Abstract
In this chapter, we study closed-loop impulse controls. The key to solving such feedback control problems is the Principle of Optimality for the related value functions. This move allows to derive related Dynamic Programming Equations. The infinitesimal form of such equations allows to calculate related value functions and the closed-loop controls. Next, it is necessary to explain how one should interpret the solution of the impulsive closed-loop system under such control. Here, we present several possible approaches complemented by examples for one- and two-dimensional systems. Finally, we discuss two problems related to feedback control, namely, the construction of reachability sets and the problem of stabilization by impulses, [1,2,3,4,5, 7].
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Notes
- 1.
This should not be confused with our notation for the directional derivative \(DV(t, x \mid \vartheta , \xi )\) of V(t, x) at time t, along direction \((\vartheta , \xi )\).
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Kurzhanski, A.B., Daryin, A.N. (2020). Closed-Loop Impulse Control. In: Dynamic Programming for Impulse Feedback and Fast Controls. Lecture Notes in Control and Information Sciences, vol 468. Springer, London. https://doi.org/10.1007/978-1-4471-7437-0_3
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DOI: https://doi.org/10.1007/978-1-4471-7437-0_3
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