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Optimal Homogeneous ℒp-Gain Controller
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DOI：10.1002/rnc.70433.png)
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Abstract
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Nonlinear -controllers are designed for arbitrarily weighted, continuous homogeneous systems with a focus on systems affine in the control input. Based on the homogeneous -norm, the input-output behavior is quantified in terms of the homogeneous -gain as a generalization of the classical -gain (i.e., -norm in the linear case). The resulting memoryless state-feedback control law minimizes the upper estimate of the homogeneous -gain from disturbance to extended output. This estimate is obtained by constructing a solution, that is, storage function, to a Hamilton-Jacobi inequality (the homogeneous differential dissipation inequality) based on a control Lyapunov function. Both the continuous, homogeneously stabilizing control law and closed-loop homogeneous -gain estimate depend on the choice of storage function. The design procedure and resulting performance are illustrated with examples and simulations.
Keywords:
affine system
continuous homogeneous system
homogeneity
nonlinear H infinity-control
nonlinear system
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