The numerical solution of discrete-time algebraic Ric-cati equations is discussed. We propose to compute an approximate solution of the discrete-time algebraic Riccati equation by the (butterry) SZ algorithm. This solution is then reened by a defect correction method based on Newton's method. The resulting method is very eecient and produces highly accurate results.

A new approach to study the indefinite stochastic linear quadratic (LQ) optimal control problems, which we called the “equivalent cost functional method”, is introduced by Yu [15] in the setup of Hamiltonian system. On the other hand, another important issue along this research direction, is the possible state feedback representation of optimal control and the solvability of associated indefini...

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...

This work proposes and investigates the existence uniqueness of solutions Riccati Fractional Differential Equation (RFDE) with constant coefficients using Banach’s fixed point theorem. theorem is a on contraction mapping norm space. Furthermore, combined Adomian Decomposition Method (ADM) Kamal’s Integral Transform (KIT) used to convert solution (FDE) into an infinite polynomial series. In addi...

We first obtain by analogy with the continuous (differential) case the general solution of a discrete Riccati equation. Our results can be considered the discrete analog of Miel-nik's construction in supersymmetric quantum mechanics [J. Moreover, we establish the full equivalence of our discrete Riccati equation and a corresponding homogeneous second order discrete linear equation. We present a...

A stochastic linear quadratic (LQ) control problem is indefinite when the cost weighting matrices for the state and the control are allowed to be indefinite. Indefinite stochastic LQ theory has been extensively developed and has found interesting applications in finance. However, there remains an outstanding open problem, which is to identify an appropriate Riccati-type equation whose solvabili...

This paper investigates the use of state-dependent Riccati equation control for closed-loop guidance of the hypersonic phase of atmospheric entry. Included are a discussion of the development of the state-dependent Riccati equations, their outgrowth from Hamilton-Jacobi-Bellman theory, a discussion of the closed-loop nonlinear system’s closed-loop stability and robustness from both a theoretica...

As in the finite-dimensional case, the appropriate state feedback for the infinitedimensional H disturbance-attenuation problem may be calculated by solving a Riccati equation. This operator Riccati equation can rarely be solved exactly. We approximate the original infinitedimensional system by a sequence of finite-dimensional systems and consider the corresponding finite-dimensional disturbanc...

Urban industrial water system parameter fluctuation producing uncertainty may not occur in a control input channel, can be applied mismatching uncertain system to describe. Based on Lyapunov direct method and linear matrix inequality, design the urban industrial water mismatching uncertain system feedback stabilization robust control scheme. Avoid the defects that the feedback stabilization con...

State-dependent Riccati equation based controllers are becoming increasingly popular because of having attractive properties like optimality, stability and robustness. This paper focuses on the design of a roll autopilot for a fin stabilized and canard controlled 122mm artillery rocket using state-dependent Riccati equation technique. Initial spin is imparted to rocket during launch and it quic...