Abstract
In this paper, the H ∞ optimal control for a class of continuous-time nonlinear systems is investigated using event-triggered method. First, the H ∞ optimal control problem is formulated as a two-player zero-sum differential game. Then, an adaptive triggering condition is derived for the closed loop system with an event-triggered control policy and a time-triggered disturbance policy. For implementation purpose, the event-triggered concurrent learning algorithm is proposed, where only one critic neural network is required. Finally, an illustrated example is provided to demonstrate the effectiveness of the proposed scheme.
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Basar, T., Olsder, G.J., Clsder, G.J., et al.: Dynamic noncooperative game theory. Academic Press, London (1995)
Zhao, D., Zhu, Y.: MEC—A Near-Optimal Online Reinforcement Learning Algorithm for Continuous Deterministic Systems. IEEE Transactions on Neural Networks and Learning Systems 26(2), 346–356 (2015)
Zhao, D., Xia, Z., Wang, D.: Model-Free Optimal Control for Affine Nonlinear Systems With Convergence Analysis. IEEE Transactions on Automation Science and Engineering (2015), doi:10.1109/TASE.2014.2348991
Alippi, C., Ferrero, A., Piuri, V.: Artificial intelligence for instruments and measurement applications. IEEE Instrumentation & Measurement Magazine 1(2), 9–17 (1998)
Al-Tamimi, A., Abu-Khalaf, M., Lewis, F.L.: Adaptive critic designs for discrete-time zero-sum games with application to control. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 37(1), 240–247 (2007)
Abu-Khalaf, M., Lewis, F.L., Huang, J.: Policy iterations on the Hamilton-Jacobi-Isaacs equation for state feedback control with input saturation. IEEE Transactions on Automatic Control 51(12), 1989–1995 (2006)
Vamvoudakis, K.G., Lewis, F.L.: Online solution of nonlinear two-player zero-sum games using synchronous policy iteration. International Journal of Robust and Nonlinear Control 22(13), 1460–1483 (2012)
Sahoo, A., Xu, H., Jagannathan, S.: Event-based optimal regulator design for nonlinear networked control systems. In: 2014 IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning, pp. 1–8. IEEE Press, Orlando (2014)
Zhong, X., Ni, Z., He, H., Xu, X., Zhao, D.: Event-triggered reinforcement learning approach for unknown nonlinear continuous-time system. In: 2014 International Joint Conference on Neural Networks, pp. 3677–3684. IEEE Press, Beijing (2014)
Vamvoudakis, K.G.: Event-triggered optimal adaptive control algorithm for continuous-time nonlinear systems. IEEE/CAA Journal of Automatica Sinica 1(3), 282–293 (2014)
Chowdhary, G., Johnson, E.: Concurrent learning for convergence in adaptive control without persistency of excitation. In: 49th IEEE Conference on Decision and Control (CDC), pp. 3674–3679. IEEE Press, Atlanta (2010)
Modares, H., Lewis, F.L., Naghibi-Sistani, M.B.: Integral reinforcement learning and experience replay for adaptive optimal control of partially-unknown constrained-input continuous-time systems. Automatica 50(1), 193–202 (2014)
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© 2015 Springer International Publishing Switzerland
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Zhao, D., Zhang, Q., Li, X., Kong, L. (2015). Event-Triggered H ∞ Control for Continuous-Time Nonlinear System. In: Hu, X., Xia, Y., Zhang, Y., Zhao, D. (eds) Advances in Neural Networks – ISNN 2015. ISNN 2015. Lecture Notes in Computer Science(), vol 9377. Springer, Cham. https://doi.org/10.1007/978-3-319-25393-0_8
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DOI: https://doi.org/10.1007/978-3-319-25393-0_8
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