Convergence of an iterative algorithm for solving Hamilton-Jacobi type equations
Mathematics of Computation
Successive approximation approach of optimal control for nonlinear discrete-time systems
International Journal of Systems Science
Nonlinear feedback controllers and compensators: a state-dependent Riccati equation approach
Computational Optimization and Applications
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Solutions of the optimal control and $H_\infty$-control problems for nonlinear affine systems can be found by solving Hamilton--Jacobi equations. However, these first-order nonlinear partial differential equations can, in general, not be solved analytically. This paper introduces an iterative algorithm which solves these equations numerically for points near the origin. The procedure converges to the stabilizing solution exponentially with respect to the iteration variable. The algorithm is implemented on both illustrative and comparative examples.