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.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, the nonlinear Schrodinger equation, describing the propagation of ultra-short optical solitons through parabolic law medium, has been studied analytically, and perturbations that are third-order dispersion, fourth-order dispatch, and self-steepening are taken into account.
Abstract: The nonlinear Schrodinger equation, describing the propagation of ultra-short optical solitons through parabolic law medium, has been studied analytically. The perturbations that are third-order dispersion, fourth-order dispersion, and self-steepening are taken into account. The Ricatti equation expansion approach and Ansatz method are applied. Finally, Bright, dark as well as singular solitons are constructed under some constraint conditions.
115 citations
TL;DR: In this article, the fractional derivatives in the sense of modified Riemann-Liouville derivative and the Backlund transformation of fractional Riccati equation are employed for constructing the exact solutions of nonlinear fractional partial differential equations.
114 citations
TL;DR: In this article, a Riccati substitution was proposed for discrete-time optimal control problems with Bolza objective functions, which produces the Newton step exactly, even when the dynamical equations are nonlinear.
Abstract: Naive implementations of Newton's method for unconstrainedN-stage discrete-time optimal control problems with Bolza objective functions tend to increase in cost likeN
3 asN increases. However, if the inherent recursive structure of the Bolza problem is properly exploited, the cost of computing a Newton step will increase only linearly withN. The efficient Newton implementation scheme proposed here is similar to Mayne's DDP (differential dynamic programming) method but produces the Newton step exactly, even when the dynamical equations are nonlinear. The proposed scheme is also related to a Riccati treatment of the linear, two-point boundary-value problems that characterize optimal solutions. For discrete-time problems, the dynamic programming approach and the Riccati substitution differ in an interesting way; however, these differences essentially vanish in the continuous-time limit.
114 citations
Book•
01 Apr 1993
TL;DR: In this article, the authors present a parallel algorithm for solving algebraic Riccati Equation and a linear regression model of an F-8 aircraft with an LQG controller.
Abstract: One - Theoretical Concepts.- 2. Linear-Quadratic Control Problems.- 2.1 Introduction.- 2.2 Recursive Methods for Singularly Perturbed Linear Continuous Systems.- 2.2.1 Parallel Algorithm for Solving Algebraic Lyapunov Equation.- 2.2.2 Parallel Algorithm for Solving Algebraic Riccati Equation.- 2.2.3 Case Study: Magnetic Tape Control Problem.- 2.3 Recursive Methods for Weakly Coupled Linear Continuous Systems.- 2.3.1 Parallel Algorithm for Solving Algebraic LyapIIDov Equation.- 2.3.2 Parallel Algorithm for Solving Algebraic Riccati Equation.- 2.4 Approximate Linear Regulator Problem for Continuous Systems.- 2.5 Recursive Methods for Singularly Perturbed Linear Discrete Systems.- 2.5.1 Parallel Algorithm for Solving Algebraic Lyapunov Equation.- 2.5.2 Case Study: An F-8 Aircraft.- 2.5.3 Parallel Algorithm for Solving Algebraic Riccati Equation.- 2.6 Approximate Linear Regulator for Discrete Systems.- 2.6.1 Case Study: Discrete Model of An F-8 Aircraft.