Related papers: On the maximal solution of the conjugate discrete-…
In this paper we consider a class of conjugate discrete-time Riccati equations, arising originally from the linear quadratic regulation problem for discrete-time antilinear systems. Under mild and reasonable assumptions, the existence of…
In this paper we consider a class of conjugate discrete-time Riccati equations (CDARE), arising originally from the linear quadratic regulation problem for discrete-time antilinear systems. Recently, we have proved the existence of the…
We study in this paper the linear quadratic optimal control (linear quadratic regulation, LQR for short) for discrete-time complex-valued linear systems, which have shown to have several potential applications in control theory. Firstly, an…
Algebraic Riccati equations are encountered in many applications of control and engineering problems, e.g., LQG problems and $H^\infty$ control theory. In this work, we study the properties of one type of discrete-time algebraic Riccati…
The purpose of this paper is to investigate the role that the continuous-time generalised Riccati equation plays within the context of singular linear-quadratic optimal control. This equation has been defined following the analogy with the…
Discrete algebraic Riccati equations and their fixed points are well understood and arise in a variety of applications, however, the time-varying equations have not yet been fully explored in the literature. In this article we provide 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…
We develop a discrete analogue of Hamilton-Jacobi theory in the framework of discrete Hamiltonian mechanics. The resulting discrete Hamilton-Jacobi equation is discrete only in time. We describe a discrete analogue of Jacobi's solution and…
This paper introduces a generalization of the well-known Riccati recursion for solving the discrete-time equality-constrained linear quadratic optimal control problem. The recursion can be used to compute the solutions as well as optimal…
A time-inconsistent optimal control problem is formulated and studied for a controlled linear ordinary differential equation with quadratic cost functional. A notion of equilibrium control is introduced, which can be regarded as a…
In this article we address the issue of uniqueness for differential and algebraic operator Riccati equations, under a distinctive set of assumptions on their unbounded coefficients. The class of boundary control systems characterized by…
A fundamental theory of deterministic linear-quadratic (LQ) control is the equivalent relationship between control problems, two-point boundary value problems and Riccati equations. In this paper, we extend the equivalence to a general…
Contraction properties of the Riccati operator are studied within the context of non-stationary linear-quadratic optimal control. A lifting approach is used to obtain a bound on the rate of strict contraction, with respect to the Riemannian…
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…
This paper is concerned with a linear quadratic (LQ, for short) optimal control problem with fixed terminal states and integral quadratic constraints. A Riccati equation with infinite terminal value is introduced, which is uniquely solvable…
A discrete-time stochastic LQ problem with multiplicative noises and state transmission delay is studied in this paper, which does not require any definiteness constraint on the cost weighting matrices. From some abstract representations of…
The control algebraic Riccati equation is studied for a class of systems with unbounded control and observation operators. Using a dichotomy property of the associated Hamiltonian operator matrix, two invariant graph subspaces are…
Algebraic Riccati equations (AREs) have been extensively applicable in linear optimal control problems and many efficient numerical methods were developed. The most attention of numerical solutions is the (almost) stabilizing solution in…
This paper investigates the properties of the solutions of the generalised discrete algebraic Riccati equation arising from the solution of the classic infinite-horizon linear quadratic control problem. In particular, a geometric analysis…
In this paper, we investigate a class of time-inconsistent discrete-time stochastic linear-quadratic optimal control problems, whose time-consistent solutions consist of an open-loop equilibrium control and a linear feedback equilibrium…