No abstract

This work concerns about multiscale multivalued McKean-Vlasov stochastic systems. First of all, we establish the well-posedness for multivalued McKean-Vlasov stochastic systems under non-Lipschitz conditions. Then for multiscale multivalued McKean-Vlasov stochastic systems with parameters, in accordance with the values of these parameters we obtain four different average principles. Finally, based on these results, a large deviation principle is presented by a weak convergence approach.

The work concerns the stability and path-independence of additive functionals for a type of multivalued McKean-Vlasov stochastic differential equations with non-Lipschitz coefficients. First, we prove the existence and uniqueness of strong solutions for multivalued McKean-Vlasov stochastic differential equation with non-Lipschitz coefficients. And then, the exponential stability of second moments for their solutions in terms of a Lyapunov function is shown. Next, we weaken the conditions and furthermore obtain the exponentially 2-ultimate boundedness of their solutions. Finally, the path-independence of additive functionals for their solutions is proved.

A novel robust adaptive back-stepping control scheme for attitude maneuver of over-actuated spacecraft system with redundant reaction fly-wheels (RWs) is proposed. The robust adaptive controller based on back-stepping may achieve the high accuracy and speed of the attitude control for the rigid spacecraft with uncertain inertia matrix and bounded external disturbs. The Lyapunov functions are employed to analyze and prove the systems stability, so the fine and accuracy performances are ensured. The numerical simulation results verify the effectiveness and feasibility of the control schemes derived here using the MATLAB/SIMULINK software.