Related papers: Optimal motion of a scallop: some case studies
The mechanism of swimming at very low Reynolds number conditions is a topic of interest to biologists and engineering community. We develop a novel kinematic model of a slender flexible swimmer which locomotes in a low Reynolds number…
This paper discusses modelling, controllability and gait design for a spherical flexible swimmer. We first present a kinematic model of a low Reynolds number spherical flexible swimming mechanism with periodic surface deformations in the…
A variety of swimming microorganisms, called ciliates, exploit the bending of a large number of small and densely-packed organelles, termed cilia, in order to propel themselves in a viscous fluid. We consider a spherical envelope model for…
By synergistically combining modeling, simulation and experiments, we show that there exists a regime of self-propulsion in which the inertia in the fluid dynamics can be separated from that of the swimmer. This is demonstrated by the…
In isotropic fluids like water, micrometer-scale swimmers have evolved swim strokes to translate despite their tiny size. As described by Purcell in his Scallop Theorem, reciprocal motions, like those performed by a scallop, cannot drive…
We study the fluid dynamics of two fish-like bodies with synchronised swimming patterns. Our studies are based on two-dimensional simulations of viscous incompressible flows. We distinguish between motion patterns that are externally…
Skateboarders perform a reciprocating motion on a curved ramp, called pumping, by moving their bodies up and down perpendicular to the ramp's surface. We propose a simple mechanical model for this pumping motion and solve the equation of…
We consider an optimal control problem for the Navier-Stokes system with Navier slip boundary conditions. We denote by $\alpha$ the friction coefficient and we analyze the asymptotic behavior of such a problem as $\alpha\to \infty$. More…
This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…
We propose an optimal control framework for persistent monitoring problems where the objective is to control the movement of mobile nodes to minimize an uncertainty metric in a given mission space. For multi agent in a one-dimensional…
In this paper we analyse local regularity of time-optimal controls and trajectories for an n-dimensional affine control system with a control parameter, taking values in a k-dimensional closed ball. In the case of k equal to n-1, we give…
Microorganisms ofter move in confined, disordered environments, where hydrodynamic couplings can modify their transport behavior. Using extensive finite-element simulations, we investigate the dynamics of microswimmers -- modeled as…
We consider the optimal control of switching on a coupling term between two quantum many-body systems. Specifically, we (i) quantify the energetic cost of establishing a weak junction between two quantum spin-$1/2$ chains in finite time…
Hybrid optimal control problems are studied for a general class of hybrid systems where autonomous and controlled state jumps are allowed at the switching instants and in addition to terminal and running costs switching between discrete…
We study a time-optimal control problem of a two-peakon collision. First, we state the controllability. Next, we find the time-optimal strategy. This is done via the HamiltonJacobi-Bellman equation and the dynamic programming method. We…
The main goal of this paper is developing the method of discrete approximations to derive necessary optimality conditions for a class of constrained sweeping processes with nonsmooth perturbations. Optimal control problems for sweeping…
An optimal control problem for the linear wave equation with control cost chosen as the BV semi-norm in time is analyzed. This formulation enhances piecewise constant optimal controls and penalizes the number of jumps. Existence of optimal…
We consider piecewise-deterministic optimal control problems in which the environment randomly switches among several deterministic modes, and the goal is to optimize the expected cost up to the termination while taking the likelihood of…
Nonsmooth phenomena, such as abrupt changes, impacts, and switching behaviors, frequently arise in real-world systems and present significant challenges for traditional optimal control methods, which typically assume smoothness and…
This paper investigates optimal control problems formulated over a class of piecewise-smooth vector fields. Instead of optimizing over the discontinuous system directly, we instead formulate optimal control problems over a family of…