Nonlinear Consensus Protocols Research Articles

Prescribed-time cooperative guidance law against maneuvering target based on leader-following strategy

This paper proposes a prescribed-time cooperative guidance law (PTCGL) against maneuvering target with variable line-of-sight (LOS) angle constraint for leader-following missiles, where the convergence times of the state errors can be arbitrarily set. The leader missile against the maneuvering target is provided as the modified proportional navigation (MPN) guidance law. The proposed PTCGL for follower missiles consist of two parts, in LOS direction, the range-to-go (Rgo) is selected as a co-variable, avoiding the estimation of time-to-go (Tgo), and a novel second-order nonlinear consensus protocol is developed to design the PTCGL; in normal LOS direction, considering the variable LOS angle constraint, the cooperative guidance law is designed with the proposed prescribed-time sliding model control (PTSMC) method. Besides, the prescribed-time convergence of Rgo and LOS errors are proved. Finally, the effectiveness and superiority of the proposed PTCGL with leader-following strategy is illustrated by numerical simulation results.

A Zeno-Free Self-Triggered Approach to Practical Fixed-Time Consensus Tracking With Input Delay

This article considers the practical fixed-time self-triggered consensus tracking problem of delayed multiagent networks (MANs) subject to external disturbances under undirected topology and directed topology. The fixed-time consensus implies that the consensus is reached in a finite time and the convergence time is independent of initial conditions under the nonlinear consensus protocols. A self-triggered control (STC) strategy is developed based on the event-triggered control (ETC) strategy. For the ETC strategy, the nonlinear controllers and the measurement errors are designed based on the hyperbolic tangent function to avoid a nondifferential problem and Zeno behavior. To avoid continuous monitoring, the STC strategy is presented. Furthermore, the minimal interevent interval is strictly positive, which implies that no Zeno behavior occurs in the STC strategy. Finally, a numerical example is presented to verify the availability of the algorithms.

Distributed control of multi-agents system via static feedback controllers under directed networks

During recent years, a lot of distributed control approaches based on static feedback controllers have been proposed to realize consensus of multi-agents systems with undirected topologies. However, many of these approaches have not been generalized to systems with directed topologies yet. Therefore, in this paper, for first- and second-order multi-agents systems with directed topologies, we propose a series of new nonlinear consensus protocols based on traditional design. With integral Lyapunov functions, we can prove the stability of proposed control protocols and a group of simulation results are also given to testify our theory.

Sample-and-hold solution of a consensus problem with nonlinear dynamics and input/output disturbances

The consensus problem of multi-agent systems (MASs) over directed graphs is analyzed in this paper. A sampled-data control law is induced from a nonlinear consensus protocol (continuous or not) by implementing feedback stabilization methods, in the sample-and-hold sense. Under the edge agreement framework, we show that consensus in a strongly connected network can be achieved over some suitable finite time. Furthermore, if an arbitrarily large and bounded actuator disturbance affects the MAS, we show that the sampled-data controller can be robustified to still guarantee the agreement. The case with observation errors is investigated too. The agent drift dynamics are required to be globally Lipschitz and bounded. Numerical simulations are finally proposed to validate the results.

LPV Scheme for Robust Adaptive Output Feedback Consensus of Lipschitz Multiagents Using Lipschitz Nonlinear Protocol

This article addresses the robust nonlinear adaptive consensus protocol design approach, for nonlinear multiagent (MA) systems under external perturbations with Lipschitz dynamics. Based on the existing results of the adaptive protocol using relative output information, a modified robust nonlinear adaptive consensus protocol for MAs is proposed. The Lipschitz nonlinearity in the agents’ dynamics and the adaptive protocol are reformulated using a composite linear parameter-varying (LPV) approach. Our composite LPV reformulation is less restrictive because it utilizes all the properties of Lipschitz functions. Consensus protocol design conditions based on the proposed reformulation of Lipschitz nonlinearities, Lyapunov theory, and the modified nonlinear consensus protocol are derived to attain the exponential consensus. The proposed consensus protocol approach is further extended by providing necessary and sufficient conditions for the straightforward evaluation of the robust adaptive protocol gains. The proposed fully distributed consensus protocol is robust to ensure the consensus error and adaptive gains bounded by eliminating the effect of disturbances. The resultant consensus control scheme reduces conservatism and is feasible for large values of Lipschitz constants. Finally, simulation results are presented for verifying the potency of the developed control strategies.

Nonlinear Consensus Protocol Modified from Doubly Stochastic Quadratic Operators in Networks of Dynamic Agents

This article explores nonlinear convergence to limit the effects of the consensus problem that usually occurs in multi-agent systems. Most of the existing research essentially considers the outline of linear protocols, using complex mathematical equations in various orders. In this work, however, we designed and developed an alternative nonlinear protocol based on simple and effective mathematical approaches. The designed protocol in this sense was modified from the Doubly Stochastic Quadratic Operators (DSQO) and was aimed at resolving consensus problems. Therefore, we called it Modified Doubly Stochastic Quadratic Operators (MDSQO). The protocol was derived in the context of coordinated systems to overcome the consensus issue related to multi-agent systems. In the process, we proved that by using the proposed nonlinear protocol, the consensus could be reached via a common agreement among the agents (average consensus) in a fast and easy fashion without losing any initial status. Moreover, the investigated nonlinear protocol of MDSQO realized the reaching consensus always as well as DSQO in some cases, which could not reach consensus. Finally, simulation results were given to prove the validity of the theoretical analysis.

