Set-theoretic control is a useful technique for dealing with the uncertainty introduced into power systems by renewable energy resources. Although set operations are computationally expensive in large systems, distributed approaches serve as a remedy. In this paper, we propose a novel consensus-based approach for set-theoretic frequency control in power systems. A robust controlled-invariant set (RCI) for the system is generated by composing RCIs for each bus in the network. The process of generating these sets uses a consensus-based approach in order to facilitate discovery of mutually compatible subsystem RCIs. Each bus seeks to maximize the size of its own RCI while treating the effects of coupling as an unknown-but-bounded disturbance. The consensus routine, which demonstrates linear convergence, is embedded into a backwards reachability analysis of initial safe sets. Results for a 9-bus test case show that simple model predictive controllers associated with the resulting RCIs maintain safe operation when the system is subjected to worst case (adversarial) fluctuations in net demand, where conventional controllers are shown to fail.
In this paper, we investigate the consensus problem of second-order multiagent systems under directed graphs. Simple yet robust consensus algorithms that advance existing achievements in accounting for velocity and input constraints, agent uncertainties, and lack of neighboring velocity measurements are proposed. Furthermore, we show that the proposed method can be applied to the consensus control of uncertain robotic manipulators with velocity and control torque constraints. We rigorously prove that the velocity and control inputs stay within prespecified ranges by tuning design parameters a …
In this paper, we investigate consensus control of fractional-order multi-agent systems with order in (0,1) via sampled-data control. A new scheme to design distributed controllers with rigorous analysis is presented by utilizing the unique properties of fractional-order calculus, namely hereditary and infinite memory. It is established that global boundedness of all closed-loop signals is ensured and asymptotic consensus is realized. Simulation studies are conducted to illustrate the effectiveness of the proposed control method and verify the obtained results.
Existing Nussbaum function based methods on the consensus of multi-agent systems require (partial) identical unknown control directions of all agents and cause dangerous dramatic control shocks. This paper develops a novel saturated Nussbaum function to relax such limitations and proposes a Nussbaum function based control scheme for the consensus problem of multi-agent systems with arbitrary non-identical unknown control directions and safe control progress. First, a novel type of the Nussbaum function with different frequencies is proposed in the form of saturated time-elongation functions, w…
We address the problems of bearing-only consensus and formation control, where each agent can only measure the relative bearings of its neighbors and relative distances are not available. We provide stability results for the Filippov solutions of two gradient-descent laws from non-smooth Lyapunov functions in the context of differential inclusion. For the consensus and formation control problems with undirected sensing topologies, we prove finite-time and asymptotic convergence of the proposed non-smooth gradient flows. For the directed consensus problem, we prove asymptotic convergence using …
This paper studies the consensus problem of general linear discrete-time multi-agent systems (MAS) with input constraints and bounded time-varying communication delays. We propose a robust distributed model predictive control (DMPC) consensus protocol that integrates the offline consensus design with online DMPC optimization to exploit their respective advantages. More precisely, each agent is equipped with an offline consensus protocol, which is a priori designed, depending on its immediate neighbors' estimated states. Further, the estimation errors propagated over time due to inexact neighbo…
Distributed Model Predictive Control for Optimal Consensus of Constrained Heterogeneous Multi-agent Systems
The Hong Kong University of Science and Technology（香港科技大学）；The University of Hong Kong（香港大学）；HKU Shenzhen Institute of Research and Innovation（香港大学深圳研究院创新）；Beihang University（北京航空航天大学）；Peking University（北京大学）
We consider the problem of steering a multi-agent system to multi-consensus, namely a regime where groups of agents agree on a given value which may be different from group to group. We first address the problem by using distributed proportional controllers that implement additional links in the network modeling the communication protocol among agents and introduce a procedure for the optimal selection of them. Both the cases of single integrators and of second-order dynamics are taken into account and the stability for the multi-consensus state is studied, ultimately providing conditions for …
This paper is concerned with the problem of controlling a system of constrained dynamic subsystems in a way that balances the performance degradation of decentralized control with the practical cost of centralized control. We propose a coalitional control scheme in which controllers of subsystems may, as the need arises, group together into coalitions and operate as a single entity. The scheme employs a robust form of distributed model predictive control for which recursive feasibility and stability are guaranteed, yet---uniquely---the reliance on robust invariant sets is merely implicit, thus…
Fully distributed consensus control for stochastic multi-agent systems under undirected and directed topologies
China University of Geosciences（中国地质大学）；Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems（复杂系统先进控制与智能自动化湖北省重点实验室）
In this paper, a distributed learning leader-follower consensus protocol based on Gaussian process regression for a class of nonlinear multi-agent systems with unknown dynamics is designed. We propose a distributed learning approach to predict the residual dynamics for each agent. The stability of the consensus protocol using the data-driven model of the dynamics is shown via Lyapunov analysis. The followers ultimately synchronize to the leader with guaranteed error bounds by applying the proposed control law with a high probability. The effectiveness and the applicability of the developed pro…
In this article, we update the reference [14] in two aspects. First, we note that in order for the control law (12) in [14] to be equivalent to the control law (3) in [14], we need to assume that the samplings for all subsystems must be synchronous, i.e., we need to assume that $T_{i}=T$ for all $i=1,\cdots,N$. Second, we extend our results from periodic sampling to aperiodic sampling.
