Nonlinear controller design via approximate solution of Hamilton-Jacobi equations
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This work develops a numerical algorithm for the calculation of an optimal nonlinear state feedback law for nonlinear systems. A quadratic performance index is used which contains quadratic error terms, and quadratic input penalty terms. The optimization problem is solved using the Hamilton-Jacobi equations, which determine the optimal nonlinear state feedback law. A Newton-Kantorovich iteration is developed for the solution of the pertinent Hamilton-Jacobi equations, which involves solving a Zubov partial differential equation, at each step of the iteration, using a power series method. At step N of the iteration, the method generates the (N+1)-th order truncation of the Taylor series expansion of the optimal state feedback function. The method is also applied to the problem of ISE-optimal nonminimum-phase compensation for nonlinear systems. Finally, the results are applied to the problem of controlling a nonisothermal continuous stirred tank reactor with van de Vusse kinetics.