This article considers the containment of heterogeneous linear time-invariant multi-human multi-agent systems with a distributed dynamic state feedback control law. The unique aspect of this problem lies in the presence of multiple human operators. Each operator commands a subset of the agents while observing the same or a different subset. Commanding based on their observation approach of the human operators makes them integral components of the network rather than simple providers of reference signals. This setup requires a new set of conditions distinct from the standard containment problem literature. Considering fixed-time delays in human reactions and information exchange between human operators and agents, it is shown that the containment problem is solved if the delayed closed-loop system is exponentially stable under the new set of conditions. Encompassing different graphs, system scales, and human parameters, we evaluate the largest delay without losing the closed-loop stability under various scenarios through numerical examples. The results highlight the potential for effective coordination of a large fleet of autonomous vehicles facilitated by a limited number of human operators.

The contribution of this paper is a control synthesis and stability verification framework for linear time-invariant multiagent systems with heterogeneous actuator dynamics and system uncertainties. In particular, we first propose a distributed adaptive control architecture in a leader-follower setting for this class of high-order multiagent systems. The proposed architecture uses a hedging method, which alters the ideal reference model dynamics of each agent in order to ensure correct adaptation in the presence of heterogeneous actuator dynamics of these agents. We then use Lyapunov stability theory and linear matrix inequalities to analyse the proposed architecture. This analysis reveals a stability condition, where evaluation of this condition with respect to a given graph topology allows stability verification of the controlled multiagent system. From a practical point of view, this condition also shows a fundamental tradeoff between heterogeneous agent actuation capabilities and unknown parameters in agent dynamics. Several illustrative numerical examples are also provided to demonstrate the efficacy of the proposed architecture.

Stability analyses of discrete-time adaptive control algorithms are generally predicated on quadratic Lyapunov-based frameworks that result in unavoidable complexity due to the resulting terms in the Lyapunov difference equations. This prevents generalizations of valuable continuous-time adaptive control results to their discrete-time settings. To this end, one important generalization is the consideration of actuator dynamics, which is present in any uncertain dynamical system. To address this problem, we propose a novel discrete-time adaptive control architecture predicated on the hedging method and a new projection operator. A logarithmic Lyapunov function is used for proving the asymptotic stability of the error between uncertain dynamical system states and hedging-based reference model states. An illustrative numerical example is then presented to demonstrate the efficacy of the proposed architecture.

Discrete-time architectures offer a distinct advantage over their continuous counterparts, as they can be seamlessly implemented on embedded hardware without the necessity for discretization processes. Yet, because of the difficulty of ensuring Lyapunov difference expressions, their designs, which are based on quadratic Lyapunov-based frameworks, are highly complex. As a result, various existing continuous-time results using adaptive control methods to deal with system uncertainties and coupled dynamics in agents of a multiagent system cannot be directly applied to the discrete-time context. Furthermore, compared to their continuous-time equivalent, discrete-time information exchange based on periodic time intervals is more practical in the control of multiagent systems. Motivated by these standpoints, in this paper, we first introduce a discrete-time adaptive control architecture designed for uncertain scalar multiagent systems without coupled dynamics as a preliminary result. We then introduce another discrete-time adaptive control approach for uncertain multiagent systems in the presence of coupled dynamics. Our approach incorporates observer dynamics to manage unmeasurable coupled dynamics, along with a user-assigned Laplacian matrix to induce cooperative behaviors among multiple agents. Our solution includes Lyapunov analysis with logarithmic and quadratic Lyapunov functions for guaranteeing asymptotic stability with both controllers. To demonstrate the effectiveness of the proposed control architectures, we provide an illustrative example. The illustrative numerical example shows that the standard discrete-time adaptive control in the absence of observer dynamics cannot guarantee the reference state vector tracking, while the proposed discrete-time adaptive control can ensure the tracking objective.

In this paper, we focus on designing a model reference adaptive control-based distributed control law to drive a set of agents with double-integrator dynamics in a leader–follower fashion in the presence of system anomalies such as agent-based uncertainties, unknown control effectiveness, and actuator dynamics. In particular, we introduce a novel hedging-based reference model with second-order dynamics to allow an adaptation in the presence of actuator dynamics. We show the stability of the overall closed-loop multi-agent system by utilizing the Lyapunov Stability Theory, where we analyze the stability condition by using the Linear Matrix Inequalities method to show the boundedness of the reference model and actuator states. Finally, we illustrate the efficacy of the proposed distributed adaptive controller on an undirected and connected line graph in five cases.