Over the past decades, there have been increasing demands for controller designs for stochastic systems. When dealing with these stochastic systems, one of the important practical issues in the controller design is the minimization of the randomness in the closed-loop system. Traditional stochastic control was focused on the output mean and variance under the assumption that the system variables are of Gaussian types. When it comes to nonlinear systems with non-Gaussian noises, stochastic distribution control can be used, which focuses on controlling the shape of the output probability density function (PDF) for the dynamic system.
On the other hand, sliding-mode control (SMC) is considered as an important method in modern control theory, which can be used to deal with control systems subjected to uncertainties and disturbances. In spite of its robustness and accuracy, the key problem of SMC is its high (theoretically infinite) frequency control switching which leads to the so-called chattering effect.
In this research, LIU Yu, WANG Hong and HOU Chaohuan from the Institute of Acoustics, Chinese Academy of Sciences present a hybrid control scheme that incorporates SMC with PDF shaping. The SMC part deals with the non-repeatable uncertainties and un-modeled dynamics, while stochastic control part, which is also called PDF control, shapes the PDF of the tracking error to the desired function. Kullback-Leibler divergence is introduced to the stochastic distribution control, and the parameter of the stochastic distribution controller is updated at each sample interval rather than using a batch mode. It is shown that the estimated weight vector will converge to its ideal value. And the system will be asymptotically stable under the rank-condition, which is much weaker than the persistent excitation condition. The effectiveness of the proposed algorithm is illustrated by simulation.
This research was supported in part by Natural Science Foundation of China under grants 61290323 and 61134006. Also, this research was supported by Director Foundation of Institute of Acoustics, Chinese Academy of Sciences under grant Y154221511.
The research result was released online http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6579752 and on Neural Networks and Learning Systems, IEEE Transactions on (Volume: PP, Issue: 99, 15 August, 2013).
Contact:
LIU Yu
Institute of Acoustics, Chinese Academy of Sciences
liuyu2010@mail.ioa.ac.cn