Partial-state Coupling Research Articles

Semi-global state synchronization for discrete-time multi-agent systems subject to actuator saturation and unknown nonuniform input delay

This paper studies semi-global state synchronization of discrete-time homogeneous networks with diffusive full-state coupling or partial-state coupling subject to actuator saturation and unknown nonuniform input delay. We assume that agents are at most critical unstable, that is the agents have all its eigenvalues in the closed unit disc. The communication network is associated with an undirected and weighted graph, which is represented by a row stochastic matrix. In this paper, we derive an upper bound for the input delay tolerance, which explicitly depends only on the agent dynamics. Moreover, for any unknown delay less than the upper bound, we propose a linear static protocol for MAS with full-state coupling and a linear dynamic protocol for MAS with partial-state coupling based on a low-gain methodology such that state synchronization is achieved among agents for any initial conditions in a priori given compact set.

Squared-down passivity-based H∞ and H2 almost synchronization of homogeneous continuous-time multi-agent systems with partial-state coupling via static protocol

This paper studies H∞ and H2 almost state or output synchronization of homogeneous multi-agent systems (MAS) with partial-state coupling via static protocols in the presence of external disturbances. We provide solvability conditions for designing static protocols. We characterize three classes of agents for which we can design linear static protocols for state or output synchronization of a MAS such that the impact of disturbances on the network disagreement dynamics, expressed in terms of the H∞ and H2 norms of the corresponding closed-loop transfer function, is reduced to arbitrarily small value. Meanwhile, the static protocol only needs rough information on the network graph, that is a lower bound for the real part and an upper bound for the modulus of the non-zero eigenvalues of the Laplacian matrix associated with the network graph. Our study focuses on three classes of agents which are squared-down passive, squared-down passifiable via output feedback and squared-down minimum-phase with relative degree 1.

Regulated State Synchronization of Homogeneous Discrete-Time Multi-Agent Systems via Partial State Coupling in Presence of Unknown Communication Delays

This paper studies regulated state synchronization for homogeneous discrete-time multi-agent systems (MAS) in the presence of unknown nonuniform communication delays. We consider partial state coupling, i.e., agents are coupled through part of their states. A low gain-based protocol is designed which only requires rough knowledge of the communication network, such that the state synchronization for MAS is achieved where the required synchronized trajectory is only given to some of the agents.

Leaderless finite-time consensus for second-order Lipschitz nonlinear multi-agent systems with settling time estimation

The leaderless finite-time consensus for second-order Lipschitz nonlinear multi-agent systems with partial-state coupling is investigated, where the communication network is weighted undirected and weighted. A new distributed control algorithm is proposed by designing the appropriate control parameters in the undirected connected communication topology. By using the algebraic graph theory, matrix theory, power integrator technique, and Lyapunov control approach, the leaderless finite-time consensus is achieved for the second-order Lipschitz nonlinear multi-agent systems. The main contribution of this paper is that, the settling time can be estimated by computing the value of the Lyapunov function at the initial point. Finally, the effectiveness of the results is illustrated by some numerical simulations.

Solvability conditions and design for H∞ & H2 almost state synchronization of homogeneous multi-agent systems

This paper studies the H∞ and H2 almost state synchronization problem for homogeneous multi-agent systems with general linear agents affected by external disturbances and with a directed communication topology. Agents are connected via diffusive full-state coupling or diffusive partial-state coupling. A necessary and sufficient condition is developed for the solvability of the H∞ and H2 almost state synchronization problem. Moreover, a family of protocols based on either an algebraic Riccati equation (ARE) method or a directed eigen structure assignment method are developed such that the impact of disturbances on the network disagreement dynamics, expressed in terms of the H∞ and H2 norm of the corresponding closed-loop transfer function, is reduced to any arbitrarily small value. The protocol for full-state coupling is static, while for partial-state coupling it is dynamic.

State synchronization of multi-agent systems via static or adaptive nonlinear dynamic protocols

This paper studies state synchronization of homogeneous multi-agent systems (MAS) with partial-state coupling. We identify four classes of agents, for which static linear protocol can be designed. They are agents which are squared-down passive, squared-down passifiable via output feedback, squared-down passifiable via input feedforward and squared-down minimum-phase with relative degree 1. We find that, for agents which are squared-down passive, the static protocol does not need any network information, as long as the network graph contains a directed spanning tree. For the other three classes of agents, the static protocol needs rough information on the network graph, that is either a lower bound for the real part or an upper bound for the modulus of the non-zero eigenvalues of the Laplacian matrix associated with the network graph. However, when adaptive nonlinear dynamic protocols are utilized, even this rough information about the network can be dispensed with.

