Characterization of maximum hands-off control
Copyright policy )Characterization of maximum hands-off control
Maximum hands-off control aims to maximize the length of time over which zero actuator values are applied to a system when executing specified control tasks. To tackle such problems, recent literature has investigated optimal control problems which penalize the size of the support of the control function and thereby lead to desired sparsity properties. This article gives the exact set of necessary conditions for a maximum hands-off optimal control problem using an $L_0$-(semi)norm, and also provides sufficient conditions for the optimality of such controls. Numerical example illustrates that adopting an $L_0$ cost leads to a sparse control, whereas an $L_1$-relaxation in singular problems leads to a non-sparse solution.
6 pages
Equations, Systems and Control (eess.SY), Electrical Engineering and Systems Science - Systems and Control, 510, Maximum Hands-Off Control, FOS: Electrical engineering, electronic engineering, information engineering, FOS: Mathematics, Nonlinear systems in control theory, Mathematics - Optimization and Control, Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.), Sparse Control, maximum hands-off control, Control/observation systems governed by partial differential equations, Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.), \(\mathcal{L}_0\) optimal control, sparse control, Predictive Control, Design techniques (robust design, computer-aided design, etc.), L-0 Optimal Control, Optimization and Control (math.OC), Sparse Stabilization, Model
Equations, Systems and Control (eess.SY), Electrical Engineering and Systems Science - Systems and Control, 510, Maximum Hands-Off Control, FOS: Electrical engineering, electronic engineering, information engineering, FOS: Mathematics, Nonlinear systems in control theory, Mathematics - Optimization and Control, Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.), Sparse Control, maximum hands-off control, Control/observation systems governed by partial differential equations, Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.), \(\mathcal{L}_0\) optimal control, sparse control, Predictive Control, Design techniques (robust design, computer-aided design, etc.), L-0 Optimal Control, Optimization and Control (math.OC), Sparse Stabilization, Model
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