Related papers: Generalized Differentiability and Second-Order Nec…
We study solution techniques for a linear-quadratic optimal control problem involving fractional powers of elliptic operators. These fractional operators can be realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic problem…
In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with…
Ordinary Differential Equations are a simple but powerful framework for modeling complex systems. Parameter estimation from times series can be done by Nonlinear Least Squares (or other classical approaches), but this can give…
We provide a generalization of first-order necessary conditions of optimality for infinite-dimensional optimization problems with a finite number of inequality constraints and with a finite number of inequality and equality constraints. Our…
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…
We adopt the integral definition of the fractional Laplace operator and study an optimal control problem on Lipschitz domains that involves a fractional elliptic partial differential equation (PDE) as state equation and a control variable…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex, and the system is governed by a nonlinear backward stochastic differential equation. By introducing a new approach, we…
This paper provides necessary conditions of optimality for optimal control problems with time delays in both state and control variables. Different versions of the necessary conditions cover fixed end-time problems and, under additional…
Optimal control problems for semilinear elliptic equations with control costs in the space of bounded variations are analysed. BV-based optimal controls favor piecewise constant, and hence 'simple' controls, with few jumps. Existence of…
We present a novel approach to nonlinear constrained Tikhonov regularization from the viewpoint of optimization theory. A second-order sufficient optimality condition is suggested as a nonlinearity condition to handle the nonlinearity of…
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…
A dual control problem is presented for the optimal stochastic control of a system governed by partial differential equations. Relationships between the optimal values of the original and the dual problems are investigated and two duality…
In this work, we study the control constrained distributed optimal control of a stationary doubly diffusive flow model. For the control problem, we use a well-posedness analysis based on minimal assumptions on data and domain. We show the…
In this paper, in terms of three types of generalized second-order derivatives of a nonsmooth function, we mainly study the corresponding second-order optimality conditions in a Hilbert space and prove the equivalence among these optimality…
We discretize a risk-neutral optimal control problem governed by a linear elliptic partial differential equation with random inputs using a Monte Carlo sample-based approximation and a finite element discretization, yielding finite…
This paper deals with optimal control problems of integral equations, with initial-final and running state constraints. The order of a running state constraint is defined in the setting of integral dynamics, and we work here with…
This paper presents sufficient conditions for optimal control of systems with dynamics given by a linear operator, in order to obtain an explicit solution to the Bellman equation that can be calculated in a distributed fashion. Further, the…
Following Demidovich's concept and definition of convergent systems, we analyze the optimal nonlinear damping control, recently proposed [1] for the second-order systems. Targeting the problem of output regulation, correspondingly tracking…
This paper considers the problem of determining an optimal control action based on observed data. We formulate the problem assuming that the system can be modelled by a nonlinear state-space model, but where the model parameters, state and…
In this article we study an optimal control problem subject to the Fokker-Planck equation \[ \partial_t \rho - \nu \Delta \rho - {\rm div } \big(\rho B[u]\big) = 0. \] The control variable $u$ is time-dependent and possibly…