systems with quadratic performance using neural networks

In this paper, optimal control for nonlinear singular system with quadratic performance is obtained using neural networks. This control is in the form of a state feedback function plus a time function. Furthermore, the main feature is that optimality is always preserved by this control; hence, this control is called a quasi-feedback optimal control. To obtain the optimal control, the solution of matrix Riccati differential equation (MRDE) is obtained by feedforward neural network (FFNN). Accuracy of the neural network solution to the optimal control problem is qualitatively better than Runge-Kutta (RK) solution. The advantage of the proposed approach is that, once the network is trained, it allows instantaneous evaluation of solution at any desired number of points spending negligible computing time and memory. The computation time of the proposed method is shorter than the traditional RK method. A numerical example is presented to illustrate the implementation of artificial neural networks (ANN) to obtain optimal control.

Optimal control for stochastic nonlinear singular system using neural networks

In this paper, optimal control for stochastic nonlinear singular system with quadratic performance is obtained using neural networks. The goal is to provide optimal control with reduced calculus effort by comparing the solutions of the matrix Riccati differential equation (MRDE) obtained from the well-known traditional Runge-Kutta (RK) method and nontraditional neural network method. To obtain the optimal control, the solution of MRDE is computed by feedforward neural network (FFNN). The accuracy of the solution of the neural network approach to the problem is qualitatively better. The advantage of the proposed approach is that, once the network is trained, it allows instantaneous evaluation of solution at any desired number of points spending negligible computing time and memory. The computation time of the proposed method is shorter than the traditional RK method. An illustrative numerical example is presented for the proposed method.

Solution of generalized matrix Riccati differential equation for indefinite stochastic linear quadratic singular system using neural networks

Abstract In this paper, solution of generalized matrix Riccati differential equation (GMRDE) for indefinite stochastic linear quadratic singular system is obtained using neural networks. The goal is to provide optimal control with reduced calculus effort by comparing the solutions of GMRDE obtained from well known traditional Runge Kutta (RK) method and nontraditional neural network method. To obtain the optimal control, the solution of GMRDE is computed by feed forward neural network (FFNN). Accuracy of the solution of the neural network approach to the problem is qualitatively better. The neural network solution is also compared with the solution of ode45, a standard solver available in MATLAB which implements RK method for variable step size. The advantage of the proposed approach is that, once the network is trained, it allows instantaneous evaluation of solution at any desired number of points spending negligible computing time and memory. The computation time of the proposed method is shorter than the traditional RK method. An illustrative numerical example is presented for the proposed method.

Optimal control for stochastic linear quadratic singular neuro Takagi-Sugeno fuzzy system with singular cost using genetic programming

HighlightsTakagi-Sugeno fuzzy model.Neuro-fuzzy system.Nontraditional genetic programming approach.Optimal control for Stochastic linear singular Takagi-Sugeno fuzzy singular system. In this paper, optimal control for stochastic linear quadratic singular neuro Takagi-Sugeno (T-S) fuzzy system with singular cost 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 obtained solution in this method is equivalent or very close to the exact solution of the problem. Accuracy of the solution computed by GP approach to the problem is qualitatively better. The solution of this novel method is compared with the traditional Runge-Kutta (RK) method. A numerical example is presented to illustrate the proposed method.

Singular optimal control for stochastic linear quadratic singular system using ant colony programming

In this article, singular optimal control for stochastic linear singular system with quadratic performance is obtained using ant colony programming (ACP). To obtain the optimal control, the solution of matrix Riccati differential equation is computed by solving differential algebraic equation using a novel and nontraditional ACP approach. The obtained solution in this method is equivalent or very close to the exact solution of the problem. Accuracy of the solution computed by the ACP approach to the problem is qualitatively better. The solution of this novel method is compared with the traditional Runge Kutta method. An illustrative numerical example is presented for the proposed method.

Robust stability analysis of delayed Takagi-Sugeno fuzzy genetic regulatory networks

In this paper, the nonlinear model of genetic regulatory networks is described by the Takagi‐Sugeno fuzzy model representation with time-varying delays. Due to the highly complicated nonlinear stability and robust stability problems, a fuzzy approximation method is employed to interpolate several linear genetic regulatory networks at different operation points via fuzzy bases to approximate the nonlinear genetic regulatory network. In this context, the methods of the linear matrix inequality (LMI) technique could be employed to simplify the problems related to robust stability of genetic regulatory networks. Further, by involving triple integral terms in Lyapunov‐Krasovskii functionals and LMI techniques, the stability criteria for the delayed fuzzy genetic regulatory networks are expressed as a convex combination of LMIs, which can be solved numerically by any LMI solvers. Several numerical examples are given to verify the effectiveness and applicability of the derived approach.

Solution of generalized matrix Riccati differential equation for indefinite stochastic linear quadratic singular fuzzy system with cross-term using neural networks

In this paper, solution of generalized matrix Riccati differential equation (GMRDE) for indefinite stochastic linear quadratic singular fuzzy system with cross-term is obtained using neural networks. The goal is to provide optimal control with reduced calculus effort by comparing the solutions of GMRDE obtained from well-known traditional Runge Kutta (RK) method and nontraditional neural network method. To obtain the optimal control, the solution of GMRDE is computed by feed forward neural network (FFNN). Accuracy of the solution of the neural network approach to this problem is qualitatively better. The advantage of the proposed approach is that, once the network is trained, it allows instantaneous evaluation of solution at any desired number of points spending negligible computing time and memory. The computation time of the proposed method is shorter than the traditional RK method. An illustrative numerical example is presented for the proposed method.

Optimal control for fuzzy linear partial differential algebraic equations using Simulink

In this paper, optimal control for fuzzy linear partial differential algebraic equations (FPDAE) with quadratic performance is obtained using Simulink. By using the method of lines, the FPDAE is transformed into a fuzzy differential algebraic equations (FDAE). Hence, the optimal control of FPDAE can be found out by finding the optimal control of the corresponding FDAE. The goal is to provide optimal control with reduced calculus effort by the solutions of the matrix Riccati differential equation (MRDE) obtained from Simulink. Accuracy of the solution of the Simulink approach to the problem is qualitatively better. The advantage of the proposed approach is that, once the Simulink model is constructed, it allows to evaluate the solution at any desired number of points spending negligible computing time and memory and the solution curves can be obtained from the model without writing any code. An illustrative numerical example is presented for the proposed method.

A neuro approach to solve fuzzy Riccati differential equations

There are many applications of optimal control theory especially in the area of control systems in engineering. In this paper, fuzzy quadratic Riccati differential equation is estimated using neural networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). The solution can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that NN approach shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over RK4.