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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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Journal ArticleDOI
TL;DR: This work considers the infinite horizon quadratic cost minimization problem for a linear system with finitely many inputs and outputs, and reduces the problem to a symmetric Wiener-Hopf problem, that can be solved by means of a canonical factorization of the symbol.
Abstract: We consider the infinite horizon quadratic cost minimization problem for a linear system with finitely many inputs and outputs. A common approach to treat a problem of this type is to construct a semigroup in an abstract state space, and to use infinite-dimensional control theory. However, this approach is less appealing in the case where there are discrete time delays in the impulse response, because such time delays force both the control operator and the observation operator to be unbounded at the same time. In order to be able to include this case we take an alternative approach. We work in an input-output framework, and reduce the problem to a symmetric Wiener-Hopf problem, that can be solved by means of a canonical factorization of the symbol. In a standard shift semigroup realization this amounts to factorizations of the Riccati operator and the feedback operator into convolution operators and projections. Our approach leads to a new significant discovery: in the case where the impulse response of the system contains discrete time delays, the standard Riccati equation is incorrect; to get the correct Riccati equation the feed-through matrix of the system must be partially replaced by the feed-through matrix of the spectral factor. This means that, before it is even possible to write down the correct Riccati equation, a spectral factorization problem must first be solved to find one of the weighting matrices in this equation.

47 citations

Journal ArticleDOI
TL;DR: The proposed method can handle the presence of input saturation and state constraint, and it is shown that the tracking error converges asymptotically to zero under mild conditions on the discount factor of the corresponding cost function and the desired trajectory.
Abstract: In this brief, a new technique for solving a suboptimal tracking problem for a class of nonlinear dynamical systems is presented Toward this end, an optimal tracking problem using a discounted cost function is defined and a control law with a feedback-feedforward structure is designed A state-dependent Riccati equation (SDRE) framework is used in order to find the gains of both the feedback and the feedforward parts, simultaneously Due to the significant properties of the SDRE technique, the proposed method can handle the presence of input saturation and state constraint It is also shown that the tracking error converges asymptotically to zero under mild conditions on the discount factor of the corresponding cost function and the desired trajectory Two simulation and experimental case studies are also provided to illustrate and demonstrate the effectiveness of our proposed design methodology

47 citations

Journal ArticleDOI
01 Jan 1976
TL;DR: The Riccati equation plays as important a role in scattering theory as it does in linear least squares estimation theory as mentioned in this paper, and a somewhat different framework of treating the Riemannian equation has been developed.
Abstract: The Riccati equation plays as important a role in scattering theory as it does in linear least squares estimation theory. However, in the scattering literature, a somewhat different framework of treating the Riccati equation has been developed. This framework is shown to be appropriate for estimation problems and makes possible simple derivations of known results as well as leading to several new results. Examples include the derivation of backward equations to solve forward Riccati equations, an analysis of the asymptotic behavior of the Riccati equation, the derivation of backward Markovian representations of stochastic processes, and new derivations and new insights into the Chandrasekhar and related Levinson and Cholesky equations.

47 citations

Journal ArticleDOI
TL;DR: The resulting fault-tolerant compensation control scheme is designed based on the closed- loop systems, and therefore has more practical significance than the existing FTC methodologies developed in terms of the open-loop systems.
Abstract: For digital proportional–integral–derivative control systems with unknown dynamics, the data-driven output-feedback fault-tolerant control (FTC) problem is studied in this paper. In a framework of active FTC, the issue of online recursive identification of the residual generator, the state observer, and the observability canonical form of the plant under consideration is addressed; the problem of reconfiguration of the data-driven fault-tolerant compensation controller with $L_2$ -gain properties is also dealt with by means of the above-obtained results, the prefilter and the Riccati equation related to $H_{\infty }$ control so as to accommodate faults and ensure tracking performance. The resulting fault-tolerant compensation control scheme is designed based on the closed-loop systems, and therefore has more practical significance than the existing FTC methodologies developed in terms of the open-loop systems. Finally, the effectiveness of the proposed FTC approach is validated by the speed control experiment on a dc motor.

47 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023153
2022335
2021203
2020240
2019223
2018231