Optimal control of sweeping processes in unmanned surface vehicle and nanoparticle modelling

ABSTRACT

This paper addresses novel applications to practical modelling of the newly developed theory of necessary optimality conditions in controlled sweeping/Moreau processes with free time and pointwise control and state constraints. Problems of this type appear, in particular, in dynamical models dealing with unmanned surface vehicles (USVs) and nanoparticles. We formulate optimal control problems for a general class of such dynamical systems and show that the developed necessary optimality conditions for constrained free-time controlled sweeping processes lead us to designing efficient procedures to solve practical models of this class. Moreover, the paper contains numerical calculations of optimal solutions to marine USVs and nanoparticle models in specific situations. Overall, this study contributes to the advancement of optimal control theory for constrained sweeping processes and its practical applications in the fields of marine USVs and nanoparticle modelling.

KEYWORDS:

• Sweeping processes
• optimal control
• marine surface vehicles
• nanoparticles
• variational analysis

2020 MATHEMATICS SUBJECT CLASSIFICATIONs:

• 49J52
• 49J53
• 49K24
• 49M25
• 90C30

Acknowledgments

The authors are gratefully indebted to Giovanni Colombo for his great contributions to our joint paper [36] and further discussions on the material presented in this paper. We are pleased to thank Messaoud Bounkhel, a former student of Lionel Thibault, for drawing our attention to his papers [7, 20] on the modelling and simulation in USV and nanoparticle systems. Our gratitude goes also to two anonymous referees and the handling editor whose remarks allowed us to improve the original presentation,

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Boris S. Mordukhovich: Research of this author was partially supported by the USA National Science Foundation [grant numbers DMS-1007132 and DMS-1512846], by the Australian Research Council [discovery project DP-190100555], and by Project 111 of China [grant number D21024]. Dao Nguyen: Research of this author was supported by the AMS-Simon Foundation. Trang Nguyen: Research of this author was partially supported by the USA National Science Foundation [grant number DMS-1512846].