articleIEEE Transactions on Neural Networks and Learning SystemsJul 21, 2015Closed access

<inline-formula> <tex-math notation="LaTeX">$ {H}_{ {\infty }}$ </tex-math></inline-formula> Tracking Control of Completely Unknown Continuous-Time Systems via Off-Policy Reinforcement Learning

HMHamidreza ModaresFLFrank L. LewisZJZhong‐Ping Jiang

Northeastern University · New York University

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Abstract

This paper deals with the design of an H ∞ tracking controller for nonlinear continuous-time systems with completely unknown dynamics. A general bounded L2 -gain tracking problem with a discounted performance function is introduced for the H ∞ tracking. A tracking Hamilton-Jacobi-Isaac (HJI) equation is then developed that gives a Nash equilibrium solution to the associated min-max optimization problem. A rigorous analysis of bounded L2 -gain and stability of the control solution obtained by solving the tracking HJI equation is provided. An upper-bound is found for the discount factor to assure local asymptotic stability of the tracking error dynamics. An off-policy reinforcement learning algorithm is used to…

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Topics
Keywords
  • Bounded function
  • Tracking (education)
  • Mathematics
  • Controller (irrigation)
  • Convergence (economics)
  • Tracking error
  • Reinforcement learning
  • Stability (learning theory)
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