Yu Jiang

Bio: Yu Jiang is an academic researcher from New York University. The author has contributed to research in topics: Dynamic programming & Optimal control. The author has an hindex of 18, co-authored 45 publications receiving 2278 citations. Previous affiliations of Yu Jiang include Mitsubishi Electric Research Laboratories & South China University of Technology.

Robust Adaptive Dynamic Programming and Feedback Stabilization of Nonlinear Systems

Abstract: This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The proposed RADP methodology can be viewed as an extension of ADP to uncertain nonlinear systems. Practical learning algorithms are developed in this paper, and have been applied to the controller design problems for a jet engine and a one-machine power system.

Global Adaptive Dynamic Programming for Continuous-Time Nonlinear Systems

Abstract: This paper presents a novel method of global adaptive dynamic programming (ADP) for the adaptive optimal control of nonlinear polynomial systems. The strategy consists of relaxing the problem of solving the Hamilton-Jacobi-Bellman (HJB) equation to an optimization problem, which is solved via a new policy iteration method. The proposed method distinguishes from previously known nonlinear ADP methods in that the neural network approximation is avoided, giving rise to significant computational improvement. Instead of semiglobally or locally stabilizing, the resultant control policy is globally stabilizing for a general class of nonlinear polynomial systems. Furthermore, in the absence of the a priori knowledge of the system dynamics, an online learning method is devised to implement the proposed policy iteration technique by generalizing the current ADP theory. Finally, three numerical examples are provided to validate the effectiveness of the proposed method.

Approximation theory and methods, by M. J. D. Powell. Pp 339. £25 (hardcover), £8·50 (paperback). 1981. ISBN 0-521-22472-1/29514-9 (Cambridge University Press)

Abstract: Preface 1. The approximation problem and existence of best approximations 2. The uniqueness of best approximations 3. Approximation operators and some approximating functions 4. Polynomial interpolation 5. Divided differences 6. The uniform convergence of polynomial approximations 7. The theory of minimax approximation 8. The exchange algorithm 9. The convergence of the exchange algorithm 10. Rational approximation by the exchange algorithm 11. Least squares approximation 12. Properties of orthogonal polynomials 13. Approximation of periodic functions 14. The theory of best L1 approximation 15. An example of L1 approximation and the discrete case 16. The order of convergence of polynomial approximations 17. The uniform boundedness theorem 18. Interpolation by piecewise polynomials 19. B-splines 20. Convergence properties of spline approximations 21. Knot positions and the calculation of spline approximations 22. The Peano kernel theorem 23. Natural and perfect splines 24. Optimal interpolation Appendices Index.

Optimal and Autonomous Control Using Reinforcement Learning: A Survey

Abstract: This paper reviews the current state of the art on reinforcement learning (RL)-based feedback control solutions to optimal regulation and tracking of single and multiagent systems. Existing RL solutions to both optimal $\mathcal {H}_{2}$ and $\mathcal {H}_\infty $ control problems, as well as graphical games, will be reviewed. RL methods learn the solution to optimal control and game problems online and using measured data along the system trajectories. We discuss Q-learning and the integral RL algorithm as core algorithms for discrete-time (DT) and continuous-time (CT) systems, respectively. Moreover, we discuss a new direction of off-policy RL for both CT and DT systems. Finally, we review several applications.