Interaction Topology Research Articles

Cooperative optimal control for descriptor multi-agent systems

Abstract This paper provides a theory analysis of cooperative optimal control problem for leader-follower descriptor multi-agent systems. Based on the linear quadratic regulator theory, the state feedback controller is designed to guarantee the consensus of multi-agent systems and minimize a local performance index, which is independent of the graph topology, the control gain matrix is obtained by solving a generalized Riccati equation. Because the local optimal protocol devised cannot guarantee the global optimality of the entire system, the inverse optimal control theory is applied to design distributed control protocols that ensure consensus and global optimality with respect to some global performance index. The defined performance index is related to the interaction topology, whose Laplacian matrix is constrained to be diagonalizable. Finally, two numerical examples and comparisons are supplied to verify the effectiveness of the theoretical results.

Cooperative Tracking Control of Multiagent Systems: A Heterogeneous Coupling Network and Intermittent Communication Framework.

This paper proposes a heterogeneous coupling network framework to address the cooperative tracking control problem for multiagent systems with dynamic interaction topology and bounded intermittent communication. By considering the underlying dynamic interaction topology and introducing the adjustable heterogeneous coupling weighting parameters, a bounded consensus condition of cooperative tracking control is proposed. With considering a bounded intermittent communication condition, a class of intermittent cooperative tracking control protocol is designed based on the combination of the individual agent dynamic and the exchange of information among the agents under an appropriate consensus speed constraint. It is proved in the sense of Lyapunov that the cooperative tracking control for the closed-loop multiagent systems can be achieved under the dynamic interaction topology, an appropriate feedback gain matrix, and the intermittent communication information of all agents. The results are further extended to the information consensus protocol with intermittent coordinated constraint information. Finally, two examples are presented to verify the effectiveness.

Molecular Interpretation of the Compaction Performance and Mechanical Properties of Caffeine Cocrystals: A Polymorphic Study.

The 1:1 caffeine (CAF) and 3-nitrobenzoic acid (NBA) cocrystal (CAF:NBA) displays polymorphism. Each polymorph shares the same docking synthon that connects individual CAF and NBA molecules within the asymmetric unit; however, the extended intermolecular interactions are significantly different between the two polymorphic modifications. These alternative interaction topologies translate to distinct structural motifs, mechanical properties, and compaction performance. To assist our molecular interpretation of the structure-mechanics-performance relationships for these cocrystal polymorphs, we combine powder Brillouin light scattering (p-BLS) to determine the mechanical properties with energy frameworks calculations to identify potentially available slip systems that may facilitate plastic deformation. The previously reported Form 1 for CAF:NBA adopts a 2D-layered crystal structure with a conventional 3.4 Å layer-to-layer separation distance. For Form 2, a columnar structure of 1D-tapes is displayed with CAF:NBA dimers running parallel to the (110) crystallographic direction. Consistent with the layered crystal structure, the shear modulus for Form 1 is significantly reduced relative to Form 2, and moreover, our p-BLS spectra for Form 1 clearly display the presence of low-velocity shear modes, which support the expectation of a low-energy slip system available for facile plastic deformation. Our energy frameworks calculations confirm that Form 1 displays a favorable slip system for plastic deformation. Combining our experimental and computational data indicates that the structural organization in Form 1 of CAF:NBA improves the compressibility and plasticity of the material, and from our tabletability studies, each of these contributions confers superior tableting performance to that of Form 1. Overall, mechanical and energy framework data permit a clear interpretation of the functional performance of polymorphic solids. This could serve as a robust screening approach for early pharmaceutical solid form selection and development.

Distributed containment control of singular heterogeneous multi-agent systems

This paper investigates the containment control problem of singular heterogeneous multi-agent systems under directed interaction topology. Firstly, a distributed observer, in which the eigenvalue information of the leaders is not needed, is proposed to estimate the convex hull spanned by the states of the leaders. Secondly, state feedback control and reduced-order normal observer based output feedback control are presented, respectively. Finally, some numerical simulation examples are performed to demonstrate the efficiency of the proposed theoretical results.

Formula omitted] consensus of stochastic delayed multi-agent systems with ADT switching interaction topologies

This paper investigates the L2−L∞ consensus for a class of stochastic delayed multi-agent systems subject to switching interaction topologies via utilizing an observer-based control protocol. The switching between the interaction topologies is assumed to have the average dwell time (ADT) constraint. With the aid of a simple model transformation, the L2−L∞ consensus issue is transformed into the problem of weighted stochastic L2−L∞ control. Analysis results on the weighted stochastic L2−L∞ control are proposed by constructing Lyapunov-Krasovskii functional and employing stochastic analysis methods. Then, an approach is developed to determine the desired observer-based consensus protocol. Finally, an illustrative numerical example is given to show the usefulness of our design method.

