Decentralized Tracking Control of Interconnected Nonlinear Systems with Unmatched External Disturbances

In this paper, we develop a decentralized tracking control (DTC) strategy to stabilize a class of continuous-time nonlinear interconnected large-scale systems in the presence of unmatched external disturbances. This strategy is derived from an online learning approach of optimal control. Initially, the DTC problem is formulated to ensure both tracking control of isolated subsystems and the overall stability of the large-scale system. By combining the tracking error with the reference trajectory, some augmented systems are constructed and then the DTC design is transformed into an optimal control problem. Considering external disturbances, we formulated it as a two-player zero-sum game. Critic neural networks are utilized to solve the Hamilton-Jacobi-Isaacs equation. This approach allows for the estimation of Nash equilibrium solution that encompasses both the optimal control law and the worst-case disturbance law. Notably, a novel gradient descent strategy with momentum is established to tune the weights of the critic neural network for approximating the cost function better. Finally, an experimental simulation is provided to verify the effectiveness of the developed DTC scheme.