Distributed optimal coordination control for nonlinear multi-agent systems using event-triggered adaptive dynamic programming method

This paper is concerned with the design of distributed optimal coordination control for nonlinear multi-agent systems (NMASs) based on event-triggered adaptive dynamic programming (ETADP) method. The method is firstly introduced to design the distributed coordination controllers for NMASs, which not only avoids the transmission of redundant data compared with traditional time-triggered adaptive dynamic programming (TTADP) strategy and minimizes the performance function of each agent. The event-triggered conditions are proposed based on Lyapunov functional method, which is deduced by guaranteeing the stability of NMASs. Then a new adaptive policy iteration algorithm is presented to obtain the online solutions of the Hamiton–Jocabi–Bellman (HJB) equations. In order to implement the proposed ETADP method, the fuzzy hyperbolic model based critic neural networks (NN) are utilized to approximate the value functions and help calculate the control policies. In critic NNs, the NN weight estimations are updated at the event-triggered instants leading to aperiodic weight tuning laws so that computation cost is reduced. It is proved that the weight estimation errors and the local neighborhood coordination errors is uniformly ultimately bounded (UUB). Finally, two simulation examples are provided to show the effectiveness of the proposed ETADP method.     

Command filter based adaptive fuzzy bipartite output consensus tracking of nonlinear coopetition multi-agent systems with input saturation

This paper is concerned with the adaptive bipartite output consensus tracking problem of high-order nonlinear coopetition multi-agent systems with input saturation under a signed directed graph. A distributed fuzzy-based command filtered backstepping scheme is proposed, where the unknown nonlinear dynamics are approximated by the fuzzy logic system (FLS). The errors compensation mechanism is constructed to eliminate the errors caused by filters. Under the proposed control scheme, we only need to design one adaptive law for each agent, and it is proved that the bipartite output tracking errors converge into the desired neighborhood and all the closed-loop signals are bounded although the input saturation exists. Two numerical examples are included to verify the effectiveness of given scheme.     

Decentralized stabilizability and formation control of multi-agent systems with antagonistic interactions

This paper studies the stabilizability and formation control problems of multi-agent systems with antagonistic interactions. The agents run a bipartite consensus protocol using a signed Laplacian which is different from the conventional one. By taking advantage of the proposed structurally balanced independent strongly connected components(SBiSCCs) of the signed graph, a sufficient and necessary condition is presented to solve the decentralized stabilizability problem of multi-agent systems with antagonistic interactions. Besides, formation control is considered and the sufficient and necessary condition is provided by applying the proposed results. Several simulations are given to illustrate the theoretical results.     

Distributed output-feedback consensus control of multi-agent systems with dynamically changing directed interaction topologies

This paper considers the distributed output-feedback consensus control problem for a multi-agent system with higher order linear dynamics and subject to external disturbance, under dynamically changing directed topologies and weighting factors. An extended state observer (ESO) is first designed to estimate not only the unmeasurable agent states but also the external disturbance. Based on the output of the ESO, a novel distributed control protocol is proposed. We show that, with the application of the proposed control protocol, the consensus can be achieved asymptotically by the group of agents if the union of the directed interaction graphs contains a spanning tree frequently enough. A numerical example is given to verify the effectiveness of the theoretical results.     

Sliding mode approach for formation control of multi-agent systems with unknown nonlinear interactions

This paper proposes nonlinear control approaches to solve a leader-follower formation of multi-agent system with unknown nonlinear interactions. Two distributed sliding mode control approaches are suggested here to track a leader in a desired formation with compensating unknown nonlinear terms. The nonlinear interaction terms can appear in multi-agent systems due to physical connections or cooperation between agents. Also the uncertainty in coefficient of control input is considered. Super twist algorithm is suggested for investigating this problem. Some Lyapunov functions are modified and employed to prove maintaining the formation of group, using the proposed sliding mode controllers. A simulation result for slung load transporting with quad-rotors is presented to demonstrate the capability of the proposed approaches.     

Multi-formation control of nonlinear leader-following multi-agent systems

This paper deals with the multi-formation control problem for nonlinear leader-following multi-agent systems. Both the fixed topology case and the switching topology case are considered. The neighbor-based multi-formation control protocols are proposed under the assumption that for one subgroup, the total information received from other subgroups is zero. Then, based on the Lyapunov stability theory combined with the algebraic graph theory, sufficient conditions are established to ensure that the leader-following multi-agent systems with nonlinear dynamics can reach and maintain the desired multi-formation control. Finally, simulation examples are provided to illustrate the effectiveness of the theoretical results.     

