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This paper addresses the optimal control problem of finite-horizon discrete-time nonlinear systems under state and control constraints. A novel numerical algorithm based on optimal control theory is proposed to achieve superior…
This work studies the null controllability of a system of coupled parabolic PDEs. In particular, our work specializes to an important subclass of these control problems which are coupled by first and zero-order couplings and are,…
In this chapter, we are concerned with inverse optimal control problems, i.e., optimization models which are used to identify parameters in optimal control problems from given measurements. Here, we focus on linear-quadratic optimal control…
The paper describes a continuous second-variation algorithm to solve optimal control problems where the control is defined on a closed set. A second order expansion of a Lagrangian provides linear updates of the control to construct a…
We study a control problem governed by a semilinear parabolic equation. The control is a measure that acts as the kernel of a possibly nonlocal time delay term and the functional includes a non-differentiable term with the measure-norm of…
In this paper we consider a constrained parabolic optimal control problem. The cost functional is quadratic and it combines the distance of the trajectory of the system from the desired evolution profile together with the cost of a control.…
The energy shaping method, Controlled Lagrangian, is a well-known approach to stabilize the under-actuated Euler Lagrange (EL) systems. In this approach, to construct a control rule, some nonlinear, nonhomogeneous partial differential…
In this paper we propose a new finite element method for solving elliptic optimal control problems with pointwise state constraints, including the distributed controls and the Dirichlet or Neumann boundary controls. The main idea is to use…
This work considers the problem of approximating initial condition and time-dependent optimal control and trajectory surfaces using multivariable Fourier series. A modified Augmented Lagrangian algorithm for translating the optimal control…
We propose, analyze, and test new iterative solvers for large-scale systems of linear algebraic equations arising from the finite element discretization of reduced optimality systems defining the finite element approximations to the…
This paper presents a numerical framework for the low-rank approximation of the solution to three-dimensional parabolic problems. The key contribution of this work is the tensorization process based on a tensor-train reformulation of the…
A distributed optimal control problem with final observation for a three- dimensional Lagrange averaged Navier-Stokes-? model is studied. The solvability of the optimal control problem is proved and the first-order optimality conditions are…
We study methods for solving stochastic control problems of systems of forward-backward mean-field equations with delay, in finite or infinite horizon. Necessary and sufficient maximum principles under partial information are given. The…
Parabolic optimal control problems with control constraints are generally challenging, from either theoretical analysis or algorithmic design perspectives. Conceptually, the well-known alternating direction method of multipliers (ADMM) can…
We present a unified treatment to control problems on an arbitrary time scale by introducing the study of forward-backward optimal control problems. Necessary optimality conditions for delta-nabla isoperimetric problems are proved, and…
This paper presents a novel factor graph-based approach to solve the discrete-time finite-horizon Linear Quadratic Regulator problem subject to auxiliary linear equality constraints within and across time steps. We represent such optimal…
This article contributes to a framework for a computational indirect method based on the Pontryagin maximum principle to efficiently solve a class of state constrained time-optimal control problems in the presence of a time-dependent flow…
We propose a novel continuous-time algorithm for inequality-constrained convex optimization inspired by proportional-integral control. Unlike the popular primal-dual gradient dynamics, our method includes a proportional term to control the…
One of the main objectives of science is the recognition of a general pattern in a particular phenomenon in some particular regime. In this work, this is achieved with the analytical expression for the optimal protocol that minimizes the…
A finite element analysis of a Dirichlet boundary control problem governed by the linear parabolic equation is presented in this article. The Dirichlet control is considered in a closed and convex subset of the energy space $H^1(\Omega…