Abstract
This paper investigates the finite-horizon robust event-triggered control for nonlinear multi-agent systems (NMASs) with state delay. The consensus of NMASs has been studied extensively. Robustness, as another significant topic of NMASs, has not been given enough attention. To fill the gap in this field, we are committed to studying the robust problem for NMASs and a criterion that the robust problem of the NMASs is equivalent to the optimal problem of its nominal system is given. In terms of algorithms, compared with the traditional continuous-time policy iteration algorithm, the event-triggered policy iteration algorithm is utilized to study the event-triggered HJB equation which can effectively reduce controller updates and redundant communication. After that, through the actor-critic network with the time-varying activation function, the approximate event-triggered optimal controller for the nominal state-delay NMASs is designed. In addition, this paper also excludes the Zeno behavior of the closed-loop system. Finally, the effectiveness of the proposed scheme is further verified by two examples.
Similar content being viewed by others
References
Dong X, Li Y, Lu C, Hu G, Li Q, Ren Z (2019) Time-varying formation tracking for UAV swarm systems with switching directed topologies. IEEE Trans Neural Netw Learn Syst 30(12):3674–3685
Kada B, Khalid M, Shaikh MS (2020) Distributed cooperative control of autonomous multi-agent UAV systems using smooth control. J Syst Eng Electron 31(6):1297–1307
Singh VP, Kishor N, Samuel P (2017) Distributed multi-agent system-based load frequency control for multi-area power system in smart grid. IEEE Trans Ind Electron 64(6):5151–5160
Zhang W, Liu W, Wang X, Liu L, Ferrese F (2014) Distributed multiple agent system based online optimal reactive power control for smart grids. IEEE Trans Smart Grid 5(5):2421–2431
Zheng M, Liu C, Liu F (2019) Average-consensus tracking of sensor network via distributed coordination control of heterogeneous multi-agent systems. IEEE Control Syst Lett 3(1):132–137
Li X, Hu X, Zhang R, Yang L (2020) Routing protocol design for underwater optical wireless sensor networks: a multiagent reinforcement learning approach. IEEE Internet Things J 7(10):9805–9818
Li H, Liao X, Huang T, Zhu W (2015) Event-triggering sampling based leader-following consensus in second-order multi-agent systems. IEEE IEEE Trans Autom Control 60(7):1998–2003
Werbos P (1977) Advanced forecasting methods for global crisis warning and models of intelligence. Gen Syst Yearb 22:25–38
Wang F, Zhang H, Liu D (2009) Adaptive dynamic programming: an introduction. IEEE Comput Intell Mag 4(2):39–47
Zhang H, Song R, Wei Q, Zhang T (2011) Optimal tracking control for a class of nonlinear discrete-time systems with time delays based on heuristic dynamic programming. IEEE Trans Neural Netw 22(12):1851–1862
Park J-W, Harley RG, Venayagamoorthy GK, Jang G (2008) Dual heuristic programming based nonlinear optimal control for a synchronous generator. Eng Appl Artif Intell 21(1):97–105
Wang B, Zhao D, Alippi C, Liu D (2014) Dual heuristic dynamic programming for nonlinear discrete-time uncertain systems with state delay. Neurocomputing 134(25):222–229
Al-Tamimi A, Lewis FL, Abu-Khalaf M (2008) Discrete-time nonlinear HJB solution using approximate dynamic programming: convergence proof. IEEE Trans Syst Man Cybern Part B (Cybern) 38(4):943–949
Zhang H, Wei Q, Liu D (2007) On-line learning control for discrete nonlinear systems via an improved ADDHP method. In: Advances in neural networks. Springer, Berlin, pp 387–396
Liu D, Wei Q (2014) Policy iteration adaptive dynamic programming algorithm for discrete-time nonlinear systems. IEEE Trans Neural Netw Learn Syst 25(3):621–634
Zhang H, Zhang J, Yang G, Luo Y (2015) Leader-based optimal coordination control for the consensus problem of multiagent differential games via fuzzy adaptive dynamic programming. IEEE Trans Fuzzy Syst 23(1):152–163
Zhao W, Li R, Zhang H (2017) Leader-follower optimal coordination tracking control for multi-agent systems with unknown internal states. Neurocomputing 249:171–181
Khan AT, Li S, Cao X (2021) Control framework for cooperative robots in smart home using bio-inspired neural network. Measurement 167:108253
Khan AT, Shuai LI, Cao X (2022) Human guided cooperative robotic agents in smart home using beetle antennae search. Sci China Inf Sci 65(2):122204
