Distributed Adaptive Consensus Control of High Order Unknown Nonlinear Networked Systems with Guaranteed Performance

Adaptive cooperative tracking control with prescribed performance function (PPF) is proposed for high-order nonlinear multi-agent systems. The tracking error originally within a known large set is confined to a smaller predefined set using this approach. Using output error transformation, the constrained system is relaxed and mapped to an unconstrained one. The controller is conceived under the assumption that the agents' nonlinear dynamics are unknown and the perceived network is structured and strongly connected. Under the proposed controller, all agents track the trajectory of the leader node with guaranteed uniform ultimately bounded transformed error and bounded adaptive estimate of unknown parameters and dynamics. In addition, the proposed controllers with PPF are distributed such that each follower agent requires information between its own state relative to connected neighbors. Proposed controller is validated for robustness and smoothness using highly nonlinear heterogeneous networked system with uncertain time-varying parameters and external disturbances. Index Terms: Prescribed performance, neuro-adaptive, high order, Transformed error, Multi-agents, Distributed control, Consensus, Synchronization, Transient, Steady-state error, MIMO, SISO

Bio-Inspired Adaptive Cooperative Control of Heterogeneous Robotic Networks

We introduce a new adaptive cooperative control strategy for robotic networks comprised of heterogeneous members. The proposed feedback synchronization exploits an active parameter adaptation strategy as opposed to adaptive parameter estimation of adaptive control theory. Multiple heterogeneous robots or vehicles can coordinate their motions by parameter adaptation analogous to bio-genetic mutation and adaptation. In contrast with fixed gains used by consensus theory, both the tracking control and diffusive coupling gains are automatically computed based on the adaptation law, the synchronization errors, and the tracking errors of heterogeneous robots. The optimality of the proposed adaptive cooperative control is studied via inverse optimal control theory. The proposed adaptive cooperative control can be applied to any network structure. The stability proof, by using a relatively new nonlinear stability tool, contraction theory, shows globally asymptotically synchronized motion of a heterogeneous robotic network. This adaptive cooperative control can be widely applied to cooperative control of unmanned aerial vehicles (UAVs), formation flying spacecraft, and multi-robot systems. Results of the simulation show the effectiveness of the proposed adaptive cooperative control laws especially for a network comprised of heterogeneous members

Bio-Inspired Adaptive Cooperative Control of Heterogeneous Robotic Networks

We introduce a new adaptive cooperative control strategy for robotic networks comprised of heterogeneous members. The proposed feedback synchronization exploits an active parameter adaptation strategy as opposed to adaptive parameter estimation of adaptive control theory. Multiple heterogeneous robots or vehicles can coordinate their motions by parameter adaptation analogous to bio-genetic mutation and adaptation. In contrast with fixed gains used by consensus theory, both the tracking control and diffusive coupling gains are automatically computed based on the adaptation law, the synchronization errors, and the tracking errors of heterogeneous robots. The optimality of the proposed adaptive cooperative control is studied via inverse optimal control theory. The proposed adaptive cooperative control can be applied to any network structure. The stability proof, by using a relatively new nonlinear stability tool, contraction theory, shows globally asymptotically synchronized motion of a heterogeneous robotic network. This adaptive cooperative control can be widely applied to cooperative control of unmanned aerial vehicles (UAVs), formation flying spacecraft, and multi-robot systems. Results of the simulation show the effectiveness of the proposed adaptive cooperative control laws especially for a network comprised of heterogeneous members

Multi-Agent Distributed Coordination Control: Developments and Directions

In this paper, the recent developments on distributed coordination control, especially the consensus and formation control, are summarized with the graph theory playing a central role, in order to present a cohesive overview of the multi-agent distributed coordination control, together with brief reviews of some closely related issues including rendezvous/alignment, swarming/flocking and containment control.In terms of the consensus problem, the recent results on consensus for the agents with different dynamics from first-order, second-order to high-order linear and nonlinear dynamics, under different communication conditions, such as cases with/without switching communication topology and varying time-delays, are reviewed, in which the algebraic graph theory is very useful in the protocol designs, stability proofs and converging analysis. In terms of the formation control problem, after reviewing the results of the algebraic graph theory employed in the formation control, we mainly pay attention to the developments of the rigid and persistent graphs. With the notions of rigidity and persistence, the formation transformation, splitting and reconstruction can be completed, and consequently the range-based formation control laws are designed with the least required information in order to maintain a formation rigid/persistent. Afterwards, the recent results on rendezvous/alignment, swarming/flocking and containment control, which are very closely related to consensus and formation control, are briefly introduced, in order to present an integrated view of the graph theory used in the coordination control problem. Finally, towards the practical applications, some directions possibly deserving investigation in coordination control are raised as well.Comment: 28 pages, 8 figure

Simple synchronization protocols for heterogeneous networks: beyond passivity (extended version)

