Introduces a new recursive algorithm for solving highly ill-conditioned linear algebraic equations without any cutoff error. It has the following properties: (1) all arithmetic operations are just related to integer additions, abstractions, multiplications, and divisions that can be precisely completed without any remainder; (2) the results of every recursion could be verified automatically by the algorithm itself, and (3) the total arithmetic operations are comparable with those of other direct methods. This algorithm is specially suitable for solving the highly ill-conditioned equations; it can also be used in digital signal processing and other related areas.>

The authors introduce two new one-dimensional multiplicative autoregressive (MAR) models for adaptive predictive coding of digitized images. The proposed scheme offers a number of advantages. These include easy implementability, a high signal-to-noise ratio at a moderate bit rate, and guaranteed stability of the predictive coder. Results of extensive experimental studies are presented.

A bivariate autoregressive model is introduced for the analysis and classification of closed planar shapes. The boundary coordinate sequence of a digitized binary image is sampled to produce a polygonal approximation to an object's shape. This circular sample sequence is then represented by a vector autoregressive difference equation which models the individual Cartesian coordinate sequences as well as coordinate interdependencies. Several classification features which are functions or transformations of the estimated coefficient matrices and the associated residual error covariance matrices are developed. These features are shown to be invariant to object transformations such as translation, rotation, and scaling. Laboratory experiments involving object sets representative of industrial shapes are presented. Superior classification results are demonstrated.>

A technique is proposed to identify the structure as well as the parameters of nonlinear discrete-time system models. The structure is represented in a frequency-position domain of Gabor basis functions (GBFs). A simplification to the GBFs is also presented, where the spatial Gaussian envelope of GBFs is replaced with a triangular one. A modification to the GBFs has also been introduced in order to suppress noise effects on the procedure. A three-layered neural network, augmented with nonuniform sampling, is described for solving the system identification problem.>

A dynamic model that represents an exact linearization scheme with a simplified nonlinear feedback is presented. To realize this model for robotic systems, the output functions should be chosen so that a special decomposition of the total inertial matrix is satisfied. The concept of an imaginary robot is utilized to achieve the formulation and to solve the realization problem. Two illustrative examples are given in the paper, one for the Stanford arm and the other for a PUMA type of robot. An optimal robotic physical design and a control system design based on the new model are also discussed.>

This paper formulates one-dimensional (1-D), recursive, multiplicative time series models for digital images and demonstrates their use for adaptive predictive coding of such images. The performance of the scheme presented here is superior compared to that of conventional 1-D modelling techniques, because correlation among all neighboring pixels of interest can be taken into account. Further, the projection-based constrained least squares identification technique proposed here guarantees stability of the underlying predictor, which makes the scheme more robust compared to the ones that use 2-D recursive models where predictor stability cannot be guaranteed.

A new computer aided technique for the single pass optimal design of stable one dimensional infinite impulse response (IIR) filters is proposed. The method is also applied to the single pass design of stable two dimensional (2-D) filters. The problem is formulated as a constrained non-linear programming operation subject to a convex set of constraints. In the one dimensional (1-D) case, the objective function is a convex function of the filter parameters which insures that the final design is a constrained global optimum. Stability is insured by use of a projection algorithm which continually adjusts any estimates which exceed the constraint boundaries.

The purpose of this paper is to demonstrate the advantages of hybrid, model-matching adaptive control schemes over similar discrete schemes for control of robotic manipulators. In the hybrid approach, the controller itself is a continuously adjustable one, but the adaptation mechanism uses discrete algorithms. Thus, it retains the simplicity and efficiency of discrete parameter estimation techniques and requires estimation of fewer parameters. Furthermore, it retains the minimum phase property of the original continuous time plant and thus avoids any potential problem of instability.

A nonlinear transformation for simplifying the robot dynamic formulation and control system modeling is presented. This is a canonical transformation in the Hamiltonian formulation of robot dynamics, and it can be embodied in a special decomposition of the total inertia matrix. In simplification by using this canonical transformation, the dynamic system is not only transformed to a linear model with the Brunovsky canonical form, the input formulation is also reduced to a simple recovery form. By taking advantage of the linearity of the robot dynamic equation with respect to the total inertia matrix, a detailed procedure of the realization is then described. A 3-D robot example illustrates the feasibility and computational efficiency of this procedure. And it also shows that the realization procedure for the canonical transformation can be summed up in two major steps: seek an imaginary robot and solve a reduced equation.

This paper deals with the development of a unified theory for identification of parameters of a linear, discrete time system which is described by either causal or noncausal ARMA model. We study in detail the convergence properties of a parameter identification algorithm called least squares with covariance modification (LSCOM) and show how the convergence properties of a number of other related algorithms can be derived as special cases of the LSCOM algorithm.

A noncausal ARMA model is employed to accurately account for the two-dimensional structure of imagery data. An equation error approach is taken to develop an observer-identifier for the identification of the image model parameters. The identified model is recast into a state equation form which serves as the basis for applying Kalman filtering equations. The resulting strip filter is applied to an image restoration problem. Simulated results are included to illustrate image model verification and the convergence of the model parameter observer-identifier. Also included are images demonstrating the effectiveness of the resulting image restoration filter.