- 2.7 Recursive Methods for Weakly Coupled Linear Discrete Systems.- 2.7.1 Parallel Algorithm for Solving Discrete Algebraic Lyapunov Equation.- 2.7.2 Case Study: Discrete Catalytic Cracker.- 2.7.3 Parallel Algorithm for Solving Algebraic Riccati Equation.- 2.7.4 Case Study: Discrete Model of a Chemical Plant.- 2.8 Notes and Comments.- 3. Decoupling Transformations.- 3.1 Introduction.- 3.2 Decoupling Transformation for Singularly Perturbed Linear Systems.- 3.3 Decoupling Transformation for Weakly Coupled Linear Systems.- 3.4 New Versions of Decoupling Transformations.- 3.4.1 New Decoupling Transformation for Linear Weakly Coupled System.- 3.4.2 New Decoupling Transformation for Linear Singularly Perturned Systems.- 3.5 Decomposition of the Differential Lyapunov Equations.- 3.6 Boundary Value Problem for Linear Continuous Weakly Coupled System.- 3.7 Boundary Value Problem for Linear Discrete-Time Weakly Coupled System.- 4. Output feedback control.- 4.1. Introduction.- 4.2 Output Feedback for Singularly Perturbed Linear Systems.- 4.3 Case Study: Fluid Catalytic Cracker.- 4.4 Output Feedback for Linear Weakly Coupled Systems.- 4.5 Case Study: Twelve Plate Absorption Column.- 5. Linear Stochastic Systems.- 5.1 Recursive Approach to Singularly Perturbed Linear Stochastic Systems.- 5.2 Case Study: F-S Aircraft LQG Controller.- 5.3 Recursive Approach to Weakly Coupled Linear Stochastic system.- 5.4 Case Study: Electric Power System.- 5.5 Parallel Reduced-Order Controllers for Stochastic Linear Discrete Singularly Perturbed Systems.- 5.6 Case Study: Discrete Steam Power System.- 5.7 Linear-Quadratic Gaussian Control of Discrete Weakly Coupled Systems at Steady State.- 5.8 Case Study: Distillation Column.- Appendix 5.1.- 6. Open-Loop Optimal Control Problems.- 6.1 Open-Loop Singularly Perturbed Control Problem.- 6.2 Case Study: Magnetic Tape Control.- 6.3 Open-Loop Weakly Coupled Optimal Control Problem.- 6.4 Case Study: Distillation Column.- 6.5 Open-Loop Discrete Singularly Perturbed Control Problem.- 6.6 Case Study: F-8 Aircraft Control Problem.- 6.7 Open-Loop Discrete Weakly Coupled Control Problem.- 6.8 Numerical Example.- 6.9 Conclusion.- Appendix 6.1.- Appendix 6.2.- Appendix 6.3.- Appendix 6.4.- 7. Exact Decompositions of Algebraic Riccati Equations.- 7.1 The Exact Decomposition of the Singularly Perturbed Algebraic Riccati Equation.- 7.2 Numerical Example.- 7.3 The Exact Decomposition of the Weakly Coupled Algebraic Riccati Equation.- 7.4 Case Study: A Satellite Control Problem.- 7.5 Conclusion.- Appendix 7.1.- Appendix 7.2.- Appendix 7.3.- 8. Differential and Difference Riccati Equations.- 8.1 Recursive Solution of the Singularly Perturbed Differential Riccati Equation.- 8.2 Case Study: A Synchronous Machine Connected to an Infinite Bus.- 8.3 Recursive Solution of the Riccati Differential Equation of Weakly Coupled Systems.- 8.4 Case Study: Gas Absorber.- 8.5 Reduced-Order Solution of the Singularly Perturbed Matrix Difference Riccati Equation.- 8.6 Case Study: Linearized Discrete Model of an F-8 Aircraft.- 8.7 Reduced-Order Solution of the Weakly Coupled Matrix Difference Riccati Equation.- 8.8 Numerical Example.- Appendix 8.1.- Appendix 8.2.- Appendix 8.3.- Appendix 8.4.- Two - Applications.- 9. Quasi Singularly Perturbed and Weakly Coupled Linear Systems.- 9.1 Linear Control of Quasi Singularly Perturbed Hydro Power Plants.- 9.2 Case Study: Hydro Power Plant.- 9.2.1 Weakly Controlled Fast Modes Structure.