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.

Generalized Lyapunov Equation Approach to State-Dependent Stochastic Stabilization/Detectability Criterion

Abstract: In this paper, the generalized Lyapunov equation approach is used to study stochastic stabilization/detectability with state-multiplicative noise. Some practical test criteria for stochastic stabilization and detectability, such as stochastic Popov-Belevitch-Hautus criterion for exact detectability, are obtained. Moreover, useful properties of the generalized Lyapunov equation are derived based on critical stability and exact detectability introduced in this paper. As applications, first, the stochastic linear quadratic regulator as well as the related generalized algebraic Riccati equation are discussed extensively. Second, the infinite horizon stochastic H 2/H infin control with state- and control-dependent noise is also investigated, which extends and improves the recently published results.

Position and attitude control of a spacecraft using the state-dependent Riccati equation technique

Abstract: Spacecraft which are required to remove space debris or collect disabled satellites must be able to achieve the attitude of the target while being positioned at a desired distance from the target. The six degree of freedom motion of a spacecraft performing rotational and translational maneuvers has nonlinear equations of motion. The state-dependent Riccati equation method of nonlinear regulation is used to control the position and attitude of a spacecraft in the proximity of a tumbling target. A six degree of freedom simulation of the spacecraft and target are utilized to demonstrate the effectiveness of the controller.

Linear Optimal FIR Estimation of Discrete Time-Invariant State-Space Models

Abstract: This paper addresses a general p-shift linear optimal finite impulse response (FIR) estimator intended for solving universally the problems of filtering (p = 0), smoothing (p 0) of discrete time-invariant models in state space. An optimal solution is found in the batch form with the initial mean square state function self-determined by solving the discrete algebraic Riccati equation. An unbiased solution represented both in the batch and recursive forms does not involve any knowledge about noise and initial state. The mean square errors in both the optimal and unbiased estimates are found via the noise power gain (NPG) and a recursive algorithm for fast computation of the NPG is supplied. Applications are given for FIR filtering with fixed, receding, and full averaging horizons.

Designing stabilizing controllers for uncertain systems using the Riccati equation approach

Abstract: A useful technique for determining a linear feedback control law stabilizes an uncertain system is the Riccati-equation approach of I.R. Petersen and C.V. Hollot (1986). They consider systems with time-varying uncertainty in the system matrix and obtain the constant feedback gains for the linear stabilizing controller in terms of the solutions of a Riccati equation. The technique is extended to include problems with time-varying uncertainty in the input connection matrix. Several examples are included to demonstrate the efficacy of this result. >

Remarks on the Control of Discrete-Time Distributed Parameter Systems

Abstract: The aim of this paper is to investigate limit properties of the infinite-dimensional control system described by a difference equation with a quadratic cost functional Some related results of independent interest concerning stability and the Riccati operator difference equation are given also