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This paper is concerned with a backward stochastic linear-quadratic (LQ, for short) optimal control problem with deterministic coefficients. The weighting matrices are allowed to be indefinite, and cross-product terms in the control and…
In this paper, we present a new analytical framework for determining the well-posedness of constrained optimization problems that arise in the study of optimal control device design and placement within the context of infinite dimensional…
This paper introduces and studies the optimal control problem with equilibrium constraints (OCPEC). The OCPEC is an optimal control problem with a mixed state and control equilibrium constraint formulated as a complementarity constraint and…
This paper deals with Interior Point Methods (IPMs) for Optimal Control Problems (OCPs) with pure state and mixed constraints. This paper establishes a complete proof of convergence of IPMs for a general class of OCPs. Convergence results…
This paper is concerned with the linear quadratic optimal control problem for networked system simultaneously with input delay and Markovian dropout. Different from the results in the literature, we consider the hold-input strategy, which…
We study unconstrained and constrained linear quadratic problems and investigate the suboptimality of the model predictive control (MPC) method applied to such problems. Considering MPC as an approximate scheme for solving the related fixed…
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…
Linear-quadratic optimal control problem for systems governed by forward-backward stochastic differential equations has been extensively studied over the past three decades. Recent research has revealed that for forward-backward control…
This paper investigates the stochastic linear-quadratic (LQ, for short) optimal control problems with non-Markovian regime switching in a finite time horizon where the state equation is multi-dimensional. Similar to the classical stochastic…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
A mixed linear quadratic (MLQ, for short) optimal control problem is considered. The controlled stochastic system consists of two diffusion processes which are in different time horizons. There are two control actions: a standard control…
We study the quadratic regulator problem on a finite time horizon for the wave equation with high internal damping controlled on the boundary by square integrable controls. The approach in this paper transforms the wave equation with high…
This paper addresses an optimal control problem for a robot that has to find and collect a finite number of objects and move them to a depot in minimum time. The robot has fourth-order dynamics that change instantaneously at any pick-up or…
This article explores the discrete-time stochastic optimal LQR control with delay and quadratic constraints. The inclusion of delay, compared to delay-free optimal LQR control with quadratic constraints, significantly increases the…
This paper thoroughly investigates stochastic linear-quadratic optimal control problems with the Markovian regime switching system, where the coefficients of the state equation and the weighting matrices of the cost functional are random.…
In model predictive control (MPC), an optimal control problem (OCP) is solved for the current state and the first input of the solution, the optimal feedback law, is applied to the system. This procedure requires to solve the OCP in every…
An abstract nonautonomous parabolic linear-quadratic regulator problem with very general final cost operator P_T is considered, subject to the same assumptions under which a classical solution of the associated differential Riccati equation…
Finding the state feedback control in an $% H^{\infty }$-optimal control problem involves a challenging approach of the associated algebraic Riccati equation of the generic form $A^{\ast }P+PA+P\Gamma P=F$. In view of this objective, we…
Many robotics tasks, such as path planning or trajectory optimization, are formulated as optimal control problems (OCPs). The key to obtaining high performance lies in the design of the OCP's objective function. In practice, the objective…
In this study, we focus on the numerical solution method for the optimal control problem with equilibrium constraints (OCPEC).It is extremely challenging to solve OCPEC owing to the absence of constraint regularity and strictly feasible…