Publications

2021

• Relationship Between Maximum Principle and Dynamic Programming in presence of Intermediate and Final State Constraints
  
  • Bokanowski Olivier
  • Desilles Anna
  • Zidani Hasnaa
  ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2021. In this paper, we consider a class of optimal control problems governed by a differential system. We analyze the sensitivity relations satisfied by the co-state arc of the Pontryagin maximum principle and the value function that associates the optimal value of the control problem to the initial time and state. Such a relationship has been already investigated for state-constrained problems under some controllability assumptions to guarantee Lipschitz regularity property of the value function. Here, we consider the case with intermediate and final state constraints, without any controllability assumption on the system, and without Lipschitz regularity of the value function. Because of this lack of regularity, the sensitivity relations cannot be expressed with the sub-differentials of the value function. This work shows that the constrained problem can be reformulated with an auxiliary value function which is more regular and suitable to express the sensitivity of the adjoint arc of the original state-constrained control problem along an optimal trajectory. Furthermore, our analysis covers the case of normal optimal solutions, and abnormal solutions as well. (10.1051/cocv/2021084)
  DOI : 10.1051/cocv/2021084
• Variational Methods for Acoustic Radiation in a Duct with a Shear Flow and an Absorbing Boundary
  
  • Mercier Jean-François
  SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2021, 81 (6), pp.2658-2683. The well-posedness of the acoustic radiation in a 2D duct in presence of both a shear flow and an absorbing wall described by the Myers boundary condition is studied thanks to variational methods. Without flow the problem is found well-posed for any impedance value. The presence of a flow complicates the results. With a uniform flow the problem is proven to be always of the Fredholm type but is found well-posed only when considering a dissipative radiation problem. With a general shear flow, the Fredholm property is recovered for a weak enough shear and the dissipative radiation problem requires to introduce extra conditions to be well-posed: enough dissipation, a large enough frequency and non-intuitive conditions on the impedance value. (10.1137/20M1384026)
  DOI : 10.1137/20M1384026
• ROUGH PATHS AND REGULARIZATION
  
  • Gomes André O
  • Ohashi Alberto
  • Russo Francesco
  • Teixeira Alan
  Journal of Stochastic Analysis, Louisiana State University, 2021, 2 (4), pp.1-21. Calculus via regularizations and rough paths are two methods to approach stochastic integration and calculus close to pathwise calculus. The origin of rough paths theory is purely deterministic, calculus via regularization is based on deterministic techniques but there is still a probability in the background. The goal of this paper is to establish a connection between stochastically controlled-type processes, a concept reminiscent from rough paths theory, and the so-called weak Dirichlet processes. As a by-product, we present the connection between rough and Stratonovich integrals for càdlàg weak Dirichlet processes integrands and continuous semimartingales integrators. (10.31390/josa.2.4.01)
  DOI : 10.31390/josa.2.4.01
• Optimal Ciliary Locomotion of Axisymmetric Microswimmers
  
  • Guo Hanliang
  • Zhu Hai
  • Liu Ruowen
  • Bonnet Marc
  • Veerapaneni Shravan
  Journal of Fluid Mechanics, Cambridge University Press (CUP), 2021, 927, pp.A22. Many biological microswimmers locomote by periodically beating the densely-packed cilia on their cell surface in a wave-like fashion. While the swimming mechanisms of ciliated microswimmers have been extensively studied both from the analytical and the numerical point of view, the optimization of the ciliary motion of microswimmers has received limited attention, especially for non-spherical shapes. In this paper, using an envelope model for the microswimmer, we numerically optimize the ciliary motion of a ciliate with an arbitrary axisymmetric shape. The forward solutions are found using a fast boundary integral method, and the efficiency sensitivities are derived using an adjoint-based method. Our results show that a prolate microswimmer with a 2:1 aspect ratio shares similar optimal ciliary motion as the spherical microswimmer, yet the swimming efficiency can increase two-fold. More interestingly, the optimal ciliary motion of a concave microswimmer can be qualitatively different from that of the spherical microswimmer, and adding a constraint to the ciliary length is found to improve, on average, the efficiency for such swimmers. (10.1017/jfm.2021.744)
  DOI : 10.1017/jfm.2021.744