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Title: Sensitivity and Optimal Control Theory for Linear Complementarity Systems
This article focuses on sensitivity and control theory for linear complementarity systems (LCSs), a type of dynamical system that experiences hybrid continuous/discrete behavior and is therefore nonsmooth. In particular, a sensitivity theory is given that characterizes generalized derivative information of solutions of LCSs with respect to parametric perturbations. With this theory in hand, a computationally-relevant open-loop optimal control theory is provided using a direct method (i.e., the control is parametrically discretized and generalized gradients of the objective function are described). The approach here is based on lexicographic directional differentiation theory, a relatively new tool in nonsmooth analysis, being applied to nonlinear complementarity systems (NCSs). The optimal control theory is illustrated with an example. As a byproduct of the sensitivity theory, well-posedness results for a new class of hybrid dynamical system, called the lexicographic linear complementarity system (LexLCS), are also established.  more » « less
Award ID(s):
2318773 2318772
PAR ID:
10676262
Author(s) / Creator(s):
; ;
Editor(s):
Kilgour, D_M; Kunze, H; Makarov, R_N; Melnik, R; Wang, X
Publisher / Repository:
Springer Nature Switzerland
Date Published:
ISBN:
978-3-031-84868-1
Page Range / eLocation ID:
517 to 527
Subject(s) / Keyword(s):
Complementarity systems Hybrid systems Generalized derivatives Sensitivity analysis Optimal control
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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