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- W1567906773 abstract "SUMMARY The main bottleneck for the application of H ∞ control theory on practical nonlinear systems is the need to solve the Hamilton–Jacobi–Isaacs (HJI) equation. The HJI equation is a nonlinear partial differential equation (PDE) that has proven to be impossible to solve analytically, even the approximate solution is still difficult to obtain. In this paper, we propose a simultaneous policy update algorithm (SPUA), in which the nonlinear HJI equation is solved by iteratively solving a sequence of Lyapunov function equations that are linear PDEs. By constructing a fixed point equation, the convergence of the SPUA is established rigorously by proving that it is essentially a Newton's iteration method for finding the fixed point. Subsequently, a computationally efficient SPUA (CESPUA) based on Galerkin's method, is developed to solve Lyapunov function equations in each iterative step of SPUA. The CESPUA is simple for implementation because only one iterative loop is included. Through the simulation studies on three examples, the results demonstrate that the proposed CESPUA is valid and efficient. Copyright © 2012 John Wiley & Sons, Ltd." @default.
- W1567906773 created "2016-06-24" @default.
- W1567906773 creator A5000266144 @default.
- W1567906773 creator A5012004938 @default.
- W1567906773 date "2012-04-16" @default.
- W1567906773 modified "2023-10-17" @default.
- W1567906773 title "Computationally efficient simultaneous policy update algorithm for nonlinear<i>H</i><sub>∞</sub>state feedback control with Galerkin's method" @default.
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- W1567906773 doi "https://doi.org/10.1002/rnc.2814" @default.
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