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We develop the dynamic programming approach for a family of infinite horizon boundary control problems with linear state equation and convex cost. We prove that the value function of the problem is the unique regular solution of the…
In this article, we discuss two algorithms tailored to discrete-time deterministic finite-horizon nonlinear optimal control problems or so-called deterministic trajectory optimization problems. Both algorithms can be derived from an…
A new formulation of boundary value problems in gradient elasticity is presented in this work. The main outcome is the construction of partial differential systems of second order, which are typically equivalent with the well known fourth…
A general setup for deterministic system identification problems on graphs with Dirichlet and Neumann boundary conditions is introduced. When control nodes are available along the boundary, we apply a discretize-then-optimize method to…
We consider a system that is exactly controllable. For given initial state, terminal state and objective function, an optimal control is often well-defined. Such an optimal control has the disadvantage that although it works perfectly well…
Optimal control problem with a goal to squeeze wave packet of a trapped quantum particle is considered and solved analytically using adiabatic approximation. The analytical solution that drives the particle into a highly localized final…
We explore singular second-order boundary value problems with mixed boundary conditions on a general time scale. Using the lower and upper solutions method combined with the Brouwer fixed point theorem we demonstrate the existence of a…
This paper is concerned with a constrained stochastic linear-quadratic optimal control problem, in which the terminal state is fixed and the initial state is constrained to lie in a stochastic linear manifold. The controllability of…
We consider a boundary value problem of the stationary transport equation with the incoming boundary condition in two or three dimensional bounded convex domains. We discuss discontinuity of the solution to the boundary value problem…
In this manuscript, we consider a control system governed by a general ordinary differential equation on a Riemannian manifold, with its endpoints satisfying some inequalities and equalities, and its control constrained to a closed convex…
In this paper, we study a linear-quadratic optimal control problem for mean-field stochastic differential equations driven by a Poisson random martingale measure and a multidimensional Brownian motion. Firstly, the existence and uniqueness…
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…
In this paper, we derive sufficient and necessary maximum principles for a stochastic optimal control problem where the system state is given by a controlled stochastic differential equation with default. We prove existence of a unique…
We consider the energy-optimal control problem for double-integrator systems subject to state and control constraints, with fixed terminal time and free terminal speed. When the constraints become active, the optimal trajectory consists of…
We consider the terminal value problem (or called final value problem, initial inverse problem, backward in time problem) of determining the initial value, in a general class of time-fractional wave equations with Caputo derivative, from a…
We study an optimal control problem with a quadratic cost functional for non-Newtonian fluids of differential type. More precisely, we consider the system governing the evolution of a second grade fluid filling a two-dimensional bounded…
In this paper, we solve an open problem and obtain a general maximum principle for a stochastic optimal control problem where the control domain is an arbitrary non-empty set and all the coefficients (especially the diffusion term and the…
We study the optimal investment stopping problem in both continuous and discrete case, where the investor needs to choose the optimal trading strategy and optimal stopping time concurrently to maximize the expected utility of terminal…
In this paper, a general stochastic model with controls applied at the moments when the random process hits the boundary of a given subset of the state set is proposed and studied. The general concept of the model is formulated and its…
A general bilinear optimal control problem subject to an infinite-dimensional state equation is considered. Polynomial approximations of the associated value function are derived around the steady state by repeated formal differentiation of…