In this paper, a novel learning scheme is proposed to speed up the learning process in cerebellar model articulation controllers (CMAC). In the conventional CMAC learning scheme, the correct numbers of errors are equally distributed into all addressed hypercubes, regardless of the credibility of the hypercubes. The proposed learning approach uses the inverse of learned times of the addressed hypercubes as the credibility (confidence) of the learned values, resulting in learning speed becoming very fast. To further demonstrate online learning capability of the proposed credit assigned CMAC learning scheme, this paper also presents a learning robust controller that can actually learn online. Based on robust controllers presented in the literature, the proposed online learning robust controller uses previous control input, current output acceleration, and current desired output as the state to define the nominal effective moment of the system from the CMAC table. An initial trial mechanism for the early learning stage is also proposed. With our proposed credit-assigned CMAC, the robust learning controller can accurately trace various trajectories online.

Credit assigned CMAC and its application to online learning robust controllers

This paper demonstrates an application of the parametric cerebellar model articulation controller (P-CMAC) network - a neural structure derived from Albus' CMAC algorithm and Takagi-Sugeno-Kang parametric fuzzy inference systems. It resembles the original CMAC proposed by Albus in the sense that it is a local network, i.e., for a given input vector, only a few of the networks neurons will be active and will effectively contribute to the corresponding network output. The internal mapping structure is built in such a way that it implements, for each CMAC memory location, one linear parametric equation of the network input strengths. First, a new approach to design neural optimal control (NOC) systems is proposed. Gradient-descent techniques are still used here to adjust network weights, but this approach has many differences when compared to classical error backpropagation algorithm. Then, P-CMAC is used to control the output voltage of a proton exchange membrane fuel cell (PEM-FC), by means of NOC. The proposed control system allows the definition of an arbitrary performance/cost criterion to be maximized/minimized, resulting in an approximated optimal control strategy. Practical results of PEM-FC voltage behavior at different load conditions are shown, to demonstrate the effectiveness of the NOC algorithm.

Neural optimal control of PEM-fuel cells with parametric CMAC networks

An adaptive cerebellar model articulation controller (CMAC) is proposed for command to line-of-sight (CLOS) missile guidance law design. In this design, the three-dimensional (3-D) CLOS guidance problem is formulated as a tracking problem of a time-varying nonlinear system. The adaptive CMAC control system is comprised of a CMAC and a compensation controller. The CMAC control is used to imitate a feedback linearization control law and the compensation controller is utilized to compensate the difference between the feedback linearization control law and the CMAC control. The online adaptive law is derived based on the Lyapunov stability theorem to learn the weights of receptive-field basis functions in CMAC control. In addition, in order to relax the requirement of approximation error bound, an estimation law is derived to estimate the error bound. Then the adaptive CMAC control system is designed to achieve satisfactory tracking performance. Simulation results for different engagement scenarios illustrate the validity of the proposed adaptive CMAC-based guidance law.

Missile guidance law design using adaptive cerebellar model articulation controller

Some control strategies for a high-angle-of-attack missile autopilot

In this paper, the online learning capability and the robust property for the learning algorithms of cerebellar model articulation controllers (CMAC) are discussed. Both the traditional CMAC and fuzzy CMAC are considered. In the study, we find a way of embedding the idea of M-estimators into the CMAC learning algorithms to provide the robust property against outliers existing in training data. An annealing schedule is also adopted for the learning constant to fulfil robust learning. In the study, we also extend our previous work of adopting the credit assignment idea into CMAC learning to provide fast learning for fuzzy CMAC. From demonstrated examples, it is clearly evident that the proposed algorithm indeed has faster and more robust learning. In our study, we then employ the proposed CMAC for an online learning control scheme used in the literature. In the implementation, we also propose to use a tuning parameter instead of a fixed constant to achieve both online learning and fine-tuning effects. The simulation results indeed show the effectiveness of the proposed approaches.

Robust and fast learning for fuzzy cerebellar model articulation controllers

Anovel fuzzyneuralnetworkcontrolsystem architecture,calledthefuzzycerebellarmodelarithmeticcomputer (fuzzy CMAC) neural network, is proposed. This fuzzy neural network architecture exploits a synergism between the original CMAC neural network and the theory of fuzzy logic controller. The fuzzy CMAC is able to perform arbitrary function approximation and can achieve a higher learning speed and greater accuracy than the original CMAC. It also has the capability of conveniently incorporating human knowledge into the system and processing information based on fuzzy inference rules. We evaluated the use of fuzzy CMAC in the design of advanced missile control systems. The method is demonstrated by missile interception simulations, and promising results are obtained.

Z. Jason Geng

Papers

Missile Control Using Fuzzy Cerebellar Model Arithmetic Computer Neural Networks