2014/11/01 by Richard Vinter, R. B. Vinter, Vinter, R. B.
Computer Science · Engineering · Mathematics · #49J15 #Advanced Control Systems Optimization #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Stability and Control of Uncertain Systems #math.OC #msc:49J15
paper · pdf · doi:10.48550/arxiv.1411.0155
Preliminary version of a article which will submitted to a journal for publication
openalex publication_date 2014/11/01 · arxiv created 2015/08/26 · arxiv updated 2015/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider control systems described by a differential equation with a control term or, more generally, by a differential inclusion with velocity set F(t,x). Certain properties of state trajectories can be derived when, in addition to other hypotheses, it is assumed that F(t,x) is merely measurable w.r.t. the time variable t. But sometimes a refined analysis requires the imposition of stronger hypotheses regarding the t dependence of F(t,x). Stronger forms of necessary conditions for state trajectories that minimize a cost can derived, for example, if it is hypothesized that F(t,x) is Lipschitz continuous w.r.t. t. It has recently become apparent that interesting addition properties of state trajectories can still be derived, when the Lipschitz continuity hypothesis is replaced by the weaker requirement that F(t,x) has bounded variation w.r.t. t. This paper introduces a new concept of multifunctions F(t,x) that have bounded variation w.r.t. t near a given state trajectory, of special relevance to control system analysis. Properties of such multifunctions are derived and their significance is illustrated by an application to sensitivity analysis.