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

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3 Author(s)
Abu-Khalaf, M. ; Autom. & Robotics Res. Inst., Texas Christian Univ., Fort Worth, TX ; Lewis, F.L. ; Jie Huang

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 iterations on the disturbance are shown to converge to the available storage function of the associated L2-gain dissipative dynamics. The resulting constrained optimal control feedback strategy has the largest domain of validity within which L2-performance for a given gamma is guaranteed

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Automatic Control, IEEE Transactions on  (Volume:51 ,  Issue: 12 )