# Policy Iterations on the Hamilton–Jacobi–Isaacs Equation for $H_{\infty}$ State Feedback Control With Input Saturation

@article{AbuKhalaf2006PolicyIO, title={Policy Iterations on the Hamilton–Jacobi–Isaacs Equation for \$H\_\{\infty\}\$ State Feedback Control With Input Saturation}, author={Murad Abu-Khalaf and Frank L. Lewis and Jie Huang}, journal={IEEE Transactions on Automatic Control}, year={2006}, volume={51}, pages={1989-1995} }

An Hinfin suboptimal state feedback controller for constrained input systems is derived using the Hamilton-Jacobi-Isaacs (HJI) equation of a corresponding zero-sum game that uses a special quasi-norm to encode the constraints on the input. The unique saddle point in feedback strategy form is derived. Using policy iterations on both players, the HJI equation is broken into a sequence of differential equations linear in the cost for which closed-form solutions are easier to obtain. Policy… Expand

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SUMMARY
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