Reinforcement Learning for Adaptive Optimal Stationary Control of Linear Stochastic Systems

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This paper studies the adaptive optimal stationary control of continuous-time linear stochastic systems with both additive and multiplicative noises, using reinforcement learning techniques. Based on policy iteration, a novel off-policy reinforcement learning algorithm, named optimistic least-squares-based policy iteration, is proposed which is able to find iteratively near-optimal policies of the adaptive optimal stationary control problem directly from input/state data without explicitly identifying any system matrices, starting from an initial admissible control policy. The solutions given by the proposed optimistic least-squares-based policy iteration are proved to converge to a small neighborhood of the optimal solution with probability one, under mild conditions. The application of the proposed algorithm to a triple inverted pendulum example validates its feasibility and effectiveness.

Original languageEnglish (US)
JournalIEEE Transactions on Automatic Control
StateAccepted/In press - 2022


  • Heuristic algorithms
  • Optimal control
  • Performance analysis
  • Process control
  • Reinforcement learning
  • Stochastic processes
  • Stochastic systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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