- 9.2.2 Strongly Controlled Slow Modes Structure.- 9.2.3 Weakly Controlled Fast Modes and Strongly Controlled Slow Modes Structure.- 9.3 Reduced-Order Design of Optimal Controller for Quasi Weakly Coupled Linear System.- 9.4 Case Studies.- 9.4.1 Chemical Reactor.- 9.4.2 F-4 Fighter Aircraft.- 9.4.3 Multimachine Power System.- 9.5 Reduced-Order Solution for a Class of Linear-Quadratic Optimal Control Problems.- 9.5.1 Numerical Example.- 9.6 Case Studies.- 9.6.1 Case Study 1: L-1011 Fighter Aircraft.- 9.6.2 Case Study 2: Distillation Column.- Notes.- Appendix 9.1.- 10. Singularly Perturbed Weakly Coupled Linear Control Systems.- 10.1 Introduction.- 10.2 Singularly Perturbed Weakly Coupled Linear Control Systems.- 10.3 Case Studies.- 10.3.1 Case Study 1: A Model of Supported Beam.- 10.3.2 Case Study 2: A Satellite Control Problem.- 10.4 Quasi Singularly Perturbed Weakly Coupled Linear Control Systems.- 10.5 Case Studies.- 10.6 Conclusion.- Appendix 10.1.- 11. Stochastic Output Feedback of Linear Discrete Systems.- 11.1 Introduction.- 11.2 Output Feedback of Quasi Weakly Coupled Linear Stochastic Discrete Systems.- 11.3 Case Study: Flight Control System for Aircrafts.- 11.4 Output Feedback of Singularly Perturbed Stochastic Discrete Systems.- 11.4.1 Problem Formulation.- 11.4.2 Slow-Fast Lower Order Decomposition.- 1111.5 Case Study: Discrete Model of a Steam Power System.- 12. Applications to Differential Games.- 12.1 Weakly Coupled Linear-Quadratic Nash Games.- 12.2 Solution of Coupled Algebraic Riccati Equations.- 12.2.1 Zeroth-Order Approximation.- 12.2.2 Solution of Higher Order of Accuracy.- 12.3 Numerical Examples.- Appendix 12.1.- Appendix 12.2.- 13. Recursive Approach to High Gain and Cheap Control Problems.- 13.1 Linear-Quadratic Cheap and High Gain Control Problems.- 13.1.1 High Gain Feedback Control.- 13.1.2 Cheap Control Problem.- 13.1.3 Parallel Algorithm for Solving Algebraic Riccati Equations for Cheap Control and High Gain Feedback.- 13.2 Case Study: Large Space Structure.- 13.3 Decomposition of the Open-Loop Cheap Control Problem.- 13.4 Numerical Example.- 13.5 Exact Decomposition of the Algebraic Riccati Equation for Cheap Control Problem.- 13.6 Numerical Example.- Appendix 13.1.- 14. Linear Approach to Bilinear Control Systems.- 14.1 Introduction.- 14.2 Reduced-Order Open Loop Optimal Control of Bilinear Systems.- 14.3 Reduced-Order Closed Loop Optimal Control of Bilinear Systems.- 14.3.1 Composite Near-Optimal Control of Bilinear Systems.- 14.4 Case Study: Induction Motor Drives.- 14.5 Near-Optimal Control of Singularly Perturbed Bilinear Systems.- 14.6 Optimal Control of Weakly Coupled Bilinear Systems.- 14.6.1 Open-Loop Control of Weakly Coupled Bilinear Systems.- 14.6.2 Closed-Loop Control of Weakly Coupled Bilinear Systems.- 14.7 Case Study: A Paper Making Machine.- 14.8 Conclusion.
113 citations
TL;DR: A new necessary and sufficient condition for the existence of a positive semidefinite solution of coupled Riccati equations occurring in jump linear systems is derived by verifying a RicCati inequality.
Abstract: A new necessary and sufficient condition for the existence of a positive semidefinite solution of coupled Riccati equations occurring in jump linear systems is derived. By verifying a Riccati inequality it is shown that such a solution exists; in addition two numerical algorithms are given to compute it. An example is given to illustrate the proposed method. >
113 citations