Abstract
In this paper, we present an approach to the solution of the Hamilton–Jacobi–Isaacs equation (HJIE) arising in the H ∞ control problem for nonlinear systems. We show that the HJIE can be solved analogously to a scalar quadratic equation with some additional side conditions, and present a computational procedure for determining symmetric solutions. Examples are given for second-order affine nonlinear systems to illustrate the procedure, and the method can be extended to higher-order systems.
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