Relaxation and existence of optimal controls of systems governed by evolution inclusions in separable Banach spaces
We examine relaxed control systems governed by evolution inclusions in a separable Banach space. First, we establish the existence of admissible trajectories, correcting an earlier result of \textit{N. U. Ahmed} [J. Optimization Theory Appl. 50, 213-237 (1986; Zbl 0577.49025); SIAM J. Control Optimization 21, 953-967 (1983; Zbl 0524.49008)]. Then, we obtain a compactness result for the set of admissible trajectories. Using this compactness result, we prove the existence of optimal solutions for optimal control problems; furthermore, we show that the values of the original and relaxed problems are equal. Finally, we show that the original trajectories are dense in the set of relaxed trajectories. An example is worked out.
scientific article; zbMATH DE number 4115370
scientific article