Abstract
In this chapter, we aim at improving the critic learning criterion to cope with the event-based nonlinear \(H_{\infty }\) state feedback control design. First of all, the \(H_{\infty }\) control problem is regarded as a two-player zero-sum game and the adaptive critic mechanism is used to achieve the minimax optimization under event-based environment. Then, based on an improved updating rule, the event-based optimal control law and the time-based worst-case disturbance law are obtained approximately by training a single critic neural network. The initial stabilizing control is no longer required during the implementation process of the new algorithm. Next, the closed-loop system is formulated as an impulsive model and its stability issue is handled by incorporating the improved learning criterion. The infamous Zeno behavior of the present event-based design is also avoided through theoretical analysis on the lower bound of the minimal inter-sample time. Finally, the applications to an aircraft dynamics and a robot arm plant are carried out to verify the efficient performance of the present novel design method.
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Bian, T., Jiang, Y., Jiang, Z.P.: Decentralized adaptive optimal control of large-scale systems with application to power systems. IEEE Trans. Industr. Electron. 62(4), 2439–2447 (2015)
Cheng, L., Wang, Y., Ren, W., Hou, Z.G., Tan, M.: Containment control of multi-agent systems with dynamic leaders based on a \(PI^n\)-type approach. IEEE Trans. Cybern. 46(12), 3004–3017 (2016)
Dierks T., Jagannathan, S.: Optimal control of affine nonlinear continuous-time systems. In: Proceedings of the American Control Conference, pp. 1568–1573 (2010)
Dierks, T., Thumati, B.T., Jagannathan, S.: Optimal control of unknown affine nonlinear discrete-time systems using offline-trained neural networks with proof of convergence. Neural Netw. 22(5–6), 851–860 (2009)
Gao, W., Jiang, Z.P.: Adaptive dynamic programming and adaptive optimal output regulation of linear systems. IEEE Trans. Autom. Control 61(12), 4164–4169 (2016)
He, W., Yin, Z., Sun, C.: Adaptive neural network control of a marine vessel with constraints using the asymmetric barrier Lyapunov function. IEEE Trans. Cybern. 47(7), 1641–1651 (2017)
Heydari, A., Balakrishnan, S.N.: Finite-horizon control-constrained nonlinear optimal control using single network adaptive critics. IEEE Trans. Neural Netw. Learn. Syst. 24(1), 145–157 (2013)
Jiang, Y., Jiang, Z.P.: Global adaptive dynamic programming for continuous-time nonlinear systems. IEEE Trans. Autom. Control 60(11), 2917–2929 (2015)
Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice-Hall, New Jersey (2002)
Kim, Y.H., Lewis, F.L., Abdallah, C.T.: A dynamic recurrent neural-network-based adaptive observer for a class of nonlinear systems. Automatica 33(8), 1539–1543 (1997)
Li, H., Liu, D.: Optimal control for discrete-time affine non-linear systems using general value iteration. IET Control Theory Appl. 6(18), 2725–2736 (2012)
Liu, D., Li, H., Wang, D.: Neural-network-based zero-sum game for discrete-time nonlinear systems via iterative adaptive dynamic programming algorithm. Neurocomputing 110, 92–100 (2013)
Liu, D., Li, H., Wang, D.: Online synchronous approximate optimal learning algorithm for multiplayer nonzero-sum games with unknown dynamics. IEEE Trans. Syst. Man Cybern. Syst. 44(8), 1015–1027 (2014)
Liu, D., Wang, D., Wang, F.Y., Li, H., Yang, X.: 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 (2014)
Liu, Y.J., Tong, S., Chen, C.L.P., Li, D.J.: Neural controller design-based adaptive control for nonlinear MIMO systems with unknown hysteresis inputs. IEEE Trans. Cybern. 46(1), 9–19 (2016)
Luo, B., Wu, H.N.: Computationally efficient simultaneous policy update algorithm for nonlinear \(H_{\infty }\) state feedback control with Galerkin’s method. Int. J. Robust Nonlinear Control 23(9), 991–1012 (2013)
Modares, H., Lewis, F.L.: Linear quadratic tracking control of partially-unknown continuous-time systems using reinforcement learning. IEEE Trans. Autom. Control 59(11), 3051–3056 (2014)
