Authors:
Elena Goncharova
and
Maxim Staritsyn
Affiliation:
Matrosov Institute for System Dynamics and Control Theory of the Siberian Branch of the Russian Academy of Sciences, Russian Federation
Keyword(s):
Hybrid Systems, Impulsive Control, Lagrangian Mechanics, Trajectory Relaxation, Approximation.
Related
Ontology
Subjects/Areas/Topics:
Informatics in Control, Automation and Robotics
;
Modeling, Analysis and Control of Hybrid Dynamical Systems
;
Signal Processing, Sensors, Systems Modeling and Control
;
System Modeling
Abstract:
The paper compresses some results on modeling and optimization in a class of hybrid systems with control
switches of dynamics. The study is motivated by widespread physical phenomena of impulsive nature, faced
in contact dynamics, such as unilateral contacts of rigid bodies and impactively blockable degrees of freedom.
The developed modeling approach is based on a representation of hybrid events as impulsive control actions
produced by distributions or Borel measures under constraints on states before and after the action. Basically,
such systems are described by measure differential equations with states of bounded variation, and the relations
between the trajectory and the control measure are given by a specific mixed condition of a complementarity
type. The main goal of the study is to describe the closure of the tube of solutions to the addressed system.
For this, we design an approximation of the hybrid property, and develop a specific singular time-spatial
transformati
on of the original system. A convexification of the transformed system then defines – after the
inverse transform – the closed set of generalized, limit solutions. The main result concerns the asymptotic
behavior of these generalized solutions, stating that the hybrid property is preserved after the relaxation.
(More)