Partial Differential Equation for Evolution of Star-Shaped Reachability Domains of Differential Inclusions

MAZURENKO, Stanislav. Partial Differential Equation for Evolution of Star-Shaped Reachability Domains of Differential Inclusions. SET-VALUED AND VARIATIONAL ANALYSIS. 2016, vol. 24, No 2, p. 333-354. ISSN 1877-0533. Available from: https://dx.doi.org/10.1007/s11228-015-0345-4.

Basic information

• Original name: Partial Differential Equation for Evolution of Star-Shaped Reachability Domains of Differential Inclusions
• Authors: MAZURENKO, Stanislav (643 Russian Federation, guarantor, belonging to the institution).
• Edition: SET-VALUED AND VARIATIONAL ANALYSIS, 2016, 1877-0533.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: Netherlands
• Confidentiality degree: is not subject to a state or trade secret
• WWW: URL
• Impact factor: Impact factor: 0.886
• RIV identification code: RIV/00216224:14310/16:00092840
• Organization unit: Faculty of Science
• Doi: http://dx.doi.org/10.1007/s11228-015-0345-4
• UT WoS: 000375418300009
• Keywords in English: Reachability sets; Differential inclusion; Star-shaped sets; Radial (gauge) function; Viability; Optimal control synthesis
• Tags: AKR, rivok

Abstract

The problem of reachability for differential inclusions is an active topic in the recent control theory. Its solution provides an insight into the dynamics of an investigated system and also enables one to design synthesizing control strategies under a given optimality criterion. The primary results on reachability were mostly applicable to convex sets, whose dynamics is described through that of their support functions. Those results were further extended to the viability problem and some types of nonlinear systems. However, non-convex sets can arise even in simple bilinear systems. Hence, the issue of nonconvexity in reachability problems requires a more detailed investigation. The present article follows an alternative approach for this cause. It deals with star-shaped reachability sets, describing the evolution of these sets in terms of radial (Minkowski gauge) functions. The derived partial differential equation is then modified to cope with additional state constraints due to on-line measurement observations. Finally, the last section is on designing optimal closed-loop control strategies using radial functions.

Links

• LO1214, research and development project: Name: Centrum pro výzkum toxických látek v prostředí (Acronym: RECETOX)

Investor: Ministry of Education, Youth and Sports of the CR