Inference of the High-Level Interaction Topology between the Metabolic and Cell-Cycle Oscillators from Single-Cell Dynamics.

Recent evidence suggests that the eukaryotic metabolism is an autonomous oscillator. Together with oscillating elements of the cyclin/CDK machinery, this oscillator might form a coupled oscillator system, from which cell-cycle control emerges. The topology of interactions between the metabolic oscillator and the elements of the cyclin/CDK machinery, however, remains unknown. Using single-cell metabolic and cell-cycle dynamics in yeast, and solving an inverse problem with a system of Kuramotooscillators, we inferred how the metabolic oscillator interacts with the cyclin/CDK machinery. The identified and experimentally validated interaction topology shows that the early and late cell cycle are independently driven by metabolism. While in this topology, the S phase is coordinated by START. We obtained no support for a strong interaction between early and late cell cycle. The identified high-level interaction topology will guide future efforts to discover the molecular links between metabolism and the cell cycle.

From asynchronous to synchronous chimeras in ecological multiplex network

We study the emergence of chimera states in coupled ecological systems consisting of prey–predator patches organized in a framework of multiplex network with regular coupling topology. The nodes in each layer of the multiplex network are modeled by a three-component Hastings–Powell model exhibiting chaotic dynamics. The existence of different dynamical states in each layer namely, incoherent, chimera and coherent states is characterized through the strength of incoherence measurement. Our investigation reveals that due to multiplexing the chimera state in one layer completely overlaps with the chimera state in another layer for a suitable range of the intra-layer coupling strengths. The transition scenario from asynchronous to synchronous chimera states is realized through the computation of the inter-layer synchronization error. Besides nonlocal interaction, a similar phenomenon is observed in the nearest-neighbor as well as in all-to-all interaction topology. Furthermore, the presence of distinct collective dynamical states is portrayed in an appropriate range of the various parameter spaces.

Distributed Consensus Observer for Multiagent Systems With High-Order Integrator Dynamics

This article presents a distributed consensus observer for multiagent systems with high-order integrator dynamics to estimate the leader state. Stability analysis is carefully studied to explore the convergence properties under undirected and directed communication, respectively. Using Lyapunov functions, fixed-time (resp. finite-time) stability is guaranteed for the undirected (resp. directed) interaction topology. Finally, simulation results are presented to demonstrate the theoretical findings.

Non-fragile H∞ consensus tracking of nonlinear multi-agent systems with switching topologies and transmission delay via sampled-data control

In this paper, the sampled-data non-fragile H∞ consensus tracking problem for Lipschitz nonlinear multi-agent systems with switching topologies and exogenous disturbances is investigated. Each possible interaction topology in the switching topologies set is assumed to contain a directed spanning tree. With introducing a sampled-data mechanism, the information is only capable of being aperiodically transmitted in the network at each sampling instant and unavoidably subject to a transmission delay. Then a protocol collecting the delayed sampled-data information from neighboring agents is proposed not only to provide robustness against some level of controller gain perturbations, but also to regulate consensus performance with an H∞ disturbance attenuation level. By using tools from algebraic graph theory and Lyapunov–Krasovskii functional technique, it is proved that the concerned consensus tracking problem is solvable if the resultant consensus error system can be asymptotically stabilized. Simulation results verify the theoretical analysis.

Understanding the Tabletability Differences between Indomethacin Polymorphs Using Powder Brillouin Light Scattering

The unconventional tabletability of the indomethacin polymorphs - α and γ - are investigated from a topological and mechanical perspective using powder Brillouin light scattering (p-BLS) to identify the specific structure-performance relationship in these materials. Indomethacin (γ-form) was purchased and used to prepare the α polymorph. Powder X-ray diffraction was used to confirm phase identity, while p-BLS was used to obtain the mechanical properties. Energy frameworks were determined with Crystal Explorer to visualize the interaction topologies. Using a Carver press and a stress-strain analyzer, the tableting performance of each polymorph was determined. Polymorph-specific acoustic frequency distributions were observed with distinct, zero-porosity, aggregate elastic moduli determined. The p-BLS spectra for α-indomethacin display a population of low-velocity shear modes, indicating a direction of facilitated shear. This improves slip-mediated plasticity and tabletability. Our p-BLS spectra experimentally indicates that a low-energy slip system is available to α-indomethacin which supports ours and previous energy framework calculations. Despite a 2d-layered crystal motif favorable for shear deformation, the γ-form displays a higher shear modulus that is supported by our hydrogen-bonding analysis of γ-indomethacin. Our experimental, mechanical data is consistent with the predicted interaction topologies and these two inputs combined permit a comprehensive, molecular understanding of polymorph-specific tabletability.

