Optimal disturbance rejection control for nonlinear impulsive dynamical systems |
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Institution: | 1. School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150, USA;2. Lola Institute, Kneza Vi?eslava 70a, 11000 Belgrade, Yugoslavia;3. Mechanical, Aerospace, and Biomedical Engineering, The University of Tennessee, Knoxville, TN 37996-2210, USA |
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Abstract: | In this paper, we develop an optimality-based framework for addressing the problem of nonlinear–nonquadratic hybrid control for disturbance rejection of nonlinear impulsive dynamical systems with bounded exogenous disturbances. Specifically, we transform a given nonlinear–nonquadratic hybrid performance criterion to account for system disturbances. As a consequence, the disturbance rejection problem is translated into an optimal hybrid control problem. Furthermore, the resulting optimal hybrid control law is shown to render the closed-loop nonlinear input–output map dissipative with respect to general supply rates. In addition, the Lyapunov function guaranteeing closed-loop stability is shown to be a solution to a steady-state hybrid Hamilton–Jacobi–Isaacs equation and thus guaranteeing optimality. |
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