Mu, C., Sun, C., Song, A., Yu, H.: Iterative GDHP-based approximate optimal tracking control for a class of discrete-time nonlinear systems. Neurocomputing 214, 775–784 (2016)
Mu, C., Ni, Z., Sun, C., He, H.: Air-breathing hypersonic vehicle tracking control based on adaptive dynamic programming. IEEE Trans. Neural Netw. Learn. Syst. 28(3), 584–598 (2017)
Sahoo, A., Xu, H., Jagannathan, S.: Neural network-based event-triggered state feedback control of nonlinear continuous-time systems. IEEE Trans. Neural Netw. Learn. Syst. 27(3), 497–509 (2016)
Vamvoudakis, K.G., Lewis, F.L.: Online actor-critic algorithm to solve the continuous-time infinite horizon optimal control problem. Automatica 46(5), 878–888 (2010)
Vamvoudakis, K.G., Mojoodi, A., Ferraz, H.: Event-triggered optimal tracking control of nonlinear systems. Int. J. Robust Nonlinear Control 27(4), 598–619 (2017)
Wang, D., Liu, D., Wei, Q., Zhao, D., Jin, N.: Optimal control of unknown nonaffine nonlinear discrete-time systems based on adaptive dynamic programming. Automatica 48(8), 1825–1832 (2012)
Wang, D., Liu, D., Li, H.: Policy iteration algorithm for online design of robust control for a class of continuous-time nonlinear systems. IEEE Trans. Autom. Sci. Eng. 11(2), 627–632 (2014)
Wang, D., Liu, D., Zhang, Q., Zhao, D.: Data-based adaptive critic designs for nonlinear robust optimal control with uncertain dynamics. IEEE Trans. Syst. Man Cybern. Syst. 46(11), 1544–1555 (2016)
Wang, D., Li, C., Liu, D., Mu, C.: Data-based robust optimal control of continuous-time affine nonlinear systems with matched uncertainties. Inf. Sci. 366, 121–133 (2016)
Wang, D., He, H., Liu, D.: Improving the critic learning for event-based nonlinear \(H_{\infty }\) control design. IEEE Trans. Cybern. 47(10), 3417–3428 (2017)
Wang, D., Mu, C., He, H., Liu, D.: Event-driven adaptive robust control of nonlinear systems with uncertainties through NDP strategy. IEEE Trans. Syst. Man Cybern. Syst. 47(7), 1358–1370 (2017)
Wang, D., Mu, C., Liu, D.: Adaptive critic designs for solving event-based \(H_{\infty }\) control problems. In: Proceedings of American Control Conference, Seattle, WA, USA, May 2017, pp. 2435–2440 (2017)
Werbos, P.J.: Approximate dynamic programming for real-time control and neural modeling. Handbook of Intelligent Control: Neural, Fuzzy, and Adaptive Approaches, pp. 493–526 (1992)
Yang, X., Liu, D., Ma, H., Xu, Y.: Online approximate solution of HJI equation for unknown constrained-input nonlinear continuous-time systems. Inf. Sci. 328, 435–454 (2016)
Zhang, H., Qin, C., Jiang, B., Luo, Y.: Online adaptive policy learning algorithm for \(H_{\infty }\) state feedback control of unknown affine nonlinear discrete-time systems. IEEE Trans. Cybern. 44(12), 2706–2718 (2014)
Zhang, H., Jiang, H., Luo, Y., Xiao, G.: Data-driven optimal consensus control for discrete-time multi-agent systems with unknown dynamics using reinforcement learning method. IEEE Trans. Industr. Electron. 64(5), 4091–4100 (2017)
Zhang, Q., Zhao, D., Zhu, Y.: Event-triggered \(H_{\infty }\) control for continuous-time nonlinear system via concurrent learning. IEEE Trans. Syst. Man Cybern. Syst. 47(7), 1071–1081 (2017)
Zhao, Q., Xu, H., Jagannathan, S.: Near optimal output feedback control of nonlinear discrete-time systems based on reinforcement neural network learning. IEEE/CAA J. Autom. Sin. 1(4), 372–384 (2014)
Zhong, X., He, H.: An event-triggered ADP control approach for continuous-time system with unknown internal states. IEEE Trans. Cybern. 47(3), 683–694 (2017)
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Wang, D., Mu, C. (2019). Event-Triggered Nonlinear \(H_{\infty }\) Control Design via an Improved Critic Learning Strategy. In: Adaptive Critic Control with Robust Stabilization for Uncertain Nonlinear Systems. Studies in Systems, Decision and Control, vol 167. Springer, Singapore. https://doi.org/10.1007/978-981-13-1253-3_8
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