Mathematical description of program diagram
Maximum principle and its extension for bounded control problems with boundary conditions.
Measure solutions for semilinear evolution equations with polynomial growth and their optimal control
In this paper we introduce a new concept of generalized solutions generalizing the notion of relaxed solutions recently introduced by Fattorini. We present some results on the question of existence of generalized or measure valued solutions for semilinear evolution equations on Banach spaces with polynomial nonlinearities. The results are illustrated by two examples one of which arises in nonlinear quantum mechanics. The results are then applied to some control problems.
Minimax control of nonlinear evolution equations
In this paper we study the minimax control of systems governed by a nonlinear evolution inclusion of the subdifferential type. Using some continuity and lower semicontinuity results for the solution map and the cost functional respectively, we are able to establish the existence of an optimal control. The abstract results are then applied to obstacle problems, semilinear systems with weakly varying coefficients (e.gȯscillating coefficients) and differential variational inequalities.
Mixed type semicontinuous differential inclusions in Banach spaces
We consider a class of differential inclusions in (nonseparable) Banach spaces satisfying mixed type semicontinuity hypotheses and prove the existence of solutions for a problem with state constraints. The cases of dissipative type conditions and with time lag are also studied. These results are then applied to control systems.
Model reduction methods for chaotic systems