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Model‐Free H ∞ Control Design for Unknown Continuous‐Time Linear System Using Adaptive Dynamic Programming
Author(s) -
Qin Chunbin,
Zhang Huaguang,
Luo Yanhong
Publication year - 2016
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1102
Subject(s) - algebraic riccati equation , dynamic programming , riccati equation , convergence (economics) , differential game , computer science , sequential game , mathematical optimization , system dynamics , control theory (sociology) , optimal control , algebraic number , state (computer science) , linear quadratic regulator , linear programming , control (management) , game theory , mathematics , differential equation , algorithm , artificial intelligence , mathematical analysis , mathematical economics , economic growth , economics
In this paper, a new online model‐free adaptive dynamic programming algorithm is developed to solve the H ∞ control problem of the continuous‐time linear system with completely unknown system dynamics. Solving the game algebraic Riccati equation, commonly used in H ∞ state feedback control design, is often referred to as a two‐player differential game where one player tries to minimize the predefined performance index while the other tries to maximize it. Using data generated in real time along the system trajectories, this new method can solve online the game algebraic Riccati equation without requiring the full knowledge of system dynamics. A rigorous proof of convergence of the proposed algorithm is given. Finally, simulation studies on two examples demonstrate the effectiveness of the proposed method.