Related papers: Analytical solution for optimal protocols of weak …
When a system deviates from equilibrium, it is possible to manipulate and control it to drive it towards equilibrium within a finite time $t_f$, even reducing its natural relaxation time scale $\tau_{relax}$. Although numerous theoretical…
Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver…
We identify generic protocols achieving optimal power extraction from a single active particle subject to continuous feedback control under the assumption that its spatial trajectory, but not its instantaneous self-propulsion force, is…
A new primal-dual weak Galerkin (PDWG) finite element method is introduced and analyzed for the ill-posed elliptic Cauchy problems with ultra-low regularity assumptions on the exact solution. The Euler-Lagrange formulation resulting from…
Algebraically speaking, linear time-invariant (LTI) systems can be considered as modules. In this framework, controllability is translated as the freeness of the system module. Optimal control mainly relies on quadratic Lagrangians and the…
The study is devoted to mathematical modeling and optimal control design of longitudinal motions of a rectilinear elastic rod. The control inputs are a force, which is normal to the cross section and distributed piecewise constantly along…
This paper aims at obtaining, by means of integral transforms, analytical approximations in short times of solutions to boundary value problems for the one-dimensional reaction-diffusion equation with constant coefficients. The general form…
This is a survey highlighting several recent results concerning well/ill posedness of the Euler system of gas dynamics. Solutions of the system are identified as limits of consistent approximations generated either by physically more…
A method for solving model nonlinear equations describing plasma oscillations in the presence of viscosity and resistivity is given. By first going to the Lagrangian variables and then transforming the space variable conveniently, the…
It is known that the Eulerian and Lagrangian structures of fluid flow can be drastically different; for example, ideal fluid flow can have a trivial (static) Eulerian structure, while displaying chaotic streamlines. Here we show that ideal…
We prove necessary optimality conditions of Euler-Lagrange type for a problem of the calculus of variations with time delays, where the delay in the unknown function is different from the delay in its derivative. Then, a more general…
Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an…
In this paper, we present a method that enables to solve in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets…
This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple…
Consider a rectangular matrix describing some type of communication or transportation between a set of origins and a set of destinations, or a classification of objects by two attributes. The problem is to infer the entries of the matrix…
Certain systems of inviscid fluid dynamics have the property that for solutions that are only slightly better than differentiable in Eulerian variables, the corresponding Lagrangian trajectories are analytic in time. We elucidate the…
We show that any dissipative (measure-valued) solution of the compressible Euler system that complies with Dafermos' criterion of maximal dissipation is necessarily an admissible weak solution. In addition, we propose a simple, at most two…
In this work, we solve a discrete optimal transport problem in a nonuniform environment. To solve the optimal transport problem, we build the cost matrix and then use classical solvers for discrete optimal transport. The challenge is to…
As we move to increasingly complex cyber-physical systems (CPS), new approaches are needed to plan efficient state trajectories in real-time. In this paper, we propose an approach to significantly reduce the complexity of solving optimal…
In this paper, we present a method that enables solving in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets…