H Static Output-Feedback Control Design for Discrete-Time Systems Using Reinforcement Learning

• Published in: IEEE transaction on neural networks and learning systems Vol. 31; no. 2; pp. 396 - 406
• Main Authors: Valadbeigi, Amir Parviz, Sedigh, Ali Khaki, Lewis, F. L.
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.02.2020
• Subjects: <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">H ∞ static output feedback (OPFB); Discrete-time (DT) systems; Games; Heuristic algorithms; Learning systems; Optimal control; Performance analysis; reinforcement learning (RL); Uncertainty
• ISSN: 2162-237X; 2162-2388
• DOI: 10.1109/TNNLS.2019.2901889

This paper provides necessary and sufficient conditions for the existence of the static output-feedback (OPFB) solution to the H ∞ control problem for linear discrete-time systems. It is shown that the solution of the static OPFB H ∞ control is a Nash equilibrium point. Furthermore, a Q-learning algorithm is developed to find the H ∞ OPFB solution online using data measured along the system trajectories and without knowing the system matrices. This is achieved by solving a game algebraic Riccati equation online and using the measured data. A simulation example shows the effectiveness of the proposed method.