Related papers: On the uniqueness of the optimal control for 2-dim…
In this work, we investigate optimal control of a Brinkman equation couple with sixth-order Cahn-Hilliard equation. The Cahn-Hilliard equation is endowed with a source term accounting for mass exchange and the velocity equation contains a…
We present a general approach to prove existence of solutions for optimal control problems not based on typical convexity conditions which quite often are very hard, if not impossible, to check. By taking advantage of several relaxations of…
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…
This paper investigates the exact controllability problem for multi-dimensional stochastic first-order symmetric hyperbolic systems with control inputs acting in two distinct ways: an internal control applied to the diffusion term and a…
We study the time-inconsistent linear quadratic optimal control problem for forward-backward stochastic differential equations with potentially indefinite cost weighting matrices for both the state and the control variables. Our research…
This work deals with the existence of optimal solution and the maximum principle for optimal control problem governed by Navier-Stokes equations with state constraint in 3-D. Strong results in 2-D also are given.
In this paper, we consider the stochastic optimal control problem for the interacting particle system. We obtain the stochastic maximum principle of the optimal control system by introducing a generalized backward stochastic differential…
A class of time-optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints and final point constraints is considered. By introducing the so-called locally optimal solution to time-optimal control…
This paper is concerned with the problem of shape optimization of two-dimensional flows governed by the time-dependent Navier-Stokes equations. We derive the structures of shape gradients with respect to the shape of the variable domain for…
This paper focuses on the analysis of an optimal control problem governed by a nonsmooth quasilinear partial differential equation that models a stationary incompressible shear-thickening fluid. We start by studying the directional…
This paper develops a comprehensive extension of the $\Lambda$-set framework for optimal control, introducing second-order $\Lambda$-sets and generalizing the theory to non-smooth, hybrid, and stochastic hybrid systems. We first establish…
We consider an optimal control problem where the state is governed by a free boundary problem called the two-phase membrane problem and the control appears in the coefficients of the characteristic function of the positivity and negativity…
We derive necessary conditions for optimality in control problems governed by hyperbolic partial differential equations in Goursat-Darboux form. The conditions consist of a set of Hamiltonian equations in Goursat form, side conditions for…
This paper presents an inverse optimality method to solve the Hamilton-Jacobi-Bellman equation for a class of nonlinear problems for which the cost is quadratic and the dynamics are affine in the input. The method is inverse optimal because…
The paper studies a class of quadratic optimal control problems for partially observable linear dynamical systems. In contrast to the full information case, the control is required to be adapted to the filtration generated by the…
We study the small-time global approximate controllability for incompressible magnetohydrodynamic (MHD) flows in smoothly bounded two- or three-dimensional domains. The controls act on arbitrary nonempty open portions of each connected…
In this work, we analyse the discretisation of a recently proposed new Lagrangian approach to optimal control problems of affine-controlled second-order differential equations with cost functions quadratic in the controls. We propose exact…
This article concerns the problem of computing solutions to state-constrained optimal control problems whose trajectory is affected by a flow field. This general mathematical framework is particularly pertinent to the requirements…
The evolution of two incompressible, immiscible, isothermal fluids in a bounded domain and a porous media is described by the coupled Cahn-Hilliard-Brinkman (CHB) system. The CHB system consists of the Cahn-Hilliard equation describing the…
In this paper, we consider the inverse optimal control problem for the discrete-time linear quadratic regulator, over finite-time horizons. Given observations of the optimal trajectories, and optimal control inputs, to a linear…