Polarizability, Consensusability, and Neutralizability of Opinion Dynamics on Coopetitive Networks

Opinion dynamics on social networks with coopetitive (cooperative-competitive) interactions may result in polarity, consensus or neutrality under different opinion protocols. The antecedent of protocol design is to study the accessibility problem: whether or not there exist admissible control rules to polarize, consensus, or neutralize individual opinions in a large population. From an operational perspective, this technical note is aimed at the investigation of polarizability, consensusability, and neutralizability of opinion dynamics in question. Particular emphasis is on the joint impact of the dynamical properties of individuals and the interaction topology among them on polarizability, consensusability, and neutralizability, respectively. Sufficient and/or necessary conditions for those accessibility problems are provided by using powerful tools from spectral analysis and algebraic graph theory. To characterize the individual diversity in real life, we further investigate the solvability of opinion formation problems in heterogeneous systems with nonidentical dynamics. Accordingly, sufficient and/or necessary criteria for heterogeneous network polarizability, consensusability, and neutralizability are derived.

Distributed Community Detection via Metastability of the 2-Choices Dynamics

We investigate the behavior of a simple majority dynamics on networks of agents whose interaction topology exhibits a community structure. By leveraging recent advancements in the analysis of dynamics, we prove that, when the states of the nodes are randomly initialized, the system rapidly and stably converges to a configuration in which the communities maintain internal consensus on different states. This is the first analytical result on the behavior of dynamics for nonconsensus problems on non-complete topologies, based on the first symmetry-breaking analysis in such setting.Our result has several implications in different contexts in which dynamics are adopted for computational and biological modeling purposes. In the context of Label Propagation Algorithms, a class of widely used heuristics for community detection, it represents the first theoretical result on the behavior of a distributed label propagation algorithm with quasi-linear message complexity. In the context of evolutionary biology, dynamics such as the Moran process have been used to model the spread of mutations in genetic populations (Lieberman, Hauert, and Nowak 2005); our result shows that, when the probability of adoption of a given mutation by a node of the evolutionary graph depends super-linearly on the frequency of the mutation in the neighborhood of the node and the underlying evolutionary graph exhibits a community structure, there is a non-negligible probability for species differentiation to occur.

Distributed Voltage Regulation for Cyber-Physical Microgrids With Coupling Delays and Slow Switching Topologies

In this paper, a robust neighbor-based distributed cooperative control strategy is proposed for dc cyber-physical microgrids, considering communication delays and slow switching topologies. The proposed robust control strategy can synchronize the voltages of a dc microgrid to the desired value while achieving the optimal load sharing for minimizing distributed energy resources’ (DERs) generation cost to achieve their economic operation at the same layer via a sparse communication network considering communication delays and slow switching topologies synchronously. The continuous interaction of physical–electrical and cyber networks generally exacerbates the occurrence of communication delays. Moreover, the arbitrary switching topologies could destroy the system’s transient characteristics at the switching time instants. To further quantify these impacts on the system stability, the communication delay and average switching dwell-time-dependent control conditions for the proposed control strategy are proved based on the Lyapunov–Krasovskii theory. Some sufficient conditions for the exponential stability of the cyber-physical delayed-switching system are developed, which guarantees the robustness of the proposed strategy against the communication delays and dynamically changing interaction topologies. The proposed control protocols are shown to be fully distributed and implemented through a sparse communication network. Finally, several cases on a modified IEEE 34-bus test network are investigated which demonstrate the effectiveness and performance of the results.

The Effects of Imitation Dynamics on Vaccination Behaviours in SIR-Network Model.

We present a series of SIR-network models, extended with a game-theoretic treatment of imitation dynamics which result from regular population mobility across residential and work areas and the ensuing interactions. Each considered SIR-network model captures a class of vaccination behaviours influenced by epidemic characteristics, interaction topology, and imitation dynamics. Our focus is the resultant vaccination coverage, produced under voluntary vaccination schemes, in response to these varying factors. Using the next generation matrix method, we analytically derive and compare expressions for the basic reproduction number for the proposed SIR-network models. Furthermore, we simulate the epidemic dynamics over time for the considered models, and show that if individuals are sufficiently responsive towards the changes in the disease prevalence, then the more expansive travelling patterns encourage convergence to the endemic, mixed equilibria. On the contrary, if individuals are insensitive to changes in the disease prevalence, we find that they tend to remain unvaccinated. Our results concur with earlier studies in showing that residents from highly connected residential areas are more likely to get vaccinated. We also show that the existence of the individuals committed to receiving vaccination reduces and delays the disease prevalence, and thus is essential to containing epidemics.