Guaranteed-performance consensus for descriptor nonlinear multi-agent systems based on distributed nonlinear consensus protocol

In this paper, guaranteed-performance consensus (GPC) for descriptor nonlinear multi-agent systems (DNMASs) with a leader is studied. The interactions among followers are bidirectional for leader-following DNMASs. Firstly, one designs a novel distributed nonlinear consensus protocol based on state feedback to reach consensus for DNMASs. The performance function is constructed by state errors among agents, which is time integration of quadratic function. Secondly, not only are sufficient conditions presented for guaranteed-performance consensus to ensure the scalability of DNMASs based on the Riccati inequality, but also an upper bound of the cost function is derived. It is shown that the guaranteed-performance costs are dependent on initial states of agents. Moreover, the conclusions are extended to achieve the leaderless GPC. Finally, simulation examples are presented to demonstrate the effectiveness of theoretical results.

Finite-Time Coordination Under State-Dependent Communication Graphs With Inherent Links

This brief investigates distributed coordination control problems under a state-dependent communication graph with several inherent links. In the network, an interaction arises between two agents if either their states differ by less than a fixed range or an inherent communication link exists between them. By considering that each agent has a state-dependent control gain, a nonlinear consensus protocol is proposed for single-integrator modeled multi-agent systems. With the validity of some initial condition, the communication graph is shown to be connected at any time, which guarantees asymptotic consensus. It is further shown that this result can apply to the opinion consensus problem. This brief also provides a novel approach to finite-time coordination protocols synthesis. By simply multiplying a time-varying gain, any coordination protocol can be transformed into a finite-time protocol. A simulation example is presented to illustrate the effectiveness of the theoretical result.

Nonlinear Consensus Protocols With Applications to Quantized Communication and Actuation

Nonlinearities are present in all real applications. Two types of general nonlinear consensus protocols are considered in this paper, namely, the systems with nonlinear communication and actuator constraints. The solutions of the systems are understood in the sense of Filippov to handle the possible discontinuity of the controllers. For each case, we prove the asymptotic stability of the systems with minimal assumptions on the nonlinearity, for both directed and undirected graphs. These results extend the literature to more general nonlinear dynamics and topologies. As applications of established theorems, we interpret the results on quantized consensus protocols.

Event-Triggered Finite-Time Integral Sliding Mode Controller for Consensus-Based Formation of Multirobot Systems With Disturbances

This paper deals with the distributed fast and finite-time consensus problem of multiagent systems with bounded disturbances in a leader-follower-based frame work. A novel integral sliding mode-based robust finite-time event-triggered control strategy has been proposed. A fast reaching law is also utilized to improve the speed of convergence. The triggering condition is derived based on the defined novel measurement error, suited for systems with model uncertainties/disturbances. The expression for the lower bound for the interexecution time has been derived to ensure that the zeno behavior is avoided. The proposed nonlinear consensus protocol is such that the desired relative state deviation between the agents can be achieved with a directed graph topology. The theoretical results are validated through real-time experimentations done using Pioneer P3-DX as well as FireBird VI robots.

A lifting method for analyzing distributed synchronization on the unit sphere

Abstract This paper introduces a new lifting method for analyzing convergence of continuous-time distributed synchronization/consensus systems on the unit sphere. Points on the d -dimensional unit sphere are lifted to the ( d + 1 ) -dimensional Euclidean space. The consensus protocol on the unit sphere is the classical one, where agents move toward weighted averages of their neighbors in their respective tangent planes. Only local and relative state information is used. The directed interaction graph topologies are allowed to switch as a function of time. The dynamics of the lifted variables are governed by a nonlinear consensus protocol for which the weights contain ratios of the norms of state variables. We generalize previous convergence results for hemispheres. For a large class of consensus protocols defined for switching uniformly quasi-strongly connected time-varying graphs, we show that the consensus manifold is uniformly asymptotically stable relative to closed balls contained in a hemisphere. Compared to earlier projection based approaches used in this context such as the gnomonic projection, which is defined for hemispheres only, the lifting method applies globally. With that, the hope is that this method can be useful for future investigations on global convergence.

A new class of fixed-time bipartite consensus protocols for multi-agent systems with antagonistic interactions

In this paper, we study the fixed-time consensus problem for multi-agent systems with structurally balanced signed graph. A new class of fixed-time nonlinear consensus protocols is designed by employing the neighbor’s information. By using Lyapunov stability method, states of all agents can be guaranteed to reach agreement in a fixed time under our presented protocols, and the consensus values are the same in modulus but different in sign. Moreover, it is shown that the settling time is not dependent on the initial conditions, and it makes a good convenience to estimate the convergence time by just knowing the graph topology and the information flow of the multi-agent systems. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed consensus protocols.

