Topic
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.
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TL;DR: In this paper, the authors derive an inverse optimality result for receding-horizon control schemes using the nonlinear analog of the Fake Riccati equation developed for linear systems.
160 citations
TL;DR: By means of Riccati transformation techniques, the authors established some oscillation criteria for a second order nonlinear dynamic equation on time scales in terms of the coefficients, and gave examples of dynamic equations to which previously known oscillation rules are not applicable.
Abstract: By means of Riccati transformation techniques, we establish some oscillation criteria for a second order nonlinear dynamic equation on time scales in terms of the coefficients. We give examples of dynamic equations to which previously known oscillation criteria are not applicable.
159 citations
TL;DR: In this article, a new analytic technique is proposed to solve non-linear Riccati differential equation with fractional order, which provides us with a simple way to adjust and control the convergence region of solution series by introducing an auxiliary parameter.
Abstract: In this paper, based on the homotopy analysis method (HAM), a new analytic technique is proposed to solve non-linear Riccati differential equation with fractional order. Different from all other analytic methods, it provides us with a simple way to adjust and control the convergence region of solution series by introducing an auxiliary parameter ℏ . Besides, it is proved that well-known Adomian’s decomposition method is a special case of the homotopy analysis method when ℏ = −1. This work illustrates the validity and great potential of the homotopy analysis method for the non-linear differential equations with fractional order. The basic ideas of this approach can be widely employed to solve other strongly non-linear problems in fractional calculus.
159 citations
TL;DR: In this article, the authors analyzed the symmetric periodic positive semidefinite (SPPS) solution of the DPRE under appropriate assumptions of stabilizability and detectability of the periodic system.
Abstract: Gives a comprehensive treatment of several important aspects of the discrete-time periodic Riccati equation (DPRE) arising from the prediction problem for linear discrete-time periodic systems. The authors analyze the symmetric periodic positive semidefinite (SPPS) solution of the DPRE under appropriate assumptions of stabilizability and detectability of the periodic system. Among the results obtained are necessary and sufficient conditions for the existence and uniqueness of the SPPS solution and the stability of the resulting closed-loop system. Some of these results can be seen as extensions of the corresponding results for the time-invariant case; however, a number of them contain contributions to the time-invariant case as well. The paper also gives a numerical algorithm based on an iterative linearization procedure for computing the SPPS solution. The algorithm is a periodic version of Kleinman's algorithm for the time-invariant case. >
158 citations
04 Dec 2001
TL;DR: A generalized difference Riccati equation is introduced and it is proved that its solvability is necessary and sufficient for the existence of an optimal control which can be either of state feedback or open-loop form.
Abstract: This paper deals with the discrete-time stochastic LQ problem involving state and control dependent noises, whereas the weighting matrices in the cost function are allowed to be indefinite. We show that the well-posedness and the attainability of the LQ problem are equivalent. Furthermore, the set of all optimal controls is identified in terms of the solution to a generalized difference Riccati equation.
158 citations