Open Access Dissertation
Date of Award
Boris S. Mordukhovich
The dissertation is devoted to 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 dif- ferential inclusions with pointwise state constraints, which are immensely challenging in control theory and prevent employing conventional variation techniques to derive neces- sary 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 minimiz- ers of the controlled sweeping process expressed entirely via the problem data. Besides illustrative examples, we apply the obtained results to an optimal control problem asso- ciated with of the crowd motion model of traffic flow in a corridor, which is formulated in this thesis. 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.
Cao, Tan Hoang, "Optimal Control Of A Perturbed Sweeping Process With Applications To The Crowd Motion Model" (2016). Wayne State University Dissertations. 1520.