Khan AT, Li S, Li Z (2022) Obstacle avoidance and model-free tracking control for home automation using bio-inspired approach. Adv Control Appl 4(1):e63
Modares H, Lewis FL, Jiang Z (2015) \( {H}_{ {\infty }}\) tracking control of completely unknown continuous-time systems via off-policy reinforcement learning. IEEE Trans Neural Netw Learn Syst 26(10):2550–2562
Jiao Q, Modares H, Xu S, Lewis FL, Vamvoudakis KG (2016) Multi-agent zero-sum differential graphical games for disturbance rejection in distributed control. Automatica 69:24–34
Liu D, Wang D, Wang F, Li H, Yang X (2014) Neural-network-based online HJB solution for optimal robust guaranteed cost control of continuous-time uncertain nonlinear systems. IEEE Trans Cybern 44(12):2834–2847
Mu C, Wang D (2017) Neural-network-based adaptive guaranteed cost control of nonlinear dynamical systems with matched uncertainties. Neurocomputing 245:46–54
Heemels WPMH, Johansson KH, Tabuada P (2012) An introduction to event-triggered and self-triggered control. In: IEEE 51st IEEE conference on decision and control (CDC), pp 3270–3285
Wang D, Liu D (2018) Neural robust stabilization via event-triggering mechanism and adaptive learning technique. Neural Netw 102:27–35
Yang X, He H (2019) Adaptive critic designs for event-triggered robust control of nonlinear systems with unknown dynamics. IEEE Trans Cybern 49(6):2255–2267
Yang X, He H (2021) Decentralized event-triggered control for a class of nonlinear-interconnected systems using reinforcement learning. IEEE Trans Cybern 51(2):635–648
Zhang H, Liang Y, Su H, Liu C (2020) Event-driven guaranteed cost control design for nonlinear systems with actuator faults via reinforcement learning algorithm. IEEE Trans Syst Man Cybern Syst 50(11):4135–4150
Huo X, Karimi HR, Zhao X, Wang B, Zong G (2022) Adaptive-critic design for decentralized event-triggered control of constrained nonlinear interconnected systems within an identifier-critic framework. IEEE Trans Cybern 52(8):7478–7491
Wen G, Chen CLP, Liu Y, Liu Z (2017) Neural network-based adaptive leader-following consensus control for a class of nonlinear multiagent state-delay systems. IEEE Trans Cybern 47(8):2151–2160
Cui X, Zhang H, Luo Y, Jiang H (2017) Finite-horizon optimal control of unknown nonlinear time-delay systems. Neurocomputing 238:277–285
Zhang H, Park JH, Yue D, Xie X (2020) Finite-horizon optimal consensus control for unknown multiagent state-delay systems. IEEE Trans Cybern 50(2):402–413
Zhang H, Yue D, Dou C, Zhao W, Xie X (2019) Data-driven distributed optimal consensus control for unknown multiagent systems with input-delay. IEEE Trans Cybern 49(6):2095–2105
Ning B, Jin J, Zheng J, Man Z (2018) Finite-time and fixed-time leader-following consensus for multi-agent systems with discontinuous inherent dynamics. Int J Control 91(6):1259–1270
Zhong X, He H (2020) GrHDP solution for optimal consensus control of multiagent discrete-time systems. IEEE Trans Syst Man Cybern Syst 50(7):2362–2374
Abu-Khalaf M, Lewis FL (2005) Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach. Automatica 41(5):779–791
Bokov GV (2011) Pontryagin’s maximum principle of optimal control problems with time-delay. J Math Sci 172(5):623–634
Liu C, Liu L, Cao J, Abdel-Aty M (2021) Intermittent event-triggered optimal leader-following consensus for nonlinear multi-agent systems via actor-critic algorithm. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2021.3122458
Khalil HK (2002) Nonlinear systems, 3rd edn. Prentice-Hall Inc, Upper Saddle River
Sun J, Long T (2021) Event-triggered distributed zero-sum differential game for nonlinear multi-agent systems using adaptive dynamic programming. ISA Trans 110:39–52
Dong L, Zhong X, Sun C, He H (2017) Event-triggered adaptive dynamic programming for continuous-time systems with control constraints. IEEE Trans Neural Netw Learn Syst 28(8):1941–1952
Xu W, Ho DWC (2016) Clustered event-triggered consensus analysis: an impulsive framework. IEEE Trans Ind Electron 63(11):7133–7143
Liu X, Fu H, Liu L (2021) Leader-following mean square consensus of stochastic multi-agent systems via periodically intermittent event-triggered control. Neural Process Lett 53(1):1–24
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Liu, C., Liu, L. Finite-Horizon Robust Event-Triggered Control for Nonlinear Multi-agent Systems with State Delay. Neural Process Lett 55, 5167–5191 (2023). https://doi.org/10.1007/s11063-022-11085-0
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11063-022-11085-0