To extend the decentralized controller to handle more general plant dynamics, such as nonlinear or time-varying systems, several approaches can be considered. One option is to incorporate adaptive techniques that can adjust the decentralized control strategy based on the observed system behavior. This adaptation can involve updating the local sensitivity information dynamically or adjusting the decentralized control law to account for nonlinearities or time-varying dynamics.
Another approach is to introduce learning mechanisms within each agent to improve the approximation of the sensitivity matrix or to adapt the control inputs based on past experiences. Reinforcement learning or online learning algorithms can be utilized to enhance the performance of the decentralized controller in handling more complex plant dynamics. By continuously updating the local models and control strategies based on real-time data, the decentralized controller can become more robust and effective in optimizing the system's performance.
Furthermore, exploring distributed optimization techniques that can handle non-convex objective functions or constraints can also enhance the capabilities of the decentralized controller in dealing with general plant dynamics. By incorporating advanced optimization algorithms that can handle nonlinearity and time-varying dynamics, the decentralized controller can achieve better performance in optimizing the system's behavior.