Asymptotic controllability and optimal control

Monica Motta; Franco Rampazzo

doi:10.1016/j.jde.2013.01.006

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arXiv · 1210.4281

Asymptotic controllability and optimal control

Monica Motta·Franco Rampazzo

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Abstract

We consider a control problem where the state must reach asymptotically a target while paying an integral payoff with a non-negative Lagrangian. The dynamics is just continuous, and no assumptions are made on the zero level set of the Lagrangian. Through an inequality involving a positive number $\bar p_0$ and a Minimum Restraint Function $U=U(x)$ --a special type of Control Lyapunov Function-- we provide a condition implying that (i) the control system is asymptotically controllable, and (ii) the value function is bounded above by $U/\bar p_0$.

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BibTeX RIS

Monica Motta, Franco Rampazzo. 2012-10-16. Asymptotic controllability and optimal control. https://doi.org/10.1016/j.jde.2013.01.006

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