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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
More filters
Proceedings ArticleDOI
04 Jun 1997
TL;DR: An overview of state-dependent Riccati equation (SDRE) design techniques can be found in this paper, including nonlinear regulation, nonlinear H/sub /spl infin//, SDRE nonlinear h/sub 2/, and nonlinear filtering.
Abstract: State-dependent Riccati equation (SDRE) techniques are rapidly emerging as general design methods which provide a systematic and effective means of designing nonlinear controllers, observers, and filters. This paper provides an overview of several SDRE design techniques including SDRE nonlinear regulation, SDRE nonlinear H/sub /spl infin//, SDRE nonlinear H/sub 2/, and SDRE nonlinear filtering.

452 citations

Journal ArticleDOI
TL;DR: In this article, the standard H∞ optimal control problem using state feedback for smooth nonlinear control systems was studied, and the main theorem obtained roughly states that the L2-induced norm (from disturbances to inputs and outputs) can be made smaller than a constant γ > 0 if the corresponding H ∞ norm for the system linearized at the equilibrium can be reduced by linear state feedback.

450 citations

Book
01 Jan 1968
TL;DR: This chapter discusses filter theory, applications, and applications of filter theory and modeling techniques for free flight and powered flight navigation, and error analyses and sub-optimal modeling.
Abstract: Part I. Theory: Ordinary differential equations and stability Random processes and stochastic models Observability and controllability Filtering theory Global theory of filtering Stochastic stability Optimal filtering for correlated noise processes Approximate optimal non-linear filtering Optimum filtering for discrete time random processes Stochastic control Open questions and historical comments Part II. Applications: Application to navigation Applications of filter theory and modeling techniques Free flight and powered flight navigation Error analyses and sub-optimal modeling Errors in the filtering process Appendix A. Least squares curve fitting Appendix B. Probability review References Appendix C. The Riccati equation and its bounds Appendix D. Further references Index.

445 citations

Journal ArticleDOI
01 Mar 2007
TL;DR: It is proven that the algorithm ends up to be a model-free iterative algorithm to solve the (GARE) of the linear quadratic discrete-time zero-sum game.
Abstract: In this paper, the optimal strategies for discrete-time linear system quadratic zero-sum games related to the H-infinity optimal control problem are solved in forward time without knowing the system dynamical matrices. The idea is to solve for an action dependent value function Q(x,u,w) of the zero-sum game instead of solving for the state dependent value function V(x) which satisfies a corresponding game algebraic Riccati equation (GARE). Since the state and actions spaces are continuous, two action networks and one critic network are used that are adaptively tuned in forward time using adaptive critic methods. The result is a Q-learning approximate dynamic programming model-free approach that solves the zero-sum game forward in time. It is shown that the critic converges to the game value function and the action networks converge to the Nash equilibrium of the game. Proofs of convergence of the algorithm are shown. It is proven that the algorithm ends up to be a model-free iterative algorithm to solve the (GARE) of the linear quadratic discrete-time zero-sum game. The effectiveness of this method is shown by performing an H-infinity control autopilot design for an F-16 aircraft.

441 citations

Journal ArticleDOI
Pascal Gahinet1
TL;DR: In this article, the problem of reliable computation of H"~ controllers given a solution (R, S) of the characteristic system of linear matrix inequalities (LMI) is addressed.

434 citations


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