Synchronization among autonomous agents via local interactions is one of the benchmark problems in multi-agent control. Whereas synchronization algorithms for identical agents have been thoroughly studied, synchronization of heterogeneous networks still remains a challenging problem. The existing algorithms primarily use the internal model principle, assigning to each agent a local copy of some dynamical system (internal model). Synchronization of heterogeneous agents thus reduces to global synchronization of identical generators and local synchronization between the agents and their internal models. The internal model approach imposes a number of restrictions and leads to sophisticated dynamical (and, in general, nonlinear) controllers. At the same time, passive heterogeneous agents can be synchronized by a very simple linear protocol, which is used for consensus of first-order integrators. A natural question arises whether analogous algorithms are applicable to synchronization of agents that do not satisfy the passivity condition. In this paper, we study the synchronization problem for heterogeneous agents that are not passive but satisfy a weaker input feedforward passivity (IFP) condition. We show that such agents can also be synchronized by a simple linear protocol, provided that the interaction graph is strongly connected and the couplings are sufficiently weak. We demonstrate how stability of cooperative adaptive cruise control algorithms and some microscopic traffic flow models reduce to synchronization of heterogeneous IFP agents.Comment: accepted to IFAC World Congres

A hybrid approach for cooperative output regulation with sampled compensator

This work investigates the cooperative output regulation problem of linear multi-agent systems with hybrid sampled data control. Due to the limited data sensing and communication, in many practical situations, only sampled data are available for the cooperation of multi-agent systems. To overcome this problem, a distributed hybrid controller is presented for the cooperative output regulation, and cooperative output regulation is achieved by well designed state feedback law. Then it proposed a method for the designing of sampled data controller to solve the cooperative output regulation problem with continuous linear systems and discrete-time communication data. Finally, numerical simulation example for cooperative tracking and a simulation example for optimal control of micro-grids are proposed to illustrate the result of the sampled data control law

Coordination of Multi-Agent Systems under Switching Topologies via Disturbance Observer Based Approach

In this paper, a leader-following coordination problem of heterogeneous multi-agent systems is considered under switching topologies where each agent is subject to some local (unbounded) disturbances. While these unknown disturbances may disrupt the performance of agents, a disturbance observer based approach is employed to estimate and reject them. Varying communication topologies are also taken into consideration, and their byproduct difficulties are overcome by using common Lyapunov function techniques. According to the available information in difference cases, two disturbance observer based protocols are proposed to solve this problem. Their effectiveness is verified by simulations.Comment: 12 pages, 4 figures, 2 table

Small noise may diversify collective motion in Vicsek model

Natural systems are inextricably affected by noise. Within recent decades, the manner in which noise affects the collective behavior of self-organized systems, specifically, has garnered considerable interest from researchers and developers in various fields. To describe the collective motion of multiple interacting particles, Vicsek et al. proposed a well-known self-propelled particle (SPP) system, which exhibits a second-order phase transition from disordered to ordered motion in simulation; due to its non-equilibrium, randomness, and strong coupling nonlinear dynamics, however, there has been no rigorous analysis of such a system to date. To decouple systems consisting of deterministic laws and randomness, we propose a general method which transfers the analysis of these systems to the design of cooperative control algorithms. In this study, we rigorously analyzed the original Vicsek model under both open and periodic boundary conditions for the first time, and developed extensions to heterogeneous SPP systems (including leaderfollower models) using the proposed method. Theoretical results show that SPP systems switch an infinite number of times between ordered and disordered states for any noise intensity and population density, which implies that the phase transition indeed takes a nontraditional form. We also investigated the robust consensus and connectivity of these systems. Moreover, the findings presented in this paper suggest that our method can be used to predict possible configurations during the evolution of complex systems, including turn, vortex, bifurcation and flock merger phenomena as they appear in SPP systems

Nonlinear Consensus Strategies for Multi-Agent Networks in Presence of Communication Delays and Switching Topologies: Real-Time Receding Horizon Approach

This paper presents a novel framework which combines a non-iterative solution of Real-Time Nonlinear Receding Horizon Control (NRHC) methodology to achieve consensus within complex network topologies with existing time-delays and in presence of switching topologies. In this formulation, we solve the distributed nonlinear optimization problem for multi-agent network systems directly, \emph{in real-time}, without any dependency on iterative processes, where the stability and convergence guarantees are provided for the solution. Three benchmark examples on non-linear chaotic systems provide validated results which demonstrate the significant outcomes of such methodology.Comment: 26 pages, 8 figures (under review). arXiv admin note: substantial text overlap with arXiv:1510.0779

Distributed PID Control for Consensus of Homogeneous and Heterogeneous Networks

We investigate the use of distributed PID actions to achieve consensus in networks of homogeneous and heterogeneous linear systems. Convergence of the strategy is proved for both cases using appropriate state transformations and Lyapunov functions. The effectiveness of the theoretical results is illustrated via its application to a representative power grid model recently presented in the literature.Comment: 10 pages, 7 Figures, Accepted for Publication in IEEE Transactions on Control of Network System