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Algebraic Riccati equations
Peter Lancaster,Leiba Rodman +1 more
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TLDR
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 Indexread more
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Essentials of Robust Control
Kemin Zhou,John Doyle +1 more
TL;DR: In this article, the authors introduce linear algebraic Riccati Equations and linear systems with Ha spaces and balance model reduction, and Ha Loop Shaping, and Controller Reduction.
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Network Information Theory
Abbas El Gamal,Young-Han Kim +1 more
TL;DR: In this article, a comprehensive treatment of network information theory and its applications is provided, which provides the first unified coverage of both classical and recent results, including successive cancellation and superposition coding, MIMO wireless communication, network coding and cooperative relaying.
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Reinforcement learning and adaptive dynamic programming for feedback control
Frank L. Lewis,Draguna Vrabie +1 more
TL;DR: This work describes mathematical formulations for reinforcement learning and a practical implementation method known as adaptive dynamic programming that give insight into the design of controllers for man-made engineered systems that both learn and exhibit optimal behavior.
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Discrete-Time Nonlinear HJB Solution Using Approximate Dynamic Programming: Convergence Proof
TL;DR: It is shown that HDP converges to the optimal control and the optimal value function that solves the Hamilton-Jacobi-Bellman equation appearing in infinite-horizon discrete-time (DT) nonlinear optimal control.
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Reinforcement Learning and Feedback Control: Using Natural Decision Methods to Design Optimal Adaptive Controllers
TL;DR: In this article, the authors describe the use of reinforcement learning to design feedback controllers for discrete and continuous-time dynamical systems that combine features of adaptive control and optimal control, which are not usually designed to be optimal in the sense of minimizing user-prescribed performance functions.
References
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Journal ArticleDOI
Exact controllability, stabilization and perturbations for distributed systems
TL;DR: In this paper, a systematic method (called HUM, for Hilbert Uniqueness Method) is introduced for exact controllability of distributed systems, of hyperbolic type or for Petrowsky systems (like plate equations).
Journal Article
Non homogeneous boundary value problems for second order hyperbolic operators
TL;DR: Soit A(x,t) un operateur elliptique d'ordre 2 sur Ω ouvert borne de R n a frontiere Γ lisse On etudie des problemes de regularite sur un intervalle fini [0,T], T<∞ du probleme hyperbolique d'' d''ORDre 2 mixte a conditions aux limites de Dirichlet as discussed by the authors.
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Infinite-dimensional linear systems with unbounded control and observation: a functional analytic approach
TL;DR: In this article, a unified framework for the functional analytic representation of infinite dimensional linear systems with unbounded input and output operators is developed, based on which new results are derived on the wellposedness of feedback systems and on the linear quadratic control problem.
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Decay of solutions of wave equations in a bounded region with boundary dissipation
John E. Lagnese,John E. Lagnese +1 more
TL;DR: In this article, an energy decay rate was obtained for solutions of wave type equations in a bounded region in Rn whose boundary consists partly of a nontrapping reflecting surface and partly of an energy absorbing surface.