Optimal Consensus Control for Continuous-Time Linear Multiagent Systems: A Dynamic Event-Triggered Approach.

Fuzzy approximation-based optimal consensus control for nonlinear multiagent systems via adaptive dynamic programming

In this brief, a novel distributed leader-following consensus controller for linear multi-agent systems (MASs) with one leader and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> followers is designed for optimal leader-following consensus control. A user-friendly global objective function is well designed in a quadratic form. The proper choice of the weighting matrices and necessary and sufficient conditions for optimizing the objective function are given. The proposed controller can guarantee the optimization of the objective function and the achievement of the leader-following consensus of the MASs. To deal with the coupling in the controllers, we propose a dynamic average consensus-based algorithm to estimate the controller distributedly, and the estimate errors converge to zero in finite time. A simulation example is provided to demonstrate the results.

This article addresses the event-based adaptive optimal fault-tolerant consensus control problem for a class of nonlinear multiagent systems (MASs) under a directed graph. It can be solved that both control gains and actuator failure parameters are unknown in considered MASs, which enhances the practicability of optimal consensus control. First, a reinforcement learning-based distributed optimal control law is designed by constructing the identifier-critic-actor learning networks. Furthermore, by utilizing the distributed optimal control law as an auxiliary variable, an adaptive fault-tolerant controller is proposed to effectively compensate for actuator failures. Meanwhile, a co-design scheme is proposed for the construction of an event-triggered control input with the fault-tolerant property. It is proven that the designed control input ensures the boundedness of closed-loop systems through rigorous stability analysis. Finally, the effectiveness of the developed approach can be illustrated via simulations of numerical nonlinear MASs and a group of autonomous underwater vehicles.

This paper investigates the consensus disturbance rejection problem for general linear multi-agent systems in the presence of matched disturbances under the directed communication topology. Firstly, based on the local output information among agents, the disturbance observer is proposed to estimate the disturbances and compensate for their influences on the multi-agent systems. Secondly, the fully distributed output feedback consensus protocol is designed to guarantee that all agents can reach an agreement value. Finally, a simulation example is presented to illustrate the effectiveness of the results.

This paper deals with the optimal bipartite consensus control (OBCC) for heterogeneous multi-agent systems (MASs) with time-delay based on reinforcement learning (RL) scheme. MASs, denoted by communication network, is modeled as a signed graph, and the competitive (cooperative) relationship is represented by negative (positive) edges. Firstly, Heterogeneous MASs is depicted by cooperative and competitive (hereinafter referred to as coopetition) network, and local neighborhood bipartite consensus errors and their performance index function (PIF) are put forward to formulate OBCC problem. Secondly, a proper model reduction method is developed to tackle time-delay in coopetition network, and then MASs with time-delay can be transformed into a delay-free MASs. Thirdly, a RL algorithm is employed to solve the solution of Hamilton-Jacobi-Bellman (HJB) equations under OBCC laws, and substantially we adopt neural networks (NNs) to calculate the control policy and PIF online. Finally, the pivotal simulation validates availability of proposed algorithm.

Dual ML-ADHDP method for heterogeneous discrete-time nonlinear multi-agent systems with unknown dynamics and time delay

In this paper, we study an optimal output consensus problem for a multiagent network with agents in the form of multi-input multioutput minimum-phase dynamics. Optimal output consensus can be taken as an extended version of the existing output consensus problem for higher-order agents with an optimization requirement, where the output variables of agents are driven to achieve a consensus on the optimal solution of a global cost function. To solve this problem, we first construct an optimal signal generator, and then propose an embedded control scheme by embedding the generator in the feedback loop. We give two kinds of algorithms based on different available information along with both state feedback and output feedback, and prove that these algorithms with the embedded technique can guarantee the solvability of the problem for high-order multiagent systems under standard assumptions.

This paper investigates the optimal couple-group consensus control (OCGCC) for heterogeneous multi-agent systems (HeMASs) with completely unknown dynamics. The agents in HeMASs are divided into two groups according to order differences. Meanwhile, heterogeneous systems are transformed into homogeneous ones by adding virtual velocities. Then, a novel data-driven distributed control protocol for HeMASs is proposed based on policy gradient reinforcement learning (RL). The proposed algorithm is implemented asynchronously, and is specifically designed to address the issue of computational imbalance caused by individual differences among participants. It achieves this by constructing an actor-critic (AC) framework. The system’s learning efficacy is optimized using offline data sets. The convergence and stability are ensured by applying functional analysis and the Lyapunov stability theory. Finally, the effectiveness of the proposed algorithm is confirmed by various simulation examples.

