2023
DOI: 10.48550/arxiv.2302.09078
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HJ inequalities involving Lie brackets and feedback stabilizability with cost regulation

Abstract: With reference to an optimal control problem where the state has to approach asymptotically a closed target while paying a non-negative integral cost, we propose a generalization of the classical dissipative relation that defines a Control Lyapunov Function to a weaker differential inequality. The latter involves both the cost and the iterated Lie brackets of the vector fields in the dynamics up to a certain degree k ≥ 1, and we call any of its (suitably defined) solutions a degree-k Minimum Restraint Function… Show more

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