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Hamilton-Jacobi-Isaac Formulation for Constrained Input Systems: Neural Network Solution

Frank L. Lewis, Murad Abu-Khalaf,Jie Huang
University of Texas at Arlington

August 1, 2005 at  10:45 AM
Zames Seminar Room - MC437

In this talk, H-infinity non-linear state feedback control for constrained input systems is studied through the framework of Hamilton-Jacobi-Isaac equations. The constraints on the input to the system are encoded via a quasi-norm that will also enable us to perform quasi-L2-gain analysis of the corresponding closed-loop non-linear system. An iterative technique based on the game theoretic interpretation of the HJI equation and dissipativity theory is employed to solve for the value function of the game. The solution is approximated using a neural network over a predefined domain, and the constrained nearly robust control law is given in state feedback form. It is shown that the derived constrained state feedback control law has the largest region of definition than any other controller with the same attenuation gain.

A computational algorithm is given to solve the HJI equation using neural networks. The result is a closed-loop neural network feedback controller.