This study proposes a new distributed control method based on an adaptive fuzzy control for multiple collaborative autonomous underwater vehicles (AUVs) to track a desired formation shape within a fixed time. First, a formation control protocol based on a fixed-time backstepping sliding mode control is designed, in which the consensus cooperative tracking errors for each AUV will be formulated. Then, to compensate for the saturated control torques, an adaptive auxiliary variable is introduced. Finally, a fixed-time adaptive fuzzy logic control (FLC) is derived to approximate the unknown dynami…
Stochastic Average Consensus Filtering and Distributed State Estimation for Boolean Control Networks
School of Mathematics, Southwestern University of Finance and Economics（西南财经大学数学学院）；School of Computing and Artificial Intelligence, Southwestern University of Finance and Economics（西南财经大学计算机与人工智能学院）
This paper studies an optimal consensus problem for a group of heterogeneous high-order agents with unknown control directions. Compared with existing consensus results, the consensus point is further required to an optimal solution to some distributed optimization problem. To solve this problem, we first augment each agent with an optimal signal generator to reproduce the global optimal point of the given distributed optimization problem, and then complete the global optimal consensus design by developing some adaptive tracking controllers for these augmented agents. Moreover, we present an e…
Dynamic average consensus is a decentralized control/estimation framework where a group of agents cooperatively track the average of local time-varying reference signals. In this paper, we develop a novel state decomposition-based privacy preservation scheme to protect the privacy of agents when sharing information with neighboring agents. Specifically, we first show that an external eavesdropper can successfully wiretap the reference signals of all agents in a conventional dynamic average consensus algorithm. To protect privacy against the eavesdropper, a state decomposition scheme is develop…
The paper considers the problem of multi-agent consensus in the presence of adversarial agents which may try to prevent and introduce undesired influence on the coordination among the regular agents. To our setting, we extend the so-called mean subsequence reduced algorithms with the aim to reduce the amount of communication via two measures: The agents exchange information in the form of ternary data at each transmission and moreover keep the frequency of data exchange low by employing self- and event-triggered communication. We will observe that in hostile environments with adversaries, the …
A generic feature of bounded confidence type models is the formation of clusters of agents. We propose and study a variant of bounded confidence dynamics with the goal of inducing unconditional convergence to a consensus. The defining feature of these dynamics, which we name the No one left behind dynamics, is the introduction of a local control on the agents which preserves the connectivity of the interaction network. We rigorously demonstrate that these dynamics result in unconditional convergence to a consensus. The qualitative nature of our argument prevents us quantifying how fast a conse…
This paper is concerned with the consensus problem for multi-agent systems subject to communication delays between the neighboring agents. We consider a scenario where each agent is characterized by a general high-order linear system and the communication delays between the agents are non-uniform and time-varying. We design a distributed control protocol for the agents and provide an equivalent stability problem to be solved that guarantees the state consensus in the group of agents. Moreover, a delay-dependent stability criterion is provided by combining the Lyapunov-Krasovskii method with th…
In this paper, we first propose a novel maneuvering technique compatible with displacement-consensus-based formation controllers. We show that the formation can be translated with an arbitrary velocity by modifying the weights in the consensus Laplacian matrix. In fact, we demonstrate that the displacement-consensus-based formation control is a particular case of our more general method. We then uncover robustness issues with undesired steady-state motions and resultant distorted shapes in undirected displacement-consensus-based formation control. In particular, these issues are triggered when…
This paper proposes a new distributed consensus-based control method for voltage and frequency control of fully inverter-based islanded microgrids (MGs). The proposed method includes the active power sharing in voltage control to improve the reactive power sharing accuracy and thus generalizes some existing secondary frequency and voltage control methods. Firstly, frequency is regulated by distributed secondary frequency control. Secondly, voltage is regulated by distributed average voltage control and decentralized individual voltage control. It offers a tunable trade-off between voltage regu…
It is well known that the employed triggering scheme has great impact on the control performance when control loops operate under scarce communication resources. Various practical and simulative works have demonstrated the potential of event-triggered control to reduce communication while providing a similar performance level when compared to time-triggered control. For non-cooperative networked control systems, analytical performance comparisons of time- and event-triggered control support this finding under certain assumptions. While being well-studied in the non-cooperative setting, it rema…
Decentralised L1 Adaptive Primary Controllers and Distributed Consensus-Based Secondary Control for DC Microgrids with Constant-Power Loads
University College Cork（科克大学）；United Technologies Research Centre Ireland Ltd（联合技术研究中心爱尔兰有限公司）；MaREI-SFI Research Centre, University College Cork（马雷i-sfi研究中心，科克大学）
Volt-VAR control (VVC) is a critical application in active distribution network management system to reduce network losses and improve voltage profile. To remove dependency on inaccurate and incomplete network models and enhance resiliency against communication or controller failure, we propose consensus multi-agent deep reinforcement learning algorithm to solve the VVC problem. The VVC problem is formulated as a networked multi-agent Markov decision process, which is solved using the maximum entropy reinforcement learning framework and a novel communication-efficient consensus strategy. The p…
In this work, we present a novel consensus-based secondary control scheme for current sharing and voltage balancing in DC microgrids, composed of distributed generation units, dynamic RLC lines, and nonlinear ZIE (constant impedance, constant current, and exponential) loads. Situated atop a primary voltage control layer, our secondary controllers have a distributed structure, and utilize information exchanged over a communication network to compute necessary control actions. Besides showing that the desired objectives are always attained in steady state, we deduce sufficient conditions for the…
