A discrete stability theorem for set-valued Euler’s method with state constraints is proven. This theorem is combined with known stability results for differential inclusions with so-called smooth state constraints. As a consequence, order of convergence equal to 1 is proven for set-valued Euler’s method, applied to state-constrained differential inclusions.

We present a stable and efficient simulator for deformable objects with collisions and contacts. For stability, an optimization derived from the implicit time integrator is solved in each timestep under the inequality constraints coming from collisions. To achieve fast convergence, we extend the MPRGP based solver from handling box constraints only to handling general linear constraints and pro...

Predictive control of nonlinear systems subject to output and input constraints is considered. A fuzzy model is used to predict the future behavior. Two new ideas are proposed here. First, an added constraint on the applied control action is used to ensure the decrease of a quadratic Lyapunov function, and so guarantee Lyapunov exponential stability of the closed-loop system. Second, the feasib...

The peeling-ballooning model for edge localized modes (ELMs) and pedestal constraints, based upon ideal MHD instabilities driven by pressure gradients and current in the edge barrier region, has been broadly applied toward understanding ELM and pedestal behavior in a number of tokamak experiments. Due in part to multiple driving terms, multiple wavelengths and second stability access physics, t...

Due to the rise of distributed energy resources, control networks grid-forming inverters is now a pressing issue for power system operation. Droop popular strategy in literature frequency these inverters. In this article, we analyze transient stability droop-controlled inverter that are subject multiple operating constraints. Using physically meaningful Lyapunov-like function, provide two sets ...