We introduce a ultradiscretization with parity variables of the q-difference Painlevé VI system of equations. We show that ultradiscrete limit of Riccati-type solutions of q-Painlevé VI satisfies the ultradiscrete Painlevé VI system of equations with the parity variables, which is valid by using the parity variables. We study some solutions of the ultradiscrete Riccati-type equation and those o...

Abstract—In this paper Algebraic Riccati matrix equation is used for Eigen-decomposition of special structured matrices. This is achieved by similarity transformation and then using algebraic riccati matrix equation to triangulation of matrices. The process is decomposition of matrices into small and specially structured submatrices with low dimensions for fast and easy finding of Eigenpairs. N...

Under the generic assumption that zero is in the resolvent set of the generator, we show that the optimal control problem for a stable well-posed linear system is equivalent to a control problem for its reciprocal system which has bounded generating operators. Consequently, the operator X that defines the optimal cost satisfies a Riccati equation with bounded operators. Previous results needed ...

This paper presents a simple and efficient method for determining the solution of Riccati differential equation with coefficients rational. In case the differential Galois group of the differential equation (E l) : y = ry, r ∈ C(x) is reducible, we look for the rational solutions of Riccati differential equation θ + θ 2 = r, by reducing the number of check to be made and by accelerating the sea...

Here ordinary differential equations of third and higher order are considered; in particular, a class of equations which can be solved by quadratures is exploited. Indeed, crucial to obtain our result is the property of the Riccati equation, according to which, given one particular solution, then its general solution can be determined explicitly. Thus, what we term the “Riccati” Property is int...

We consider a splitting-based approximation of the abstract Riccati equation in the setting of Hilbert–Schmidt operators. The Riccati equation arises in many different areas and is important within the field of optimal control. While convergence of different methods for approximating the Riccati equation is discussed in several studies, none of them rigorously prove an order of convergence. In ...

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...

We describe a procedure based on the Krawczyk method to compute a verified enclosure for the stabilizing solution of a continuoustime algebraic Riccati equation A∗X + XA + Q = XGX, building on the work of [B. Hashemi, SCAN 2012] and adding several modifications to the Krawczyk procedure. Moreover, we describe a new O(n) direct method for verification, based on a fixed-point formulation of the e...

We consider an optimal control problem with indeenite cost for an abstract model which covers in particular hyperbolic and hyperbolic-like systems in a general bounded domain. Necessary and suucient conditions are given for the synthesis of the optimal control, which is given in terms of the Riccati operator arising from a nonstandard Riccati equation. The theory also extends a nite-dimensional...