Abstract
In this paper, a new iterative ADP algorithm is proposed to solve the finite horizon optimal tracking control problem for a class of discrete-time nonlinear systems. The idea is that using system transformation, the optimal tracking problem is transformed into optimal regulation problem, and then the iterative ADP algorithm is introduced to deal with the regulation problem with convergence guarantee. Three neural networks are used to approximate the performance index function, compute the optimal control policy and model the unknown system dynamics, respectively, for facilitating the implementation of iterative ADP algorithm. An example is given to demonstrate the validity of the proposed optimal tracking control scheme.
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References
Ha, I.J., Gilbert, E.G.: Robust tracking in nonlinear systems. IEEE Transactions Automatic Control 32, 763–771 (1987)
Cimen, T., Banks, S.P.: Nonlinear optimal tracking control with application to super-tankers for autopilot design. Automatica 40, 1845–1863 (2004)
Gao, D., Tang, G., Zhang, B.: Approximate optimal tracking control for a class of nonlinear systems with disturbances. In: Proceedings of 6th World Congress on Intelligent Control and Automation, Dalian, China, vol. 1, pp. 521–525 (2006)
Zhang, H.G., Wei, Q.L., Luo, Y.H.: A novel infinite-time optimal tracking control scheme for a class of discrete-time nonlinear systems via the greedy HDP iteration algorithm. IEEE Transactions on System, Man, and cybernetics-Part B: Cybernetics 38, 937–942 (2008)
Werbos, P.J.: A menu of designs for reinforcement learning over time. In: Miller, W.T., Sutton, R.S., Werbos, P.J. (eds.) Neural Networks for Control, pp. 67–95. MIT Press, Cambridge (1991)
Liu, D.R., Zhang, Y., Zhang, H.: A self-learning call admission control scheme for CDMA cellular networks. IEEE Trans. Neural Networks 16, 1219–1228 (2005)
Wei, Q.L., Zhang, H.G., Dai, J.: Model-free multiobjective approximate dynamic programming for discrete-time nonlinear systems with general performance index functions. Neurocomputing 72, 1839–1848 (2009)
Zhang, H.G., Wei, Q.L., Liu, D.R.: An iterative adaptive dynamic programming method for solving a class of nonlinear zero-sum differential games. Automatica 47(1), 207–214 (2011)
Zhang, H.G., Wei, Q.L., Liu, D.R.: On-Line Learning Control for Discrete Nonlinear Systems Via an Improved ADDHP Method. In: Liu, D., Fei, S., Hou, Z.-G., Zhang, H., Sun, C. (eds.) ISNN 2007. LNCS, vol. 4491, pp. 387–396. Springer, Heidelberg (2007)
Wei, Q.L., Liu, D.R., Zhang, H.G.: Adaptive Dynamic Programming for a Class of Nonlinear Control Systems with General Separable Performance Index. In: Sun, F., Zhang, J., Tan, Y., Cao, J., Yu, W. (eds.) ISNN 2008, Part II. LNCS, vol. 5264, pp. 128–137. Springer, Heidelberg (2008)
Zhang, H., Wei, Q., Liu, D.: An iterative adaptive dynamic programming method for solving a class of nonlinear zero-sum differential games. Automatica 47, 207–214 (2011)
Wang, F., Jin, N., Liu, D., Wei, Q.: Adaptive dynamic programming for finite-horizon optimal control of discrete-time nonlinear systems with ε-error bound. IEEE Transactions on Neural Networks 22, 24–36 (2011)
Al-Tamimi, A., Abu-Khalaf, M., Lewis, F.L.: Adaptive critic designs for discrete-time zero-sum games with application to H ∞ control. IEEE Trans. Systems, Man, and Cybernetics-Part B: Cybernetics 37, 240–247 (2007)
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Wei, Q., Wang, D., Liu, D. (2011). Finite Horizon Optimal Tracking Control for a Class of Discrete-Time Nonlinear Systems. In: Liu, D., Zhang, H., Polycarpou, M., Alippi, C., He, H. (eds) Advances in Neural Networks – ISNN 2011. ISNN 2011. Lecture Notes in Computer Science, vol 6676. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21090-7_71
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DOI: https://doi.org/10.1007/978-3-642-21090-7_71
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