Optimality conditions for a controlled sweeping process with applications to the crowd motion model
By Tan H. Cao, Boris S. Mordukhovich. 2015
55 citations recorded by the source corpus.
The paper concerns the study and applications of a new class of optimal control problems governed by a perturbed sweeping process of the hysteresis type with control functions acting in both play-and-stop operator and additive perturbations. Such control problems can be reduced to optimization of discontinuous and unbounded differential inclusions with pointwise state constraints, which are immensely challenging in control theory and prevent employing conventional variation techniques to derive necessary optimality conditions. We develop the method of discrete approximations married with appropriate generalized differential tools of modern variational analysis to overcome principal difficulties in passing to the limit from optimality conditions for finite-difference systems. This approach leads us to nondegenerate necessary conditions for local minimizers of the controlled sweeping process expressed entirely via the problem data. Besides illustrative examples, we apply the obtained results to an optimal control problem associated with of the crowd motion model of traffic flow in a corridor, which is formulated in this paper. The derived optimality conditions allow us to develop an effective procedure to solve this problem in a general setting and completely calculate optimal solutions in particular situations.
Subfields: Control and Systems Engineering, Modeling and Simulation, Ocean Engineering
View Paper: https://www.semanticscholar.org/paper/9af02d82dfd8ed01b452c0a8083ec27a66d4364f
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Citations in the corpus
- A Maximum Principle for the Controlled Sweeping Process (2016, methodology): “e requirement of uniform convexity. The price to pay is the inward/outward pointing assumption (M1) or (M2). A simple example permits to test our necessary conditions. The recent results contained in [8, 9] are also worth being mentioned. In such papers the control acts both on the moving set, which”
- Optimal Control Involving Sweeping Processes (2018, background): “While Moreau’s interest in these systems resided on dynamics of plasticity and friction, the range of applications of sweeping processes have rapidly increased covering now various areas from mechanics to crowd motion modelling (see, for example, [1, 7, 14, 15, 23] , to name but a few).”