Heterogeneous Unknown Multiagent Systems of Different Relative Degrees: A Distributed Optimal Coordination Design

This study delves into the distributed optimal coordination (DOC) problem, where a network comprises agents with different relative degrees. Each agent is equipped with a private cost function. The goal is to steer these agents towards minimizing the global cost function, which aggregates their individual costs. Existing literature often leans on known agent dynamics, which may not faithfully represent real-world scenarios. To bridge this gap, we delve into the DOC problem within a network of linear time-invariant (LTI) agents, where the system matrices remain entirely unknown. Our proposed solution introduces a novel distributed two-layer control policy: the top layer endeavors to find the minimizer and generates tailored reference signals for each agent, while the bottom layer equips each agent with an adaptive controller to track these references. Key assumptions include strongly convex private cost functions with local Lipschitz gradients. Under these conditions, our control policy guarantees asymptotic consensus on the global minimizer within the network. Moreover, the control policy operates fully distributedly, relying solely on private and neighbor information for execution. Theoretical insights are substantiated through simulations, encompassing both numerical and practical examples involving speed control of a multimotor network, thereby affirming the efficacy of our approach in practical settings.