A Maximum Principle for the Controlled Sweeping Process
By Chems Arroud, Giovanni Colombo. 2016
47 citations recorded by the source corpus.
We consider the free endpoint Mayer problem for a controlled Moreau process, the control acting as a perturbation of the dynamics driven by the normal cone, and derive necessary optimality conditions of Pontryagin’s Maximum Principle type. The results are also discussed through an example. We combine techniques from Sene and Thibault (Journal of Nonlinear and Convex Analysis 15, 647–663, 2014) and from Brokate and Krejčí (Discrete and Continuous Dynamical Systems Series B 18, 331–348, 2013), which in particular deals with a different but related control problem. Our assumptions include the smoothness of the boundary of the moving set C(t), but, differently from Brokate and Krejčí, do not require strict convexity and time independence of C(t). Rather, a kind of inward/outward pointing condition is assumed on the reference optimal trajectory at the times where the boundary of C(t) is touched. The state space is finite dimensional.
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/ba853ecd474227fab33474a756d8ae5ccd80f304
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Citations in the corpus
- Optimal Control Involving Sweeping Processes (2018, methodology): “As in [2] and [6], but in contrast to [3, 7, 10] and [11], we assume C to be time independent.”