Related papers: Generic Solutions to Controlled Balance Laws
In this paper we study a distributed optimal control problem for a three-dimensional Navier-Stokes-$\alpha$ model. We prove the solvability of the optimal control problem, and derive first-order optimality conditions by using a Lagrange…
We study the existence and uniqueness of source-type solutions to the Cauchy problem for the heat equation with fast convection under certain tail control assumptions. We allow the solutions to change sign, but we will in fact show that…
The paper deals with a problem of control of a system characterized by the fact that the influence of controls on the dynamics of certain functions of state variables (called observables) is relatively weak and the rates of change of these…
The purpose of this paper is to close the remaining gaps in the understanding of the role that the constrained generalized continuous algebraic Riccati equation plays in singular linear-quadratic (LQ) optimal control. Indeed, in spite of…
First, let $u_{g}$ be the unique solution of an elliptic variational inequality with source term $g$. We establish, in the general case, the error estimate between $u_{3}(\mu)=\mu u_{g_{1}}+ (1-\mu)u_{g_{2}}$ %(the convex combination of two…
In this paper, which is a continuation of the previously published discrete time paper we develop a theory for continuous time stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a…
This article is devoted to completing some aspects of the classical Cauchy-Lipschitz (or Picard-Lindel\"of) theory for general nonlinear systems posed on time scales, that are closed subsets of the set of real numbers. Partial results do…
Consider a scalar conservation law with discontinuous flux \begin{equation*}\tag{1} \quad u_{t}+f(x,u)_{x}=0, \qquad f(x,u)= \begin{cases} f_l(u)\ &\text{if}\ x<0,\\ f_r(u)\ & \text{if} \ x>0, \end{cases} \end{equation*} where $u=u(x,t)$ is…
We study the closed-loop solvability of a stochastic linear quadratic optimal control problem for systems governed by stochastic evolution equations. This solvability is established by means of solvability of the corresponding Riccati…
The solution of the global controllability problem is obtained for a class of the triangular systems of O.D.E. that are not feedback linearizable. The introduced class is a generalization of the classes of triangular systems investigated…
General hyperbolic systems of balance laws with inhomogeneous flux and source are studied. Global existence of entropy weak solutions to the Cauchy problem is established for small $BV$ data under appropriate assumptions on the decay of the…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
The main goal of this paper is to show that the blow up phenomenon (the explosion of the $ \rL^{\infty }$-norm) of the solutions of several classes of evolution problems can be controlled by means of suitable global controls $\alpha (t)$…
We consider optimal control problems involving two constraint sets: one comprised of linear ordinary differential equations with the initial and terminal states specified and the other defined by the control variables constrained by simple…
Feedback optimization refers to a class of methods that steer a control system to a steady state that solves an optimization problem. Despite tremendous progress on the topic, an important problem remains open: enforcing state constraints…
We establish the existence of an optimal control for a general class of singular control problems with state constraints. The proof uses weak convergence arguments and a time rescaling technique. The existence of optimal controls for…
This paper presents and discusses a mathematical model inspired by control theory to derive optimal public policies for minimizing costs associated with the reduction and control of criminal activity in a population. Specifically, we…
In this paper, we study a class of stochastic time-inconsistent linear-quadratic (LQ) control problems with control input constraints. These problems are investigated within the more general framework associated with random coefficients.…
We address a class of systems for which the solution to an H-infinity optimal control problem can be given on a very simple closed form. In fact, both the control law and optimal performance value are explicitly given. The class of systems…
An infinite-dimensional bilinear optimal control problem with infinite-time horizon is considered. The associated value function can be expanded in a Taylor series around the equilibrium, the Taylor series involving multilinear forms which…