Robust approximate optimal tracking control of time-varying trajectory for nonlinear affine systems

被引：3

作者：

Qu Q.-X. ^{[1
]}

Luo Y.-H. ^{[1
]}

Zhang H.-G. ^{[1
]}

机构：

[1] School of Information Science and Engineering, Northeastern University, Shenyang, 110819, Liaoning

来源：

Kongzhi Lilun Yu Yingyong/Control Theory and Applications | 2016年 / 33卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Asymptotic stability; Nonlinear affine systems; Optimal control; Time-varying trajectory; Tracking problem;

D O I：

10.7641/CTA.2016.40963

中图分类号：

学科分类号：

摘要：

For continuous time nonlinear systems, it is difficult to track their time-varying trajectory. To deal with this problem, we use a system transformation to introduce a new state variable for converting the optimal tracking problem of nonlinear systems into optimal control problem of general nonlinear time-invariant systems. For this system, we obtain the approximate optimal value function and the approximate optimal control policy based on approximate dynamic programming (ADP). Then, we use the critic network and the actor network to estimate the value function and the corresponding control strategy, and update both of them online. Besides, a robust control term is added to the controller to eliminate the residual errors generated in the process of neural network approximation. By using the Lyapunov stability theorem, we prove that the proposed control strategy can guarantee the tracking error to converge asymptotically to zero, and the control strategy is close to the optimal control strategy when the error is in a small bound. Finally, simulations of two time-varying trajectory tracking examples show the feasibility and effectiveness of the proposed method. © 2016, Editorial Department of Control Theory & Applications South China University of Technology. All right reserved.

引用

页码：77 / 84

页数：7

共 18 条

[1]

Huang Y., Liu D., Neural-network-based optimal tracking control scheme for a class of unknown discrete-time nonlinear systems using iterative ADP algorithm, Neurocomputing, 10, 3, pp. 325-331, (2012)

[2]

Song R., Xiao W., Sun C., Optimal tracking control for a class of unknown discrete-time systems with actuator saturation via databased ADP algorithm, Neurocomputing, 39, 9, pp. 1293-1302, (2010)

[3]

Zhang H., Cui L., Zhang X., Et al., Data-driven robust approximate optimal tracking control for unknown general nonlinear systems using adaptive dynamic programming method, IEEE Transactions on Neural Networks, 22, 12, pp. 2226-2236, (2011)

[4]

Wang D., Liu D., Wei Q., Finite-horizon neuro-optimal tracking control for a class of discrete-time nonlinear systems using adaptive dynamic programming approach, Neurocomputing, 78, 1, pp. 14-22, (2012)

[5]

Luo Y., Liang M., Approximate optimal tracking control for a class of discrete-time non-affine systems based on GDHP algorithm, The 4th International Workshop on Advanced Computational Intelligence, pp. 143-149, (2011)

[6]

Dierks T., Jagannathan S., Optimal tracking control of affine nonlinear discrete-time systems with unknown internal dynamics, Proceedings of the 48th IEEE Conference on Decision and Control, pp. 6750-6755, (2009)

[7]

Zhang H., Wei Q., Luo Y., 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 Systems, Man and Cybernetics, Part B, 38, 4, pp. 937-942, (2008)

[8]

Werbos P.J., Approximate dynamic programming for real time control and neural modeling, Handbook of Intelligent Control, (1992)

[9]

Li X., Liu D., Jia C., Et al., Multiple set-points tracking control method based on adaptive dynamic programming, Control Theory & Applications, 30, 6, pp. 709-716, (2013)

[10]

Lin X., Huang Y., Song C., Approximate optimal control with ε-error bound, Control Theory & Applications, 29, 1, pp. 104-108, (2012)

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