Topic
Algebraic Riccati equation
About: Algebraic Riccati equation is a research topic. Over the lifetime, 5434 publications have been published within this topic receiving 102895 citations.
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TL;DR: In this paper, the authors present an algorithm for the stabilization of a class of uncertain linear systems, which is described by state equations which depend on time-varying unknown-but-bounded uncertain parameters.
1,483 citations
1,470 citations
Book•
01 Jan 1995
TL;DR: Geometric theory: the complex case 8.
Abstract: 1. Preliminaries from the theory of matrices 2. Indefinite scalar products 3. Skew-symmetric scalar products 4. Matrix theory and control 5. Linear matrix equations 6. Rational matrix functions 7. Geometric theory: the complex case 8. Geometric theory: the real case 9. Constructive existence and comparison theorems 10. Hermitian solutions and factorizations of rational matrix functions 11. Perturbation theory 12. Geometric theory for the discrete algebraic Riccati equation 13. Constructive existence and comparison theorems 14. Perturbation theory for discrete algebraic Riccati equations 15. Discrete algebraic Riccati equations and matrix pencils 16. Linear-quadratic regulator problems 17. The discrete Kalman filter 18. The total least squares technique 19. Canonical factorization 20. Hoo control problems 21. Contractive rational matrix functions 22. The matrix sign function 23. Structured stability radius Bibliography List of notations Index
1,465 citations
TL;DR: In this paper, the optimal control of linear systems with respect to quadratic performance criteria over an infinite time interval is treated, and the integrand of the performance criterion is allowed to be fully quadratically in the control and the state without necessarily satisfying the definiteness conditions which are usually assumed in the standard regulator problem.
Abstract: The optimal control of linear systems with respect to quadratic performance criteria over an infinite time interval is treated. Both the case in which the terminal state is free and that in which the terminal state is constrained to be zero are treated. The integrand of the performance criterion is allowed to be fully quadratic in the control and the state without necessarily satisfying the definiteness conditions which are usually assumed in the standard regulator problem. Frequency-domain and time-domain conditions for the existence of solutions are derived. The algebraic Riccati equation is then examined, and a complete classification of all its solutions is presented. It is finally shown how the optimal control problems introduced in the beginning of the paper may be solved analytically via the algebraic Riccati equation.
1,436 citations
TL;DR: This book discusses Classical and Modern Control Optimization Optimal Control Historical Tour, Variational Calculus for Discrete-Time Systems, and more.
Abstract: INTRODUCTION Classical and Modern Control Optimization Optimal Control Historical Tour About This Book Chapter Overview Problems CALCULUS OF VARIATIONS AND OPTIMAL CONTROL Basic Concepts Optimum of a Function and a Functional The Basic Variational Problem The Second Variation Extrema of Functions with Conditions Extrema of Functionals with Conditions Variational Approach to Optimal Systems Summary of Variational Approach Problems LINEAR QUADRATIC OPTIMAL CONTROL SYSTEMS I Problem Formulation Finite-Time Linear Quadratic Regulator Analytical Solution to the Matrix Differential Riccati Equation Infinite-Time LQR System I Infinite-Time LQR System II Problems LINEAR QUADRATIC OPTIMAL CONTROL SYSTEMS II Linear Quadratic Tracking System: Finite-Time Case LQT System: Infinite-Time Case Fixed-End-Point Regulator System Frequency-Domain Interpretation Problems DISCRETE-TIME OPTIMAL CONTROL SYSTEMS Variational Calculus for Discrete-Time Systems Discrete-Time Optimal Control Systems Discrete-Time Linear State Regulator Systems Steady-State Regulator System Discrete-Time Linear Quadratic Tracking System Frequency-Domain Interpretation Problems PONTRYAGIN MINIMUM PRINCIPLE Constrained Systems Pontryagin Minimum Principle Dynamic Programming The Hamilton-Jacobi-Bellman Equation LQR System using H-J-B Equation CONSTRAINED OPTIMAL CONTROL SYSTEMS Constrained Optimal Control TOC of a Double Integral System Fuel-Optimal Control Systems Minimum Fuel System: LTI System Energy-Optimal Control Systems Optimal Control Systems with State Constraints Problems APPENDICES Vectors and Matrices State Space Analysis MATLAB Files REFERENCES INDEX
1,259 citations