Abstract
Based on information theory, the single neuron adaptive control problem for stochastic systems with non-Gaussian noises is investigated in this paper. Here, the statistic information of the output within a receding window rather than the output value is used for the tracking problem. Firstly, the single neuron controller structure, which has the ability of self-learning and self-adaptation, is established. Then, an improved performance criterion is given to train the weights of the single neuron. Furthermore, the mean-square convergent condition of the proposed control algorithm is formulated. Finally, comparative simulation results are presented to show that the proposed algorithm is superior to the PID controller. The contributions of this work are twofold: (1) the optimal control algorithm is formulated in the data-driven framework, which needn’t the precise system model that is usually difficult to obtain; (2) the control problem of non-Gaussian systems can be effectively dealt with by the simple single neuron controller under improved minimum entropy criterion.
Highlights
As a simple and effective controller, the proportional-integral-derivative controller (PID controller), which has advantages in terms of strong robustness, high reliability, good dynamic response and so on, has been widely used in most industrial control systems
The stochastic distribution control (SDC) method was proposed by Wang [7], where the shape of the output probability density function (PDF) rather than the output itself was considered
This paper has introduced a new statistic information-based single neuron adaptive control algorithm for general control systems with non-Gaussian noises
Summary
As a simple and effective controller, the proportional-integral-derivative controller (PID controller), which has advantages in terms of strong robustness, high reliability, good dynamic response and so on, has been widely used in most industrial control systems. The model-free adaptive control system formed by single neuron, because of its simple structure, has been studied and some results of learning algorithm and applications can be found (see e.g., [5,6]). The disturbances in practical systems are not necessarily non-Gaussian; nonlinearity in stochastic control systems could lead to non-Gaussian randomness even if the disturbances obey a Gaussian distribution For this case, the stochastic distribution control (SDC) method was proposed by Wang [7], where the shape of the output probability density function (PDF) rather than the output itself was considered. Motivated by the above results, in this paper a single neuron adaptive controller, which is a model-free controller, is developed for stochastic systems with non-Gaussian disturbances.
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