A Controllability Measure for Linear Systems with Reachable Control Equilibrium Set

Abstract

This paper proposes a new controllability measure for linear systems involving multiple control equilibria (CEs), which are states x with an input that makes dx/dt=0. We consider the transition between control equilibria (TCE) as the target class of control. Although the controllability Gramian and size of reachable sets are commonly used measures to assess the performance of systems, they include non-CE information and result in evaluations that are misaligned with the efficiency of TCE. To solve this problem, we propose an appropriate measure for the size of the reachable control equilibrium set (RCES) to quantitatively evaluate the cost of TCE utilizing this measure. The proposed measure can be easily computed. Examples demonstrate that the proposed measure enables the assessment of systems that require less energy for TCEs more effectively than traditional measures.