Decentralized adaptive control of interconnected nonlinear systems with unknown control directions

In this paper, we propose a decentralized adaptive control scheme for a class of interconnected strict-feedback nonlinear systems without a priori knowledge of subsystems' control directions. To address this problem, a novel Nussbaum-type function is proposed and a key theorem is drawn which involves quantifying the interconnections of multiple Nussbaum-type functions of the subsystems with different control directions in a single inequality. Global stability of the closed-loop system and asymptotic stabilization of subsystems' output are proved and a simulation example is given to illustrate the effectiveness of the proposed control scheme.     

Distributed formation control of fractional-order multi-agent systems with relative damping and nonuniform time-delays

A novel formation control law in the case of relative damping and nonuniform time-delays is proposed for fractional-order multi-agent systems(FOMASs) in this paper. The nonuniform time-delays can be generally divided into symmetric and asymmetric time-delays. Hence, the formation control algorithm for FOMASs in the case of symmetric time-delays and relative damping is first studied under an undirected network topology. Then, the formation control algorithm for FOMASs in the case of asymmetric time-delays and relative damping is studied under a directed network topology. By the means of frequency-domain theory, algebra graph theory and matrix theory, sufficient conditions are derived to ensure the formation control of FOMASs in the case of nonuniform time-delays and relative damping. Finally, several numerical examples are given and the corresponding simulations are provided to demonstrate the correctness of obtained results.     

Event-triggered adaptive control of a class of nonlinear systems

In this paper, the event-triggered adaptive control for a class of nonlinear systems in Brunovsky form is considered. The sensors are event-triggered thus the states are transmitted only at the discrete triggering points, which are more efficient in using communication bandwidth. To solve this problem, we design a set of event-triggered conditions and based on which the controller and parameter estimator are designed without the ISS assumption. It is shown that the proposed control schemes guarantee that all the closed-loop signals are semi-globally bounded and the stabilization error converges to the origin asymptotically. The Zeno behavior is also excluded. Simulation results illustrate the effectiveness of our scheme.     

Global adaptive control for uncertain nonaffine nonlinear hysteretic systems

In this paper, the global output tracking is investigated for a class of uncertain nonlinear hysteretic systems with nonaffine structures. By combining the solution properties of the hysteresis model with the novel backstepping approach, a robust adaptive control algorithm is developed without constructing a hysteresis inverse. The proposed control scheme is further modified to tackle the bounded disturbances by adaptively estimating their bounds. It is rigorously proven that the designed adaptive controllers can guarantee global stability of the closed-loop system. Two numerical examples are provided to show the effectiveness of the proposed control schemes.     

Robust finite-time consensus control for multi-agent systems with disturbances and unknown velocities

In this paper, we investigated the finite-time consensus tracking problem for multi-agent systems with external bounded disturbances and input bounded disturbances and unknown velocities. Based on the Lyapunov finite-time theorem, a novel finite-time consensus control is constructed by using the backstepping method. For unknown velocities, the high-gain observer is used to estimate the velocity information. It is proved that the consensus can be achieved in finite time. The consensus shows fast response and strong robustness to various disturbances. Finally, the effectiveness of the results is illustrated by numerical simulations.     

A class of cooperative relay analysis of multi-agent systems with tracking number switching and time delays

This paper investigates a complicated class of cooperative tracking problems with time-varying number of tracking agents and communication time delays. During the entire tracking process, tracking agents are dynamically changing and the number is not fixed. This results in jumping of tracking errors and dynamic dimensions of the corresponding Laplacian matrices. Consequently, the stability analysis turns to be difficult especially when the effect of communication time delays is taken into consideration. In order to solve this issue, a new type of average Lyapunov function is constructed to compensate the unmatched dimensions of communication topologies over different time intervals. Generalized reciprocally convex Lemma and a more relaxed switched technique are employed to achieve a less conservative switched stability condition for the multi-agent system with variable tracking number and time delays. Finally, through a series of numerical simulations, the effectiveness and feasibility of derived results are verified. The relationship between maximum allowable communication time delays and various control parameters is obtained in a quantitative way.     

