Related papers: State constrained control problems in Banach latti…
This paper studies an optimal dividend problem with a drawdown constraint in a Brownian motion model, requiring the dividend payout rate to remain above a fixed proportion of its historical maximum. This leads to a path-dependent stochastic…
In this paper, a quadratic optimal control problem is considered for second-order parabolic PDEs with homogeneous Dirichlet boundary conditions, in which the "point" control function (depending only on time) constitutes a source term. These…
The paper concerns the infinite dimensional Hamilton-Jacobi-Bellman equation related to optimal control problem regulated by a transport equation with boundary control. A suitable viscosity solution approach is needed in view of the…
We study a class of infinite-dimensional singular stochastic control problems with applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially-ordered…
The positive-real and bounded-real lemmas solve two important linear-quadratic optimal control problems for passive and non-expansive systems, respectively. The lemmas assume controllability, yet a passive or non-expansive system can be…
We consider a stochastic optimal control problem governed by a stochastic differential equation with delay in the control. Using a result of existence and uniqueness of a sufficiently regular mild solution of the associated…
This paper considers the optimal control for hybrid systems whose trajectories transition between distinct subsystems when state-dependent constraints are satisfied. Though this class of systems is useful while modeling a variety of…
The aim of this work is to deal with a discontinuous Hamilton-Jacobi equation in the whole euclidian N-dimensional space, associated to a possibly unbounded optimal control problem. Here, the discontinuities are located on a hyperplane and…
This paper studies a class of continuous-time scalar-state stochastic Linear-Quadratic (LQ) optimal control problem with the linear control constraints. Applying the state separation theorem induced from its special structure, we develop…
Proximal gradient methods are a popular tool for the solution of structured, nonsmooth minimization problems. In this work, we investigate an extension of the former to general Banach spaces and provide worst-case convergence rates for,…
We introduce the optimality question to the relaxation in multiple control problems described by Sobolev type nonlinear fractional differential equations with nonlocal control conditions in Banach spaces. Moreover, we consider the…
Stochastic optimal control problems with constraints on the probability distribution of the final output are considered. Necessary conditions for optimality in the form of a coupled system of partial differential equations involving a…
This paper considers the class of deterministic continuous-time optimal control problems (OCPs) with piecewise-affine (PWA) vector field, polynomial Lagrangian and semialgebraic input and state constraints. The OCP is first relaxed as an…
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…
We obtain weighted uniform estimates for the gradient of the solutions to a class of linear parabolic Cauchy problems with unbounded coefficients. Such estimates are then used to prove existence and uniqueness of the mild solution to a…
We address H-infinity structured static state feedback and give a simple form for an optimal control law applicable to linear time invariant systems with symmetric and Hurwitz state matrix. More specifically, the control law as well as the…
The article examines a linear-quadratic Neumann control problem that is governed by a non-coercive elliptic equation. Due to the non-self-adjoint nature of the linear control-to-state operator, it is necessary to independently study both…
The second part of our study is devoted to an analysis of the exactness of penalty functions for optimal control problems with terminal and pointwise state constraints. We demonstrate that with the use of the exact penalty function method…
An analysis of the motion of a relativistic electron under a linear constraint in four dimensions is presented. Interesting results are given that show that the state of the electron is well defined under the formalism of time optimal…
H-infinity optimal control and estimation are addressed for a class of systems governed by partial differential equations with bounded input and output operators. Diffusion equations are an important example in this class. Explicit formulas…