Hybrid Dynamical Systems with Controlled Discrete Transitions in Bumpless Transfer, Systems with Impact-induced Motion, and Distributed Heterogeneous Multiagent Networks under Mrac Laws

Discrete transitions, or instantaneous switchings between system configurations, constitute the defining attribute of a hybrid, or switching, system behavior. These transitions have been traditionally viewed as nondynamic. In recent years, however, a realization has started to form that such a simplification does not unambiguously support some basic phenomena exhibited by hybrid systems, such as formation of accumulationtype points (Zeno behavior) and subsequent motion beyond these points. This simplification also tacitly implies the absence of control action during switchings. In many cases, however, such as impact-induced motion, it is of interest to consider sensing and actuation during the transition, or impact, itself for possible motion enhancement. The latter capability gives rise to the concept of controlled transition that in the limit, as the transition time interval shrinks to zero, becomes controlled discrete transition. The goal of the present talk is to demonstrate that dynamical systems with controlled discrete transitions constitute a new general class of hybrid systems. Widely divergent applications with these characteristics as well as distinctly different transition properties within a single application domain will be presented, including bumpless transfer under controller uncertainty, control of systems with impact-induced motion, and structure reconfiguration in distributed heterogeneous multiagent networks under MRAC Laws. The breakthrough capability of this system class in obtaining well-posed description of systems with uncontrolled discrete transitions characterized by accumulation points and unique extensibility beyond them will be pointed out.