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It is a longstanding unsolved problem to characterize the optimal feedback controls for general linear quadratic optimal control problem of stochastic evolution equation with random coefficients. A solution to this problem is given in [21]…
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…
One of the fundamental issues in Control Theory is to design feedback controls. It is well-known that, the purpose of introducing Riccati equations in the deterministic case is to provide the desired feedback controls for linear quadratic…
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…
This paper deals with some reachability issues for piecewise linear switched systems with time-dependent coefficients and multiplicative noise. Namely, it aims at characterizing data that are almost reachable at some fixed time T > 0…
In this paper, we discuss numerical methods for solving large-scale continuous-time algebraic Riccati equations. These methods have been the focus of intensive research in recent years, and significant progress has been made in both the…
A control in feedback form is derived for linear quadratic, time-invariant optimal control problems subject to parabolic partial differential equations with coefficients depending on a countably infinite number of uncertain parameters. It…
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…
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…
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…
We prove existence and uniqueness of the mild solution of an infinite dimensional, operator valued, backward stochastic Riccati equation. We exploit the regularizing properties of the semigroup generated by the unbounded operator involved…
We generalize the classical theory on algebraic Riccati equations and optimization to infinite-dimensional well-posed linear systems, thus completing the work of George Weiss, Olof Staffans and others. We show that the optimal control is…
Algebraic Riccati equations with indefinite quadratic terms play an important role in applications related to robust controller design. While there are many established approaches to solve these in case of small-scale dense coefficients,…
This paper presents a survey of some new applications of algebraic Riccati equations. In particular, the paper surveys some recent results on the use of algebraic Riccati equations in testing whether a system is negative imaginary and in…
The paper considers the suboptimal H-infinity control problem for a general discrete-time system (whose transfer function matrix is allowed to be improper or polynomial). The parametrization of output feedback controllers is given in a…
We consider the algebraic Riccati equation for which the four coefficient matrices form an M-matrix K. When K is a nonsingular M-matrix or an irreducible singular M-matrix, the Riccati equation is known to have a minimal nonnegative…
This paper is concerned with the linear quadratic (LQ) optimal control of continuous-time system with terminal state constraint. In particular, multiple agents exist in the system which can only access partial information of the matrix…
Matrix Riccati differential equations arise in many different areas and are particular important within the field of control theory. In this paper we consider numerical integration for large-scale systems of stiff matrix Riccati…
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…
We derive an explicit solution to the operator Riccati equation solving the Linear-Quadratic (LQ) optimal control problem for a class of boundary controlled hyperbolic partial differential equations (PDEs). Different descriptions of the…