Control law synthesis for distributed multi-agent systems: Application to active clock distribution networks

International audienceIn this paper, the problem of active clock distribution network synchronization is considered. The network is made of identical oscillators interconnected through a distributed array of phase-locked-loops (PLLs). The problem of the PLL network design is reformulated, from a control theory point of view, as a control law design for a distributed multi-agent system. Inspired by the decentralized control law design methodology using the dissipativity input-output approach, the particular topology of interconnected subsystems is exploited to solve the problem by applying a convex optimization approach involving simple Linear Matrix Inequality (LMI) constraints. After choosing the dissipativity properties which is satisfied by the interconnection matrix, the constraints are transformed into an H ∞ norm constraint on a particular transfer function that must be fulfilled for global stability. Additional constraints on inputs and outputs are introduced in order to ensure the desired performance specifications during the H ∞ control design procedure

Leader-following Formation Control Based on Pursuit Strategies

Abstract-The paper studies formation control of multi-agent systems under a directed acyclic graph. In a directed acyclic graph, the agents without neighbors are leaders and the others are followers. Leaders move in a formation with a time-varying velocity and followers can access the relative positions of their neighbors and the leaders' velocity. A local formation control law is proposed in the paper based on pursuit strategies and necessary and sufficient conditions for stability and convergence are derived. Moreover, the results are extended to the case with arbitrary communication delays, for which the steady-state formation is presented according both the control parameters and time delays

Distributed Adaptive Consensus Tracking Control of Uncertain High-order Nonlinear Systems under Directed Graph Condition

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Adaptive Tracking Control of Second-Order Multiagent Systems with Jointly Connected Topologies

This paper considers a consensus problem of leader-following multiagent system with unknown dynamics and jointly connected topologies. The multiagent system includes a self-active leader with an unknown acceleration and a group of autonomous followers with unknown time-varying disturbances; the network topology associated with the multiagent system is time varying and not strongly connected during each time interval. By using linearly parameterized models to describe the unknown dynamics of the leader and all followers, we propose a decentralized adaptive tracking control protocol by using only the relative position measurements and analyze the stability of the tracking error and convergence of the adaptive parameter estimators with the help of Lyapunov theory. Finally, some simulation results are presented to demonstrate the proposed adaptive tracking control

Adaptive Formation Control of Cooperative Multi-Vehicle Systems

The literature comprises many approaches and results for the formation control of multi-vehicle systems; however, the results established for the cases where the vehicles contain parametric uncertainties are limited. Motivated by the need for explicit characterization of the effects of uncertainties on multi-vehicle formation motions, we study distributed adaptive formation control of multi-vehicle systems in this thesis, focusing on different interrelated sub-objectives. We first examine the cohesive motion control problem of minimally persistent formations of autonomous vehicles. Later, we consider parametric uncertainties in vehicle dynamics in such autonomous vehicle formations. Following an indirect adaptive control approach and exploiting the features of the certainty equivalence principle, we propose control laws to solve maneuvering problem of the formations, robust to parametric modeling uncertainties. Next, as a formation acquisition/closing ranks problem, we study the adaptive station keeping problem, which is defined as positioning an autonomous mobile vehicle $A$ inside a multi-vehicle network, having specified distances from the existing vehicles of the network. In this setting, a single-integrator model is assumed for the kinematics for the vehicle $A$, and $A$ is assumed to have access to only its own position and its continuous distance measurements to the vehicles of the network. We partition the problem into two sub-problems; localization of the existing vehicles of the network using range-only measurements and motion control of $A$ to its desired location within the network with respect to other vehicles. We design an indirect adaptive control scheme, provide formal stability and convergence analysis and numerical simulation results, demonstrating the characteristics and performance of the design. Finally, we study re-design of the proposed station keeping scheme for the more challenging case where the vehicle $A$ has non-holonomic motion dynamics and does not have access to its self-location information. Overall, the thesis comprises methods and solutions to four correlated formation control problems in the direction of achieving a unified distributed adaptive formation control framework for multi-vehicle systems