Robust optimal control for a class of nonlinear dynamic systems using single network adaptive dynamic programming

In this paper, the robust optimal control for a class of nonlinear systems with uncertainties is investigated by using single network adaptive dynamic programming approach. The robust controller of the original uncertain nonlinear system is derived by adding a feedback gain to the optimal controller of the nominal system. It is proved that the robust controller can achieve optimality under a specified cost function. Then, a single neural network is constructed for solving the Hamilton-Jacobi-Bellman equation corresponding to the nominal system, where an additional stabilizing term is introduced to check the stability. Furthermore, the obtained results are extended to establish the decentralized optimal control strategy for a class of nonlinear interconnected large-scale systems. Finally, a simulation example is provided to illustrate the effectiveness of the control scheme.

[1]  Derong Liu,et al.  Decentralized Stabilization for a Class of Continuous-Time Nonlinear Interconnected Systems Using Online Learning Optimal Control Approach , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[2]  Zhong-Ping Jiang,et al.  Robust adaptive dynamic programming for linear and nonlinear systems: An overview , 2013, Eur. J. Control.

[3]  F. Lewis,et al.  Reinforcement Learning and Feedback Control: Using Natural Decision Methods to Design Optimal Adaptive Controllers , 2012, IEEE Control Systems.

[4]  Huaguang Zhang,et al.  Adaptive Dynamic Programming: An Introduction , 2009, IEEE Computational Intelligence Magazine.

[5]  Feng Lin,et al.  Robust Control of Nonlinear Systems: Compensating for Uncertainty , 1990, 1990 American Control Conference.

[6]  Dongbin Zhao,et al.  Full-range adaptive cruise control based on supervised adaptive dynamic programming , 2014, Neurocomputing.

[7]  Li Hongliang,et al.  Optimal control of unknown discrete-time nonlinear systems with constrained inputs using GDHP technique , 2012, Proceedings of the 31st Chinese Control Conference.

[8]  Li Hongliang,et al.  A learning optimal control scheme for robust stabilization of a class of uncertain nonlinear systems , 2013, Proceedings of the 32nd Chinese Control Conference.

[9]  Huai-Ning Wu,et al.  Neural Network Based Online Simultaneous Policy Update Algorithm for Solving the HJI Equation in Nonlinear $H_{\infty}$ Control , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[10]  Jian Chen,et al.  Robust Feedback Control for a Class of Uncertain MIMO Nonlinear Systems , 2008, IEEE Transactions on Automatic Control.

[11]  Haibo He,et al.  Online Learning Control Using Adaptive Critic Designs With Sparse Kernel Machines , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[12]  Qinglai Wei,et al.  Optimal control of unknown nonaffine nonlinear discrete-time systems based on adaptive dynamic programming , 2012, Autom..

[13]  Feng Lin,et al.  An optimal control approach to robust control of robot manipulators , 1998, IEEE Trans. Robotics Autom..

[14]  Frank L. Lewis,et al.  Multi-agent differential graphical games , 2011, Proceedings of the 30th Chinese Control Conference.

[15]  Haibo He,et al.  Reactive power control of grid-connected wind farm based on adaptive dynamic programming , 2014, Neurocomputing.

[16]  Jean-Jacques E. Slotine,et al.  Neural Network Control of Unknown Nonlinear Systems , 1989, 1989 American Control Conference.