Abstract
We consider the solvability of Hamilton-Jacobi-Isaacs equations that arise in finite and infinite-horizon nonlinear H ∞ control problems where the system is affine in the control and the disturbance, while the cost function is not necessarily continuous in the state and the control. In each case we prove the existence of viscosity supersolutions under the assumption that the value function is finite, and provide a method for constructing H∞ disturbance attenuating feedback controllers by using only the viscosity supersolution. We also obtain a result on global asymptotic stability of the closed-loop system under the H∞ controller and the worst-case disturbance.
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Xiao, M., Başar, T. (1999). Nonlinear H ∞ Controller Design via Viscosity Supersolutions of the Isaacs Equation. In: McEneaney, W.M., Yin, G.G., Zhang, Q. (eds) Stochastic Analysis, Control, Optimization and Applications. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1784-8_9
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DOI: https://doi.org/10.1007/978-1-4612-1784-8_9
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7281-6
Online ISBN: 978-1-4612-1784-8
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