Chun-Shin Lin

Learning convergence of CMAC technique

CMAC is one useful learning technique that was developed two decades ago but yet lacks adequate theoretical foundation. Most past studies focused on development of algorithms, improvement of the CMAC structure, and applications. Given a learning problem, very little about the CMAC learning behavior such as the convergence characteristics, effects of hash mapping, effects of memory size, the error bound, etc. can be analyzed or predicted. In this paper, we describe the CMAC technique with mathematical formulation and use the formulation to study the CMAC convergence properties. Both information retrieval and learning rules are described by algebraic equations in matrix form. Convergence characteristics and learning behaviors for the CMAC with and without hash mapping are investigated with the use of these equations and eigenvalues of some derived matrices. The formulation and results provide a foundation for further investigation of this technique.

CMAC-based adaptive critic self-learning control

A technique that integrates the cerebellar model articulation controller (CMAC) into a self-learning control scheme developed by A.G. Barto et al. (IEEE Trans. Syst. Man., Cybern., vol.SMC-13, p.834-46, Sept./Oct. 1983) is presented. Instead of reserving one input line (as a memory) for each quantized state, the integrated technique distributively stores learned information; this reduces the required memory and makes the self-learning control scheme applicable to problems of larger size. CMACs capability with regard to information interpolation also helps improve the learning speed.

Selection of learning parameters for CMAC-based adaptive critic learning

The CMAC-based adaptive critic learning structure consists of two CMAC modules: the action and the critic ones. Learning occurs in both modules. The critic module learns to evaluate the system status. It transforms the system response, usually some occasionally provided reinforcement signal, into organized useful information. Based on the knowledge developed in the critic module, the action module learns the control technique. One difficulty in using this scheme lies on selection of learning parameters. In our previous study on the CMAC-based scheme, the best set of learning parameters were selected from a large number of test simulations. The picked parameter values are not necessarily adequate for generic cases. A general guideline for parameter selection needs to be developed. In this study, the problem is investigated. Effects of parameters are studied analytically and verified by simulations. Results provide a good guideline for parameter selection.

Use of adaptive resolution for better CMAC learning

The quantization of the input space affects the performance of cerebellar model arithmetic computer (CMAC)-based systems. The conventional CMAC uses equal-size quantization without considering the variation of the target function in different areas. The new scheme presented is capable of adaptively changing the input quantization through the use of the so-called mapping functions. For a fixed number of blocks and elements, larger blocks and elements are used for the areas with less variation in control signal. Memory is efficiently used. Through the repeated learning and mapping function updating, better learning results can be achieved. Simulation results for a single-variable case are encouraging.<<ETX>>

Gait synthesis of a biped robot using backpropagation through time algorithm

A neural network architecture is developed for the gait synthesis of a five-link biped walking robot. The learning scheme uses a multilayered feedforward neural network combined with a linearized inverse biped model. It can generate walking gait by giving reference trajectory which defines a desired gait in several stages. The algorithm used to train network is known as back-propagation with time-delay or so-called backpropagation through time. A three-layered neural network is used as a controller, it provides the control signals in each stage of a walking gait. The linearized inverse biped model calculates the error signals which will be used to back propagate through the controller in each stage.

Integration of CMAC technique and weighted regression for efficient learning and output differentiability

Cerebellar model articulation controllers (CMAC) have attractive properties of learning convergence and speed. Many studies have used CMAC in learning control and demonstrated successful results. However, due to the fact that CMAC is a table lookup technique, a model implemented by a CMAC does not provide a derivative of its output. This is an inconvenience when using CMAC in learning structures that require such derivatives. This paper presents a new scheme that integrates the CMAC addressing technique with weighted regression to resolve this problem. Derivatives exist everywhere except on the boundaries of quantized regions. Compared with the conventional CMAC, the new scheme requires the same amount of memory and has similar learning speed, but provides output differentiability and more precise output. Compared with the typical weighted regression technique, the new scheme offers an efficient way to organize and utilize collected information.

A new neural network structure composed of small CMACs

A new neural network structure that consists of several small CMACs is proposed. The structure is a memory based neural network. While the memory cost has been reduced and the memory technology has improved in the past decade, practical implementation of the proposed structure is inexpensive. The new structure overcomes the huge memory size problem, which exists in the conventional CMAC in high-dimensional modeling. The new neural network will be able to better utilize the memory in learning all kinds of mapping.

A learning algorithm for radial basis function networks: with the capability of adding and pruning neurons

Radial basis function networks (RBFN) have fast learning speed because of their capability of local specialization and global generalization. By allowing the use of basis functions with different sizes (covering area), locations and orientations, RBFNs behave even more powerful and require less neurons. If an algorithm can automatically add and prune neurons, the necessary number of neurons can be further reduced. In this paper, we present such an algorithm. We select the Gaussian functions as basis functions with all the above parameters adjustable. The algorithm adds new RBFs at the places having the largest errors, and prunes neurons that have insignificant contribution. With the adding and pruning capability, it is expected that developing RBFNs for high-dimensional problems will become more feasible.<<ETX>>

Genetic algorithm for control design of biped locomotion

Dynamic biped walking is a difficult control problem. The problem involves the design of the controller as well as the gait. In this paper, the design of the controller and the gait is formulated as a parameter search problem and a genetic algorithm is applied to help the design. Designs to achieve different goals, such as being able to walk on an inclined surface, walk at a high speed or with a specified step size have been evolved with the use of the genetic algorithm. Simulation results show that the genetic algorithm is capable of finding good solutions.

Integration of CMAC and radial basis function techniques

In this paper, we integrate the techniques of radial basis functions (RBF) and CMAC to develop a more efficient scheme. Both the CMAC and RBF use the basis functions that may have significant values only in a local input space. CMAC uses the plateau basis while the RBF often uses the Gaussian. Merits of RBF include the continuity and differentiability of the approximate function, and the better accuracy. CMAC has however very attractive convergence properties. In this study, we combine these two techniques with an intention to take the merits from both.