Adaptive fuzzy wavelet network control of second order multi-agent systems with unknown nonlinear dynamics

In this paper, consensus problem is considered for second order multi-agent systems with unknown nonlinear dynamics under undirected graphs. A novel distributed control strategy is suggested for leaderless systems based on adaptive fuzzy wavelet networks. Adaptive fuzzy wavelet networks are employed to compensate for the effect of unknown nonlinear dynamics. Moreover, the proposed method is developed for leader following systems and leader following systems with state time delays. Lyapunov functions are applied to prove uniformly ultimately bounded stability of closed loop systems and to obtain adaptive laws. Three simulation examples are presented to illustrate the effectiveness of the proposed control algorithms.     

H2 consensus control of time-delayed multi-agent systems: A frequency-domain method

An analytical H2 controller design approach of homogeneous multi-agent systems with time delays is presented to improve consensus performance. Firstly, a closed-loop multi-input multi-output framework in frequency domain is introduced, and a consensus tracking condition is given. Secondly, the decomposition method is utilized to simplify the analysis of internal stability and H2 performance index of the whole system to a set of independent optimization problems. Finally, the H2 optimal controller can be computed from all the stabilizing controllers. The contributions of the new approach are that the design procedure is conducted analytically for arbitrary delayed multi-agent systems, and a simple quantitative tuning way is developed to trade off the nominal performance and robustness. The simulation examples show the effectiveness of the proposed control strategy.     

Multilevel adaptive control of nonlinear interconnected systems

This paper presents an adaptive backstepping-based multilevel approach for the first time to control nonlinear interconnected systems with unknown parameters. The system consists of a nonlinear controller at the first level to neutralize the interaction terms, and some adaptive controllers at the second level, in which the gains are optimally tuned using genetic algorithm. The presented scheme can be used in systems with strong couplings where completely ignoring the interactions leads to problems in performance or stability. In order to test the suitability of the method, two case studies are provided: the uncertain double and triple coupled inverted pendulums connected by springs with unknown parameters. The simulation results show that the method is capable of controlling the system effectively, in both regulation and tracking tasks.     

Finite-time synchronization for second-order nonlinear multi-agent system via pinning exponent sliding mode control

In this paper we investigate the finite-time synchronization for second-order multi-agent system via pinning exponent sliding mode control. Firstly, for the nonlinear multi-agent system, differential mean value theorem is employed to transfer the nonlinear system into linear system, then, by pinning only one node in the system with novel exponent sliding mode control, we can achieve synchronization in finite time. Secondly, considering the 3-DOF helicopter system with nonlinear dynamics and disturbances, the novel exponent sliding mode control protocol is applied to only one node to achieve the synchronization. Finally, the simulation results show the effectiveness and the advantages of the proposed method.     

Event-triggered consensus control of disturbed multi-agent systems using output feedback

In this article, the event-triggered consensus control is investigated for general linear multi-agent systems with external disturbances, by using the accessible measurement outputs. In particular, a novel protocol is proposed using the local observed state variables at event-triggered instants, which are respectively derived by adopting an observer to each agent based on output signal. Then it is proved that under the designed event-triggered control protocol consensus can be achieved with the desired disturbance attenuation ability and no Zeno behavior occurs. A numerical simulation is given to demonstrate the effectiveness of the developed control strategy     

Distributed MPC based consensus for single-integrator multi-agent systems

This paper addresses model predictive control schemes for consensus in multi-agent systems (MASs) with discrete-time single-integrator dynamics under switching directed interaction graphs. The control horizon is extended to be greater than one which endows the closed-loop system with extra degree of freedom. We derive sufficient conditions on the sampling period and the interaction graph to achieve consensus by using the property of infinite products of stochastic matrices. Consensus can be achieved asymptotically if the sampling period is selected such that the interaction graph among agents has a directed spanning tree jointly. Significantly, if the interaction graph always has a spanning tree, one can select an arbitrary large sampling period to guarantee consensus. Finally, several simulations are conducted to illustrate the effectiveness of the theoretical results.     

Guaranteed cost consensus protocol design for linear multi-agent systems with sampled-data information: An input delay approach

To investigate the energy consumption involved in a sampled-data consensus process, the problem of guaranteed cost consensus for sampled-data linear multi-agent systems is considered. By using an input delay approach, an equivalent system is constructed to convert the guaranteed cost consensus problem to a guaranteed cost stabilization problem. A sufficient condition for guaranteed cost consensus is given in terms of linear matrix inequalities (LMIs), based on a refined time-dependent Lyapunov functional analysis. Reduced-order protocol design methodologies are proposed, with further discussions on determining sub-optimal protocol gain and enlarging allowable sampling interval bound made as a complement. Simulation results illustrate the effectiveness of the theoretical results.