The problem of designing an Extended Regulator is defined as designing an algorithm that can adjust the optimal regulator gains for a time-variant linear system appropriately to match the variations in system parameters with time. Due to conditions of positive definiteness on the unknown variable in the Riccati equation for quadratic optimal control it is possible to show that repetitive iterat...

The multidelays linear control systems described by difference differential equations are often studied in modern control theory. In this paper, the delay-independent stabilization algebraic criteria and the theorem of delay-independent stabilization for linear systems with multiple time-delays are established by using the Lyapunov functional and the Riccati algebra matrix equation in the matri...

A brief presentation of the basic concepts in quantum probability theory is given in comparison to the classical one. The notion of quantum white noise, its explicit representation in Fock space, and necessary results of noncommutative stochastic analysis and integration are outlined. Algebraic differential equations that unify the quantum non Markovian diffusion with continuous non demolition ...

The algebraic Riccati equation plays the central role in the computation of the optimal control in the infinite time deterministic and stochastic linear regulator problem (Theorem 1). The problem of adaptive control of stochastic system combines the problems of identification and control of unknown system [3]. The most desirable solution of a stochastic adaptive control problem is to exhibit a ...

A new method to decide the invertibility of a given high-dimensional function over a domain is presented. The problem arises in the field of verified solution of differential algebraic equations (DAEs) related to the need to perform projections of certain constraint manifolds over large domains. The question of invertibility is reduced to a verified linear algebra problem involving first partia...

We consider the nonsymmetric algebraic Riccati equation for which the four coefficient matrices form an M -matrix. Nonsymmetric algebraic Riccati equations of this type appear in applied probability and transport theory. The minimal nonnegative solution of these equations can be found by Newton’s method and basic fixed-point iterations. The study of these equations is also closely related to th...

We study large-scale, continuous-time linear time-invariant control systems with a sparse or structured state matrix and a relatively small number of inputs and outputs. The main contributions of this paper are numerical algorithms for the solution of large algebraic Lyapunov and Riccati equations and linearquadratic optimal control problems, which arise from such systems. First, we review an a...

‎In this paper‎, ‎a spectral Tau method for solving fractional Riccati‎ ‎differential equations is considered‎. ‎This technique describes‎ ‎converting of a given fractional Riccati differential equation to a‎ ‎system of nonlinear algebraic equations by using some simple‎ ‎matrices‎. ‎We use fractional derivatives in the Caputo form‎. ‎Convergence analysis of the proposed method is given an...

‎in this paper‎, ‎a spectral tau method for solving fractional riccati‎ ‎differential equations is considered‎. ‎this technique describes‎ ‎converting of a given fractional riccati differential equation to a‎ ‎system of nonlinear algebraic equations by using some simple‎ ‎matrices‎. ‎we use fractional derivatives in the caputo form‎. ‎convergence analysis of the proposed method is given an...

For consensus on measurement-based distributed filtering (CMDF), through infinite fusion operations during each sampling interval, node in the sensor network can achieve optimal performance with centralized filtering. However, due to limited communication resources physical systems, number of steps cannot be infinite. To deal this issue, present paper analyzes CMDF finite operations. First, by ...