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.

A state-space description for GPC controllers

Abstract: Generalized predictive control (GPC)-type control algorithms traditionally derived in the polynomial domain are derived in this paper in the state-space domain, but following the polynomial approach due to Clarke et al. (1987). Relations between the polynomial and state-space parameters are presented. Some possible state-space representations which were used earlier in different publications are discussed. The problem of deriving the GPC algorithm in the state-space domain is solved for the unrestricted case as well as for the case of restricted control and output horizons. Some properties of the state estimate for this problem are presented; in particular, two methods of Kalman filtering—optimal and asymptotic—are proposed. The solution is valid for any possible (minimal or non-minimal) state-space representation. Another approach to this problem is by the ‘dynamic programming method’ and solving the Riccati equation (Bitmead et al. 1990). This approach is also presented in this paper but the me...

On the extended applications of Homogenous Balance Method

Abstract: In this paper, we study the travelling wave reductions for certain (2+1)- and (3+1)-dimensional physically important nonlinear evolutionary equations by using the recently proposed Homogenous Balance Method (HBM). Through this analysis we explore certain new solutions for the equations we have studied.

Open-Loop and Closed-Loop Solvabilities for Stochastic Linear Quadratic Optimal Control Problems

Abstract: This paper is concerned with a stochastic linear quadratic (LQ) optimal control problem. The notions of open-loop and closed-loop solvabilities are introduced. A simple example shows that these two solvabilities are different. Closed-loop solvability is established by means of solvability of the corresponding Riccati equation, which is implied by the uniform convexity of the quadratic cost functional. Conditions ensuring the convexity of the cost functional are discussed, including the issue of how negative the control weighting matrix-valued function $R(\cdot)$ can be. Finiteness of the LQ problem is characterized by the convergence of the solutions to a family of Riccati equations. Then, a minimizing sequence, whose convergence is equivalent to the open-loop solvability of the problem, is constructed. Finally, some illustrative examples are presented.

Recursive structure of noncausal Gauss-Markov random fields

Abstract: An approach is developed for noncausal Gauss-Markov random fields (GMRFs) that enables the use of recursive procedures while retaining the noncausality of the field. Recursive representations are established that are equivalent to the original field. This is achieved by first presenting a canonical representation for GMRFs that is based on the inverse of the covariance matrix, which is called the potential matrix. It is this matrix rather than the field covariance that reflects in a natural way the MRF structure. From its properties, two equivalent one-sided representations are derived, each of which is obtained as the successive iterates of a Riccati-type equation. For homogeneous fields, these unilateral descriptions are symmetrized versions of each other, the study of only one Riccati equation being required. It is proven that this Riccati equation converges at a geometric rate, therefore the one-sided representations are asymptotically invariant. These unilateral representations make it possible to process the fields with well-known recursive techniques such as Kalman-Bucy filters and two-point smoothers. >