Related papers: Dichotomous Hamiltonians and Riccati equations for…
An operator Riccati equation from systems theory is considered in the case that all entries of the associated Hamiltonian are unbounded. Using a certain dichotomy property of the Hamiltonian and its symmetry with respect to two different…
An algebraic Riccati equation for linear operators is studied, which arises in systems theory. For the case that all involved operators are unbounded, the existence of infinitely many selfadjoint solutions is shown. To this end, invariant…
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…
This paper analyzes the properties of the solutions of the generalized continuous algebraic Riccati equation from a geometric perspective. This analysis reveals the presence of a subspace that may provide an appropriate degree of freedom to…
Solving large-scale continuous-time algebraic Riccati equations is a significant challenge in various control theory applications. This work demonstrates that when the matrix coefficients of the equation are quasiseparable, the solution…
The characterization of the solution set for a class of algebraic Riccati inequalities is studied. This class arises in the passivity analysis of linear time invariant control systems. Eigenvalue perturbation theory for the Hamiltonian…
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…
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…
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…
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…
The Riccati equation method is used for study the oscillatory and non oscillatory behavior of solutions of linear four dimensional hamiltonian systems. An oscillatory and two non oscillatory criteria are proved. On an example the obtained…
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…
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…
A Deterministic affine quadratic optimal control problem is considered. Due to the nature of the problem, optimal controls exist under some very mild conditions. Further, it is shown that under some assumptions, the value function is…
The stabilizability of a general class of abstract parabolic-like equations is investigated, with a finite number of actuators. This class includes the case of actuators given as delta distributions located at given points in the spatial…
In order to describe the impact of different geometric structures and constraints for the dynamics of a regular controlled Hamiltonian system, in this paper, we first define a kind of controlled magnetic Hamiltonian (CMH) system, and give a…
The Riccati equation method is used to establish some new oscillatory criteria for the hamiltonian systems in a new direction, which is to break the positive definiteness restriction imposed on one of coefficients of the hamiltonian system.…
A proposal for the Hamilton-Jacobi theory in the context of the covariant formulation of Hamiltonian systems is done. The current approach consists in applying Dirac's method to the corresponding action which implies the inclusion of…
In this paper we study the existence of sufficiently regular representations of Hamilton-Jacobi equations in optimal control theory with the compact control set. We introduce a new method to construct representations for a wide class of…
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…