Riccati equation

About: Riccati equation is a research topic. Over the lifetime, 10428 publications have been published within this topic receiving 210015 citations. The topic is also known as: Riccati's differential equation.

Inexact Kleinman-Newton Method for Riccati Equations

Abstract: In this paper we consider the numerical solution of the algebraic Riccati equation using Newton's method. We propose an inexact variant which allows one control the number of the inner iterates used in an iterative solver for each Newton step. Conditions are given under which the monotonicity and global convergence result of Kleinman also hold for the inexact Newton iterates. Numerical results illustrate the efficiency of this method.

Convergence and Stability Properties of the Discrete Riccati Operator Equation and the Associated Optimal Control and Filtering Problems

Abstract: The convergence properties for the solution of the discrete time Riccati matrix equation are extended to Riccati operator equations such as arise in a gyroscope noise filtering problem. Stabilizability and detectability are shown to be necessary and sufficient conditions for the existence of a positive semidefinite solution to the algebraic Riccati equation which has the following properties (i) it is the unique positive semidefinite solution to the algebraic Riccati equation, (ii) it is converged to geometrically in the operator norm by the solution to the discrete Riccati equation from any positive semidefinite initial condition, (iii) the associated closed loop system converges uniformly geometrically to zero and solves the regulator problem, and (iv) the steady state Kalman–Bucy filter associated with the solution to the algebraic Riccati equation is uniformly asymptotically stable in the large. These stability results are then generalized to time-varying problems; also it is shown that even in infini...

Observer design and detection for nonlinear descriptor systems

Abstract: A nonlinear observer is considered for a class of continuous nonlinear descriptor systems subject to unknown inputs and faults. This class is partly characterized by globally Lipschitz nonlinearities, and a member system may be singular and possibly non-causal. The observer structure chosen makes it useful for both state estimation for feedback controls and residual generation for fault detection. Results on the existence of solutions are given and some useful bounds are derived which are important in the observer design, which is based on a transformed system and on the solution of a Riccati equation. The existence, convergence properties and robustness of the observer are investigated by the use of a quadratic Lyapunov function. Conditions are given for a bound to hold on the norm of the transfer function relating the residual error to the disturbance (linear case). A design algorithm is given and applied to the estimation of the states of a flexible joint robot.

Accurate one-dimensional inverse scattering using a nonlinear renormalization technique

Abstract: A nonlinear method based on the inversion of the Riccati equation is presented here for the one-dimensional nondispersive inverse-scattering problem. This method avoids the significant errors in both amplitude and phase that plague most linearized (e.g., Born or its varients) inversion schemes. Instead, a nonlinear approximation to the Riccati equation is used for the accurate determination of the refractive-index amplitude from reflection data. This information is subsequently used to stretch the coordinates so as to remove the phase-accumulation error. The resulting refractive-index reconstructions are therefore accurate both in amplitude and in longitudinal placement as evidenced by the excellent comparison with exact theory. The method is applicable to both continuous and discontinuous refractive profiles and is supported by experimental measurements.