This paper investigates finite-horizon optimal consensus control problem for unknown multiagent systems with state delays. It is well known that optimal consensus control is the solutions to the coupled Hamilton-Jacobi-Bellman (HJB) equations. An off-policy reinforcement learning (RL) algorithm is developed to learn the two-stage optimal consensus solutions to the coupled time-varying HJB equations using the measurable state data instead of the knowledge of the state-delayed system dynamics. Subsequently, for each agent, a single critic neural network (NN) is utilized to approximate the time-varying cost function and help to calculate optimal consensus control policy. Based on the method of weighted residuals, adaptive weight update laws for the critic NNs are proposed. Finally, the simulation results are provided to illustrate the effectiveness of the proposed off-policy RL method.

Randomized optimal consensus of multi-agent systems

This brief investigates an optimal consensus problem for a set of integrator systems with dynamic uncertainties. A hierarchical distributed control framework based on partial global information is given, which can reach the optimal solution of the team objective function. Each agent has an optimal control law based on the neighbors&#x2019; information and the gradients of the local cost functions, and a compensator derived with Lyapunov redesign technique to deal with the dynamic uncertainties. Then, to remove the constraint on initial conditions and the need for global knowledge of the state, the state differences between neighbors are involved to strengthen the optimal controller while local information feedback is included in the compensator. The resulted fully distributed algorithms can guarantee asymptotic convergence of the systems in the sense of input-to-state stability (ISS). The effectiveness of the method is illustrated by numerical examples.

This brief studies the time-varying formation (TVF) control of linear multi-agent systems (MASs), where the communication topology switches from several different topologies and the switching signal is depicted by a right-continuous Markov process. The communication noises are taken into account simultaneously, which are described as independent white noises with noisy intensities. A class of stochastic-approximation type control protocols is given and certain sufficient conditions are derived for realizing the TVF stabilization in mean square sense. Moreover, the indicative function and infinitesimal generator are imported in Lyapunov functions to help proving that the MASs can be formed into stable TVF shapes with the proposed control protocols. In the end, an simulation example is performed to state the availability of the approach.

In this article, we investigate the event-triggered consensus problem for general linear multiagent systems with bounded communication network delay. To reduce the communication frequency, we propose some dynamic periodic event-triggering strategies, under which an auxiliary dynamic variable and a weighting parameter are introduced for each agent to build its event-triggering condition. Then, a distributed adaptive consensus protocol, which includes a time-varying coupling weight for each edge, is designed based on the proposed event-triggering strategies. With the well-designed updating laws of dynamic variables, coupling weights and weighting parameters, we can theoretically guarantee the consensus of the concerned multiagent systems. Our event-triggering strategies do not require agents to continuously verify the event-triggering conditions or read their neighbors’ real-time state information. Moreover, Zeno behavior is inherently excluded as the interevent intervals are bounded from below by one period in the periodic event-triggering framework. Two numerical examples are provided to verify the effectiveness of the proposed event-triggered consensus protocols.

This article investigates the cluster consensus control problem for general linear multiagent systems. The focus of this article is especially to solve the following problem: in what kinds of connection scenarios can agents achieve cluster consensus regardless of the coupling strength (CCRCS). Different from existing literature, this article extends the case to general partition graphs, including both acyclic and cyclic partition cases. New analysis methods are put forward. It is proved that, under some basic assumptions, the multiagent systems can achieve CCRCS if and only if the interaction topology satisfies the nonvicious circle condition, which is proposed for the first time. An algorithm is presented which can check whether a given interaction topology satisfies the nonvicious circle condition. The result can also be extended to heterogeneous cases that agents from different clusters possess nonidentical system dynamics.

In this paper, the inverse optimal approach is employed to design distributed consensus protocols that guarantee consensus and global optimality with respect to some quadratic performance indexes for identical linear systems on a directed graph. The inverse optimal theory is developed by introducing the notion of partial stability. As a result, the necessary and sufficient conditions for inverse optimality are proposed. By means of the developed inverse optimal theory, the necessary and sufficient conditions are established for globally optimal cooperative control problems on directed graphs. Basic optimal cooperative design procedures are given based on asymptotic properties of the resulting optimal distributed consensus protocols, and the multiagent systems can reach desired consensus performance (convergence rate and damping rate) asymptotically. Finally, two examples are given to illustrate the effectiveness of the proposed methods.