Related papers: A Multidimensional Fourier Approximation of Optima…
In this paper, a sub-optimal boundary control strategy for a free boundary problem is investigated. The model is described by a non-smooth convection-diffusion equation. The control problem is addressed by an instantaneous strategy based on…
In this work, we analyse the discretisation of a recently proposed new Lagrangian approach to optimal control problems of affine-controlled second-order differential equations with cost functions quadratic in the controls. We propose exact…
We introduce the tensor numerical method for solution of the $d$-dimensional optimal control problems with fractional Laplacian type operators in constraints discretized on large $n^{\otimes d}$ tensor-product Cartesian grids. The approach…
The purpose of this work is the development of space-time discretization schemes for phase-field optimal control problems. Specifically in the optimal control minimization problem, a tracking-type cost functional is minimized to steer the…
In this paper, a projected primal-dual gradient flow of augmented Lagrangian is presented to solve convex optimization problems that are not necessarily strictly convex. The optimization variables are restricted by a convex set with…
We investigate optimal control problems with $L^0$ constraints, which restrict the measure of the support of the controls. We prove necessary optimality conditions of Pontryagin maximum principle type. Here, a special control perturbation…
This article introduces a representation of dynamic meshes, adapted to some numerical simulations that require controlling the volume of objects with free boundaries, such as incompressible fluid simulation, some astrophysical simulations…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
These notes present preliminary results regarding two different approximations of linear infinite-horizon optimal control problems arising in model predictive control. Input and state trajectories are parametrized with basis functions and a…
We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…
There are many important practical optimization problems whose feasible regions are not known to be nonempty or not, and optimizers of the objective function with the least constraint violation prefer to be found. A natural way for dealing…
We consider convex optimization problems with prioritized equality constraints, which may be infeasible. In many applications, such as network optimization and image reconstruction, it is often desirable to compute solutions that satisfy…
The present work addresses a finite-horizon linear-quadratic optimal control problem for uncertain systems driven by piecewise constant controls. The precise values of the system parameters are unknown, but assumed to belong to a finite set…
In this paper, we consider the problem of multi-objective optimal control of a dynamical system with additive and multiplicative noises with given second moments and arbitrary probability distributions. The objectives are given by quadratic…
A finite horizon linear quadratic(LQ) optimal control problem is studied for a class of discrete-time linear fractional systems (LFSs) affected by multiplicative, independent random perturbations. Based on the dynamic programming technique,…
In this note, we develop Fourier approximation methods for the solutions of first-order nonlocal mean-field games (MFG) systems. Using Fourier expansion techniques, we approximate a given MFG system by a simpler one that is equivalent to a…
This paper is concerned with a discrete-time mean-field stochastic linear-quadratic optimal control problem arose from financial application. Through matrix dynamical optimization method, a group of linear feedback controls is investigated.…
Optimal quantum control of continuous variable systems poses a formidable computational challenge because of the high-dimensional character of the system dynamics. The framework of quantum invariants can significantly reduce the complexity…
We address the inverse problem of Lagrangian identification based on trajecto-ries in the context of nonlinear optimal control. We propose a general formulation of the inverse problem based on occupation measures and complementarity in…
Many problems in modern robotics can be addressed by modeling them as bilevel optimization problems. In this work, we leverage augmented Lagrangian methods and recent advances in automatic differentiation to develop a general-purpose…