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

References

• Moreau JJ. On unilateral constraints, friction and plasticity. In: Capriz G, Stampacchia G, editors. New Variational Techniques in Mathematical Physics. Proc. C.I.M.E. Summer Schools, Cremonese, Rome; 1974. p. 173–322.
   Google Scholar
• Adly S, Haddad T, Thibault L. Convex sweeping process in the framework of measure differential inclusions and evolution variational inequalities. Math Program. 2014;148:5–47. doi: 10.1007/s10107-014-0754-4
   Web of Science ®Google Scholar
• Bounkhel M. Mathematical modeling and numerical simulations of the motion of nanoparticles in straight tube. Adv Mech Eng. 2016;8:1–6. doi: 10.1177/1687814016656965
   Web of Science ®Google Scholar
• Brogliato B, Tanwani A. Dynamical systems coupled with monotone set-valued operators: formalisms, applications, well-posedness, and stability. SIAM Rev. 2020;62:3–129. doi: 10.1137/18M1234795
   Web of Science ®Google Scholar
• Brokate M, Sprekels J. Hysteresis and phase transitions. New York: Springer; 1996.
   Google Scholar
• Colombo G, Thibault L. Prox-regular sets and applications. In: Gao DY, Motreanu D, editors. Handbook of Nonconvex Analysis. Boston: International Press; 2010. p. 99–182.
   Google Scholar
• Hedjar R, Bounkhel M. An automatic collision avoidance algorithm for multiple marine surface vehicles. Int J Appl Math Comput Sci. 2019;29:759–768. doi: 10.2478/amcs-2019-0056
   Web of Science ®Google Scholar
• Krasnosel'skii MA, Pokrovskii AV. Systems with hysteresis. New York: Springer; 1989.
   Google Scholar
• Krečí P. Evolution variational inequalities and multidimensional hysteresis operators. In: Drabek P, KrečíP, Takac P, editors. Nonlinear Differential Equations. Res. Notes Math. Boca Raton, FL: Chapman & Hall/CRC; 1999; Vol. 404.
   Google Scholar
• Maury B. A time-stepping scheme for inelastic collisions. Numer Math. 2006;102:649–679. doi: 10.1007/s00211-005-0666-6
   Web of Science ®Google Scholar
• Monteiro Marques MDP. Differential inclusions in nonsmooth mechanical problems: shocks and dry friction. Basel: Birkhäuser; 1993.
   Google Scholar
• Siddiqi AH, Manchanda P, Brokate M. On some recent developments concerning Moreau's sweeping process. In: Trends in Industrial and Applied Mathematics. Dordrecht, The Netherlands: Kluwer; 2002; Vol. 72. p. 339–354.
   Google Scholar
• Thibault L. Sweeping process with regular and irregular sets. J Differ Equ. 2003;193:1–26. doi: 10.1016/S0022-0396(03)00129-3
   Web of Science ®Google Scholar
• Tolstonogov AA. Polyhedral sweeping processes with unbounded nonconvex-valued perturbation. J Differ Equ. 2020;63:7965–7983.
   Google Scholar
• Venel J. A numerical scheme for a class of sweeping process. Numer Math. 2011;118:367–400. doi: 10.1007/s00211-010-0329-0
   Web of Science ®Google Scholar
• Edmond JF, Thibault L. Relaxation of an optimal control problem involving a perturbed sweeping process. Math Program. 2005;104:347–373. doi: 10.1007/s10107-005-0619-y
   Web of Science ®Google Scholar
• Thibault L. Unilateral variational analysis in Banach spaces. Singapore: World Scientific; 2023. published in two volumes.
   Google Scholar
• Adam L, Outrata JV. On optimal control of a sweeping process coupled with an ordinary differential equation. Discrete Contin Dyn Syst Ser B. 2014;19:2709–2738.
   Web of Science ®Google Scholar
• Arroud CE, Colombo G. A maximum principle for the controlled sweeping process. Set-Valued Var Anal. 2018;26:607–629. doi: 10.1007/s11228-017-0400-4
   Web of Science ®Google Scholar
• Brokate M, Krejčí P. Optimal control of ODE systems involving a rate independent variational inequality. Discrete Contin Dyn Syst Ser B. 2013;18:331–348.
   Web of Science ®Google Scholar
• Cao TH, Mordukhovich BS. Optimal control of a nonconvex perturbed sweeping process. J Differ Equ. 2019;266:1003–1050. doi: 10.1016/j.jde.2018.07.066
   Web of Science ®Google Scholar
• Cao TH, Mordukhovich BS. Applications of optimal control of a nonconvex sweeping process to optimization of the planar crowd motion model. Discrete Contin Dyn Syst Ser B. 2019;24:4191–4216.
   Web of Science ®Google Scholar
• Colombo G, Henrion R, Hoang ND, et al. Optimal control of the sweeping process. Dyn Contin Discrete Impuls Syst Ser B. 2012;19:117–159.