Distributed extended Kalman filter with nonlinear consensus estimate

This paper is concerned with the distributed filtering problem for discrete-time nonlinear systems over a sensor network. In contrast with the distributed filters with linear consensus estimate, a distributed extended Kalman filter (EKF) is developed with nonlinear consensus estimate. Specifically, a new nonlinear consensus protocol with polynomial form is proposed to generate the consensus estimate. By using the variance-constrained approach, the Kalman gain matrix is determined for each node to guarantee an optimized upper bound on the state estimation error covariance despite consensus terms and linearization errors. It is shown that the Kalman gain matrix can be derived by solving two Riccati-like difference equations. The effectiveness of the proposed filter is evaluated on an indoor localization of a mobile robot with visual tracking systems.

Finite‐time event‐triggered consensus for non‐linear multi‐agent networks under directed network topology

This study investigates the finite-time consensus problem for a class of first-order non-linear multi-agent networks under directed network topology. A novel non-linear consensus protocol is proposed based on event-triggered strategy. By using the combinational measurement approach, two kinds of event triggers are designed, one depends on continuous communications between the agents, the other avoids the continuous communications. For such two classes of event-triggers, sufficient conditions guaranteeing the finite-time consensus are derived, respectively, provided that the coupling network topology contains at least a rooted directed spanning tree. Meanwhile, some numerical simulations are given to illustrate the effectiveness of the theoretical results.

Nonlinear consensus protocols with applications to quantized systems

This paper studies multi-agent systems with nonlinear consensus protocols, i.e., only nonlinear measurements of the states are available to agents. The solutions of these systems are understood in Filippov sense since the possible discontinuity of the nonlinear controllers. Under the condition that the nonlinear functions are monotonic increasing without any continuous constraints, asymptotic stability is derived for systems defines on both directed and undirected graphs. The results can be applied to quantized consensus which extend some existing results from undirected graphs to directed ones.

Attitude Consensusability in Multispacecraft Systems Using Magnetic Actuators

The leaderless attitude consensusability of multispacecraft systems by using magnetic actuators is addressed. By proposing a nonlinear consensus protocol for the actuators magnetic dipoles, it is shown that the multispacecraft system is average controllable under the consensus protocol if it is maneuvering at orbits with persistently exciting magnetic fields in the Earth-centered inertial frame. Then, under some conditions, achieving consensus in the multispacecraft system is studied. Simulation results for a team of spacecraft validate the proposed consensus strategy.

A Nonlinear Transformation for Reaching Dynamic Consensus in Multi-Agent Systems

Using a novel nonlinear time-variant transformation, we construct an explicit form of nonlinear consensus protocol that achieves dynamic consensus in multi-agent systems. A distinguishing feature of our protocol is that, under mild assumptions, exponential convergence is preserved from the consensus protocol in the original coordinates. Hence, consensus with switching graphs and large coupling delays, or consensus on general functions can be achieved if the protocol in the original coordinates does. Similar results are still rare in literature for nonlinear dynamics.

Finite‐time consensus of multi‐agent system via nonlinear event‐triggered control strategy

This study investigates the finite-time consensus problem of leaderless and leader-following multi-agent systems. Two novel nonlinear consensus protocols are presented based on event-driven strategies, which can significantly reduce the communication consumption and the frequency of the controller updates. It is shown that the multi-agent system can achieve consensus in finite time under the proposed nonlinear consensus protocols. Moreover, the bound of the triggering interval is provided to illustrate that no Zeno behaviour exists. Finally, some simulations are employed to verify the effectiveness of the proposed consensus protocols.

Nonlinear finite-time bipartite consensus protocol for multi-agent systems associated with signed graphs

In this paper, finite-time multi-agent consensus problems are considered under networks associated with signed graphs whose edge weights can be not only positive but also negative. A nonlinear consensus protocol is proposed to guarantee the states of all agents to converge in a finite time. If the signed graph is structurally balanced, then the final consensus states of all agents are the same in modulus but not in sign. Otherwise, if the signed graph is structurally unbalanced, then the states of all agents converge to zero. Moreover, the final consensus states of agents can be provided uniformly regarding a signed-average quantity that depends on both the initial states of agents and the topology structure of the whole multi-agent network. Numerical simulations illustrate that the protocol is effective in achieving the finite-time consensus of agents under signed graphs and can particularly solve the finite-time average consensus problem of agents when their associated graph has all positive edge weights.

Nonsingular fixed-time consensus tracking for second-order multi-agent networks

This paper investigates the fixed-time consensus tracking problem for second-order multi-agent systems in networks with directed topology. Global well-defined nonlinear consensus protocols are constructed with the aid of a newly-designed sliding surface for each double-integrator agent dynamics. In particular, the proposed framework eliminates the singularity and the settling time is assignable for any initial conditions. This makes it possible for network consensus problems to design and estimate the convergence time off-line. Finally, simulation is included to demonstrate the performance of the new protocols.