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Zbl 1114.65336
Balasubramaniam, P.; Samath, J.Abdul; Kumaresan, N.
Optimal control for nonlinear singular systems with quadratic performance using neural networks. (English)
[J] Appl. Math. Comput. 187, No. 2, 1535-1543 (2007). ISSN 0096-3003

Summary: 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 is obtained by feedforward neural network. 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 to obtain optimal control.

MSC 2000:: *65K10 Optimization techniques (numerical methods)
49J15 Optimal control problems with ODE (existence)
49N35 Closed-loop controls

Keywords: optimal control; nonlinear singular system; matrix Riccati differential equation; quasi-feedback; Runge-Kutta method; neural networks; numerical examples

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