In this paper, we present a numerical method for solving large continuous-time algebraic Riccati equations. This method is based on the global FOM algorithm and we call it by global FOM-Riccati-Like (GFRL) algorithm .

This contribution addresses the development of a Linear Quadratic Regulator (LQR) for a set of time-varying hyperbolic PDEs coupled with a set of time-varying ODEs through the boundary. The approach is based on an infinitedimensional Hilbert state-space realization of the system and operator Riccati equation (ORE). In order to solve the optimal control problem, the ORE is converted to a set of ...

This paper is concerned with rational matrix equations occuring in stochastic control that play an analogous role as the algebraic Riccati equation does in deterministic control. We will therefore sometimes refer to these equations as stochastic (algebraic) Riccati equations. A first rigorous treatment of a stochastic Riccati equation from LQ-control theory seems to have been undertaken by Wonh...

The problem of the continuous-time H∞ fixed-lag smoothing over the infinite horizon is studied. The first solution to the problem is derived in terms of one algebraic Riccati equation of the same dimension as in the filtering case and the mechanism by which the performance improvements with respect to the H∞ filtering occur is clarified. It is shown that the H∞ smoother exploits the information...

The aim of this paper is to examine a numerical method for the computation of approximate solution of the continuous-time algebraic Riccati equation using Krylov subspace matrix. First of all, Global Arnoldi process is initiated to construct an orthonormal basis. In addition, Krylov subspace matrix is employed as projection method because it is one of the frequently referred method in the liter...

This paper is concerned with a characterization of all symmetric solutions to the discrete-time algebraic Riccati equation (DARE). Dissipation theory and quadratic difference forms from the behavioral approach play a central role in this paper. Along the line of the continuous-time results due to Trentelman and Rapisarda [H.L. Trentelman, P. Rapisarda, Pick matrix conditions for sign-definite s...

In this paper, we use the continuous Legendre wavelets on the interval [0,1] constructed by Razzaghi M. and Yousefi S. [6] to solve the linear second kind integral equations. We use quadrature formula for the calculation of the products of any functions, which are required in the approximation for the integral equations. Then we reduced the integral equation to the solution of linear algebraic ...

In this paper, the optimal adaptive leader-follower consensus of linear continuous time multi-agent systems is considered. The error dynamics of each player depends on its neighbors’ information. Detailed analysis of online optimal leader-follower consensus under known and unknown dynamics is presented. The introduced reinforcement learning-based algorithms learn online the approximate solution...

Nonsymmetric algebraic Riccati equations for which the four coefficient matrices form an irreducible M -matrix M are considered. The emphasis is on the case where M is an irreducible singular M -matrix, which arises in the study of Markov models. The doubling algorithm is considered for finding the minimal nonnegative solution, the one of practical interest. The algorithm has been recently stud...

In recent years, several bounds have been reported for different measures of the “extent” or “size” of the solution of the algebraic matrix equation arising in control theory, such as the Riccati equation and the Lyapunov equation. This paper collects the bounds that have been presented up to now and summarizes them in an unified form. This will prove particularly convenient for those wishing t...