Passivity based state synchronization of homogeneous discrete-time multi-agent systems via static protocol in the presence of input delay

This paper studies state synchronization of homogeneous discrete-time multi-agent systems (MAS) with partial-state coupling (i.e., agents are coupled through part of their states) via static protocol in the presence of input delay. Both uniform input delay and nonuniform input delay are considered. We identify one class of agents for which a static linear protocol can be designed, which is named squared-down passifiable via input feedforward. We derive an upper bound for the input delay tolerance, which explicitly depends on the agent dynamics. Moreover, for any unknown delay satisfying this upper bound, a parameterized static protocol is proposed for each agent such that state synchronization is achieved among agents with uniform or nonuniform input delay.

Solvability conditions and design for state synchronization of multi-agent systems

This paper derives conditions on the agents for the existence of a protocol which achieves synchronization of homogeneous multi-agent systems (MAS) with partial-state coupling, where the communication network is directed and weighted. These solvability conditions are necessary and sufficient for single-input agents and sufficient for multi-input agents. The solvability conditions reveal that the synchronization problem is primarily solvable for two classes of agents. This first class consists of at most weakly unstable agents (i.e. agents have all eigenvalues in the closed left half plane) and the second class consists of at most weakly non-minimum-phase agents (i.e. agents have all zeros in the closed left half plane). Under our solvability condition, we provide in this paper a design, utilizing H∞ optimal control.

Pinning Synchronization of One-Sided Lipschitz Complex Networks

This paper studies the pinning synchronization in complex networks with node dynamics satisfying the one-sided Lipschitz condition which is less conservative than the well-known Lipschitz condition. Based on M-matrix theory and Lyapunov functional method, some simple pinning conditions are derived for one-sided Lipschitz complex networks with full-state and partial-state coupling, respectively. A selective pinning scheme is further provided to address the selection of pinned nodes and the design of pinning feedback gains for one-sided Lipschitz complex networks with general topologies. Numerical results are given to illustrate the effectiveness of the theoretical analysis.

Synchronization with Partial State Coupling on $SO(n)$

This paper studies autonomous synchronization of $k$ agent orientations $\in SO(n)$ by using links that each convey (a priori different) partial state information between two agents: the latter compare the action of their states on a common link-dependent vector of $\mathbb{R}^n$. Such setting appears when each pair of agents compares the expression, in their respective body frames, of a common external direction (force field, heading of moving object, etc.). To synchronize their states, agents must combine this information over time or throughout the network. A gradient coupling law for synchronization is proposed. Extensive convergence analysis of the coupled agents is provided, both for fixed and time-varying reference vectors. The results are compared to a similar setting with states in $\mathbb{R}^n$ and agents coupled through scalar product of their state with a reference vector.

Coordinate transformation and matrix measure approach for synchronization of complex networks

Global synchronization in complex networks has attracted considerable interest in various fields. There are mainly two analytical approaches for studying such time-varying networks. The first approach is Lyapunov function-based methods. For such an approach, the connected-graph-stability (CGS) method arguably gives the best results. Nevertheless, CGS is limited to the networks with cooperative couplings. The matrix measure approach (MMA) proposed by Chen, although having a wider range of applications in the network topologies than that of CGS, works for smaller numbers of nodes in most network topologies. The approach also has a limitation with networks having partial-state coupling. Other than giving yet another MMA, we introduce a new and, in some cases, optimal coordinate transformation to study such networks. Our approach fixes all the drawbacks of CGS and MMA. In addition, by merely checking the structure of the vector field of the individual oscillator, we shall be able to determine if the system is globally synchronized. In summary, our results can be applied to rather general time-varying networks with a large number of nodes.

Cooperative Robot Control and Concurrent Synchronization of Lagrangian Systems

Concurrent synchronization is a regime where diverse groups of fully synchronized dynamic systems stably coexist. We study global exponential synchronization and concurrent synchronization in the context of Lagrangian systems control. In a network constructed by adding diffusive couplings to robot manipulators or mobile robots, a decentralized tracking control law globally exponentially synchronizes an arbitrary number of robots, and represents a generalization of the average consensus problem. Exact nonlinear stability guarantees and synchronization conditions are derived by contraction analysis. The proposed decentralized strategy is further extended to adaptive synchronization and partial-state coupling.

Cooperative Robot Control and Concurrent Synchronization of Lagrangian Systems

Concurrent synchronization is a regime where diverse groups of fully synchronized dynamic systems stably coexist. We study global exponential synchronization and concurrent synchronization in the context of Lagrangian systems control. In a network constructed by adding diffusive couplings to robot manipulators or mobile robots, a decentralized tracking control law globally exponentially synchronizes an arbitrary number of robots, and represents a generalization of the average consensus problem. Exact nonlinear stability guarantees and synchronization conditions are derived by contraction analysis. The proposed decentralized strategy is further extended to adaptive synchronization and partial-state coupling.