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.

Factorizations of Transfer Functions

Abstract: This paper is concerned with minimal factorizations of rational matrix functions. The treatment is based on a new geometrical principle. In fact, it is shown that there is a one-to-one correspondence between minimal factorizations on the one hand and certain projections on the other. Considerable attention is given to the problem of stability of a minimal factorization. Also the numerical aspects are discussed. Along the way, a stability theorem for solutions of the matrix Riccati equation is obtained.

The optimal projection equations for reduced-order state estimation

Abstract: First-order necessary conditions for optimal, steady-state, reduced-order state estimation for a linear, time-invariant plant in the presence of correlated disturbance and nonsingular measurement noise are derived in a new and highly simplified form. In contrast to the lone matrix Riccati equation arising in the full-order (Kalman filter) case, the optimal steady-state reduced-order estimator is characterized by three matrix equations (one modified Riccati equation and two modified Lyapunov equations) coupled by a projection whose rank is precisely equal to the order of the estimator and which determines the optimal estimator gains. This coupling is a graphic reminder of the suboptimality of proposed approaches involving either model reduction followed by "full-order" estimator design or full-order estimator design followed by estimator-reduction techniques. The results given here complement recently obtained results which characterize the optimal reduced-order model by means of a pair of coupled modified Lyapunov equations [7] and the optimal fixed-order dynamic compensator by means of a coupled system of two modified Riceati equations and two modified Lyapunov equations [6].

A negative exponential solution for the matrix Riccati equation

Abstract: A new form is presented for the transient solution of the matrix Riccati equation associated with the linear optimal regulator and filter problems for time-invariant plants. The solution is expressed in a form such that the transient terms decay exponentially with time, leaving the steady-state terms. In contrast to the automatic synthesis program (ASP) matrix iteration method, the negative exponential solution does not code essential information in numbers of widely differing magnitudes.

Optimal location of measurements for distributed parameter estimation

Abstract: The problem of optimal measurement locations for state estimation in linear distributed parameter systems is considered. It has previously been shown that the optimal sensor location problem for distributed systems can be posed as an optimal control problem for a system described by the infinite-dimensional matrix Riccati equation for the filter covariance. A more efficient approach based on an upper bound of the filter covariance is developed in the present study. The relationship between the present approach and that of minimizing a measure of the filter covariance is studied. A detailed example is considered, and the results of the two approaches are compared.