   Web of Science ®Google Scholar
• Colombo G, Henrion R, Hoang ND, et al. Optimal control of the sweeping process over polyhedral controlled sets. J Differ Equ. 2016;260:3397–3447. doi: 10.1016/j.jde.2015.10.039
   Web of Science ®Google Scholar
• Colombo G, Mordukhovich BS, Nguyen D. Optimal control of sweeping processes in robotics and traffic flow models. J Optim Theory Appl. 2019;182:439–472. doi: 10.1007/s10957-019-01521-y
   Web of Science ®Google Scholar
• Colombo G, Mordukhovich BS, Nguyen D. Optimization of a perturbed sweeping process by discontinuous controls. SIAM J Control Optim. 2020;58:2678–2709. doi: 10.1137/18M1207120
   Web of Science ®Google Scholar
• de Pinho Md.R, Ferreira MMA, Smirnov GV. Optimal control involving sweeping processes. Set-Valued Var Anal. 2019;27:523–548. doi: 10.1007/s11228-018-0501-8
   Web of Science ®Google Scholar
• de Pinho Md.R, Ferreira MMA, Smirnov GV. A maximum principle for optimal control problems involving sweeping processes with a nonsmooth set. J Optim Theory Appl. 2023;199:273–297. doi: 10.1007/s10957-023-02283-4
   Google Scholar
• Henrion R, Jourani A, Mordukhovich BS. Controlled polyhedral sweeping processes: existence, stability, and optimality condition. J Differ Equ. 2023;366:408–443. doi: 10.1016/j.jde.2023.04.010
   Web of Science ®Google Scholar
• Hermosilla C, Palladino M. Optimal control of the sweeping process with a nonsmooth moving set. SIAM J Control Optim. 2022;60:2811–2834. doi: 10.1137/21M1405472
   Web of Science ®Google Scholar
• Nour C, Zeidan V. Pontryagin-type maximum principle for a controlled sweeping process with nonsmooth and unbounded sweeping set. J Convex Anal. 2024;31:1.
   Google Scholar
• Zeidan V, Nour C, Saoud H. A nonsmooth maximum principle for a controlled nonconvex sweeping process. J Differ Equ. 2020;269:9531–9582. doi: 10.1016/j.jde.2020.06.053
   Web of Science ®Google Scholar
• Clarke F. Functional analysis, calculus of variations and optimal control. London: Springer; 2013.
   Google Scholar
• Mordukhovich BS. Variational analysis and generalized differentiation, II: applications. Berlin: Springer; 2006.
   Google Scholar
• Vinter RB. Optimal control. Boston: Birkhaüser; 2000.
   Google Scholar
• Colombo G, Mordukhovich BS, Nguyen D, et al. Discrete approximations and optimality conditions for controlled free-time sweeping processes. Appl Math Optim. 2024;89:40. doi: 10.1007/s00245-024-10108-7
   Web of Science ®Google Scholar
• Mordukhovich BS. Discrete approximations and refined Euler-Lagrange conditions for differential inclusions. SIAM J Control Optim. 1995;33:882–915. doi: 10.1137/S0363012993245665
   Web of Science ®Google Scholar
• Cao TH, Colombo G, Mordukhovich BS, et al. Optimization and discrete approximation of sweeping processes with controlled moving sets and perturbations. J Differ Equ. 2021;274:461–509. doi: 10.1016/j.jde.2020.10.017
   Web of Science ®Google Scholar
• Cao TH, Mordukhovich BS. Optimality conditions for a controlled sweeping process with applications to the crowd motion model. Discrete Contin Dyn Syst Ser B. 2017;21:267–306.
   Google Scholar
• Colombo G, Gidoni P. On the optimal control of rate-independent soft crawlers. J Math Pures Appl. 2021;146:127–157. doi: 10.1016/j.matpur.2020.11.005
   Web of Science ®Google Scholar
• Mordukhovich BS, Nguyen D. Discrete approximations and optimal control of nonsmooth perturbed sweeping processes. Convex Anal. 2021;28:655–688.
   Web of Science ®Google Scholar
• Mordukhovich BS. Variational analysis and generalized differentiation, I: basic theory. Berlin: Springer; 2006.
   Google Scholar
• Mordukhovich BS. Variational analysis and applications. Cham, Switzerland: Springer; 2018.
   Google Scholar
• Rockafellar RT, Wets RJ-B. Variational analysis. Berlin: Springer; 1998.
   Google Scholar
• Mordukhovich BS. Second-order variational analysis in optimization, variational stability, and control: theory, algorithms, applications, to appear in Springer, 2024.
   Google Scholar
• Skjetne R, Fossen TI, Kokotovic PV. Adaptive maneuvering, with experiments, for a model ship in marine control laboratory. Automatica. 2005;41:289–298. doi: 10.1016/j.automatica.2004.10.006
   Web of Science ®Google Scholar
• Zhao Y, Skalak R, Chien S. Hydrodynamics in cell rolling and adhesion. In: Simon B, editor. Advances in bioengineering. New York: American Society of Mechanical Engineers; 1997. p. 79–80.
   Google Scholar
• Zhao Y, Chien S, Weinbaum S. Dynamic contact forces on leukocyte microvilli and their penetration of the endothelial glycocalyx. Biophys J. 2001;80:1124–1140. doi: 10.1016/S0006-3495(01)76090-0
   PubMed Web of Science ®Google Scholar
• Sakariassen KS, Orning L, Turitto VT. The impact of blood shear rate on arterial thrombus formation. Future Sci OA. 2015;1:FSO30. doi: 10.4155/fso.15.28
   PubMedGoogle Scholar