Off-Policy \({\mathcal {L}}_2\) -Gain Control for Discrete-Time Linear Systems with Dropout

In this paper, we introduce an online, model-free off-policy reinforcement learning algorithm to address the \(\mathcal {L}_2\) -gain control problem in discrete linear networked control systems. The algorithm is specifically proposed to handle information dropout in the feedback loop without knowledge of system dynamics. To deal with this problem, first, we utilize the Smith predictor to overcome the effects of dropout. Then, we obtain the optimal solution by solving the game algebraic Riccati equation (GARE). To enable application in linear networked control systems without requiring knowledge of system dynamics, our proposed approach utilizes measured data along the system trajectories to solve the GARE online. An example of the \(\mathcal {L}_2\) -gain control for an aircraft is given to demonstrate the validity and effectiveness of the proposed algorithm.