ABSTRACT
We present recent developments and applications of variational analysis and generalized differentiation to rather new classes of optimal control problems governed by discontinuous differential inclusions that arise in the so-called sweeping processes and the like. Such problems are particularly important for numerous applications to automatics control systems, engineering design, hysteresis, etc. To study highly challenging control problems of this type, we develop appropriate constructions of the method of discrete approximations, which allow us to investigate various theoretical and numerical aspects of optimal control for discontinuous differential systems. In particular, we establish new necessary optimality conditions for such problems including appropriate extensions of the Euler–Lagrange conditions and the Pontryagin maximum principle along with the optimality conditions of the novel type specific for the problems under consideration. New applications to practical engineering and mechanical models, robotics, traffic equilibria, etc. are also discussed.
