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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.


Papers
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Journal ArticleDOI
TL;DR: In this paper, the authors apply the methods developed in [1] and [2] to solve the problem of optimal stochastic control for a linear quadratic system.
Abstract: The purpose of this paper is to apply the methods developed in [1] and [2] to solve the problem of optimal stochastic control for a linear quadratic system.After proving some preliminary existence results on stochastic differential equations, we show the existence of an optimal control.The introduction of an ad joint variable enables us to derive extremality conditions: the control is thus obtained in random “feedback” form. By using a method close to the one used by Lions in [4] for the control of partial differential equations, a priori majorations are obtained.A formal Riccati equation is then written down, and the existence of its solution is proved under rather general assumptions.For a more detailed treatment of some examples, the reader is referred to [1].

307 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied the problem of H∞-control for linear systems with Markovian jumping parameters and parameter uncertainties, where the jumping rates were assumed to be real, time-varying, norm-bounded, appearing in the state matrix.
Abstract: This paper studies the problem of H∞-control for linear systems with Markovian jumping parameters The jumping parameters considered here are two separable continuous-time, discrete-state Markov processes, one appearing in the system matrices and one appearing in the control variable Our attention is focused on the design of linear state feedback controllers such that both stochastic stability and a prescribed H∞-performance are achieved We also deal with the robust H∞-control problem for linear systems with both Markovian jumping parameters and parameter uncertainties The parameter uncertainties are assumed to be real, time-varying, norm-bounded, appearing in the state matrix Both the finite-horizon and infinite-horizon cases are analyzed We show that the control problems for linear Markovian jumping systems with and without parameter uncertainties can be solved in terms of the solutions to a set of coupled differential Riccati equations for the finite-horizon case or algebraic Riccati equations for the infinite-horizon case Particularly, robust H∞-controllers are also designed when the jumping rates have parameter uncertainties

300 citations

Journal ArticleDOI
TL;DR: A continuous function is constructed via two Riccati equations, and it is shown that this function is a viscosity solution to the HJB equation, enabling one to explicitly obtain the efficient frontier and efficient investment strategies for the original mean-variance problem.
Abstract: This paper is concerned with mean-variance portfolio selection problems in continuous-time under the constraint that short-selling of stocks is prohibited. The problem is formulated as a stochastic optimal linear-quadratic (LQ) control problem. However, this LQ problem is not a conventional one in that the control (portfolio) is constrained to take nonnegative values due to the no-shorting restriction, and thereby the usual Riccati equation approach (involving a "completion of squares") does not apply directly. In addition, the corresponding Hamilton--Jacobi--Bellman (HJB) equation inherently has no smooth solution. To tackle these difficulties, a continuous function is constructed via two Riccati equations, and then it is shown that this function is a viscosity solution to the HJB equation. Solving these Riccati equations enables one to explicitly obtain the efficient frontier and efficient investment strategies for the original mean-variance problem. An example illustrating these results is also presented.

299 citations

Journal ArticleDOI
Laurent Praly1
TL;DR: The global asymptotic stabilization by output feedback for systems whose dynamics are in a feedback form and where the nonlinear terms admit an incremental rate depending only on the measured output is studied.
Abstract: We study the global asymptotic stabilization by output feedback for systems whose dynamics are in a feedback form and where the nonlinear terms admit an incremental rate depending only on the measured output. The output feedback we consider is of the observer-controller type where the design of the controller follows from standard robust backstepping. The novelty is in the observer which is high-gain such as with a gain coming from a Riccati equation.

296 citations

Journal ArticleDOI
TL;DR: In this paper, the authors generalize the notion of stability radius introduced in [1] to allow for structured perturbations and relate the stability radius to the existence of Hermitian solutions of an algebraic Riccati equation.

295 citations


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