Discrete-Time H₂ Neural Control Using Reinforcement Learning

Abstract

In this article, we discuss <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{2}$ </tex-math></inline-formula> control for unknown nonlinear systems in discrete time. A discrete-time recurrent neural network is used to model the nonlinear system, and then, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{2}$ </tex-math></inline-formula> tracking control is applied based on the neural model. Since this neural <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{2}$ </tex-math></inline-formula> control is very sensitive to the neural modeling error, we use reinforcement learning and another neural approximator to improve tracking accuracy and robustness of the controller. The stabilities of the neural identifier and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{2}$ </tex-math></inline-formula> tracking control are proven. The convergence of the approach is also given. The proposed method is validated with the control of the pan and tilt robot and the surge tank.