Existence trajectory and optimal control of Clarke subdifferential stochastic integrodifferential inclusions suffered by non-instantaneous impulses and deviated arguments

Abstract

In this article, the solvability, Trajectory(T-) and optimal controllability of stochastic integrodifferential inclusions with Clarke subdifferential along with deviated arguments and Poisson jumps are analyzed which are new and untreated topics in the literature. The theory of resolvent operators, stochastic analysis, semigroup theory and a multivalued fixed point theorem are used to prove the solvability of the proposed non-instantaneous impulsive stochastic integrodifferential inclusion in Hilbert space. In addition, the strongest notion of controllability called T-controllability of the system is determined using a generalized Gronwall inequality with some appropriate assumptions. Following that, we derive the existence of optimal control of the proposed problem using Balder’s theorem. A numerical example is given to validate the theoretical aspects. We study the numerical simulation of the proposed problem with challenges. An abstract application of a stochastic dam contamination model is studied to justify the developed theoretical result. This paper contains the study of T-control along with the optimal control. This work is the unique combination of theoretical and numerical simulation as well as the real life application.