Completely Distributed Guaranteed-Performance Consensualization for High-Order Multiagent Systems With Switching Topologies

The guaranteed-performance consensualization for high-order linear and nonlinear multiagent systems with switching topologies is respectively realized in a completely distributed manner in the sense that consensus design criteria are independent of interaction topologies and switching motions. This paper first proposes an adaptive consensus protocol with guaranteed-performance constraints and switching topologies, where interaction weights among neighboring agents are adaptively adjusted and state errors among all agents can be regulated. Then, a new translation-adaptive strategy is shown to realize completely distributed guaranteed-performance consensus control and an adaptive guaranteed-performance consensualization criterion is given on the basis of the Riccati inequality. Furthermore, an approach to regulate the consensus control gain and the guaranteed-performance cost is proposed in terms of linear matrix inequalities. Moreover, main conclusions for linear multiagent systems are extended to Lipschitz nonlinear cases. Finally, two numerical examples are provided to demonstrate theoretical results.

Synchronization control for multiple heterogeneous robotic systems with parameter uncertainties and communication delays

This paper investigates synchronization of multiple heterogeneous robotic systems (MHRSs) in the presence of kinematic uncertainties, dynamic uncertainties and communication delays. We develop two classes of adaptive sliding-mode controllers to deal with the aforementioned problem based on directed graphs containing a directed spanning tree, which relaxes the constraints on the interaction topologies. Furthermore, by invoking techniques of Lyapunov and input-output stability theories, we obtain the sufficient conditions on asymptotic stability of MHRSs. Thus, the position and velocity synchronization errors can asymptotically converge to the origin. Finally, numerous simulations are carried out to demonstrate the validity and advantages of the theoretical results.

Adaptive scaled consensus control of coopetition networks with high-order agent dynamics

In this paper, we consider both bipartite consensus and scaled consensus control of high-order multi-agent systems with antagonistic interactions and unknown disturbances. The interaction topology associated with the multi-agent system is described by a coopetition network and modelled by a signed graph. Linearly parameterised approaches are used to model the unknown disturbances. For the bipartite consensus problem, a distributed adaptive state-feedback controller is designed for each agent. For the scaled consensus problem, a distributed adaptive controller is designed for each agent by using a projection mechanism. The convergence of the bipartite consensus errors and the scaled consensus errors is analysed with the help of a Lyapunov function method and the Barbalat's Lemma. Some simulation results are provided to demonstrate the effectiveness of the proposed adaptive control strategies.

Hierarchical Controller-Estimator for Coordination of Networked Euler-Lagrange Systems.

This paper proposes several hierarchical controller-estimator algorithms (HCEAs) to solve the coordination problem of networked Euler-Lagrange systems (NELSs) with sampled-data interactions and switching interaction topologies, where the cases with both discontinuous and continuous signals are successfully addressed in a unified framework. The HCEAs comprise two main layers (i.e., a control layer and an estimator layer) and one optional layer (i.e., a filter layer), in which the coordination problem is tackled in the main layers and the transient response can be optionally smoothed in the filter layer. For stabilizing the corresponding cascade closed-loop systems, several sufficient conditions on the upper bound of the aperiodic sampling intervals and the lower bound of the control parameters are established. In addition, the HCEAs are extended to address the task-space coordination problem of networked heterogeneous robotic systems, which shows the versatility of the HCEAs. Finally, comparison studies and simulation results are provided to demonstrate the effectiveness, significance, and advantages of the presented algorithms.

Time-varying formation for high-order multi-agent systems with external disturbances by event-triggered integral sliding mode control

This paper investigates the time-varying formation problem for high-order multi-agent systems subject to external disturbances. The interaction topology among agents is assumed to be directed and has a directed spanning tree. A novel event-triggered integral sliding mode control strategy is proposed. It can be proved that, with the designed control law and the event-triggered condition, the desired time-varying formation will be reached. Moreover, the Zeno behavior of triggering time sequences can be avoided. Finally, a simulation example is presented to illustrate the effectiveness of the theoretical results.

Cucker–Smale flocking subject to random failure on general digraphs

This paper studies the Cucker–Smale (C–S) flocking subject to random failure under general interaction topologies, which contain the hierarchical leadership and rooted leadership as special cases. Furthermore, at each time step, each of the agents can fail to interact with any of its neighbors. The random failures are assumed to be not independent. We prove that the flocking would occur almost surely under some conditions on the initial state of the flock only. The result suggests that the C–S flocking system on general digraphs can endure random failure in interactions. Finally, several numerical simulations are provided to illustrate the obtained results.