Self-tuning prediction and control for two-dimensional processes Part 1: Fixed parameter algorithms

Least-squares optimal prediction, minimum variance control and generalized minimum variance control algorithms for a two-dimensional CARMA process are developed. Each algorithm involves the algebraic solution of a two-dimensional diophantine equation, and may be embedded within ‘classical’ two-dimensional systems theory. We show how the algorithms must be modified for any practical implementation to take into account the edges of the data field. In this case we show how we may analyse the process using multivariable theory, and explore the linkages between multivariable representations and two-dimensional systems.

[1]  Ulf Borison,et al.  Self-tuning regulators for a class of multivariable systems , 1979, Autom..

[2]  Peter Wellstead,et al.  Self-tuning filters and predictors for two-dimensional systems Part 1: Algorithms , 1985 .

[3]  Thomas S Huang,et al.  Stability of general two-dimensional recursive filters , 1981 .

[4]  M. Šebek.  On 2-D pole placement , 1985 .

[5]  S. Hwang.  Computation of correlation sequences in two-dimensional digital filters , 1981 .

[6]  William P. Heath,et al.  Two-dimensional control systems: application to the CD and MD control problem , 1994 .

[7]  P. Whittle.  ON STATIONARY PROCESSES IN THE PLANE , 1954 .

[8]  Eric Rogers,et al.  Stability Analysis for Linear Repetitive Processes , 1992 .

[9]  Björn Wittenmark,et al.  On Self Tuning Regulators , 1973 .

[10]  P. Gawthrop.  Some interpretations of the self-tuning controller , 1977 .

[11]  Ettore Fornasini,et al.  Structure and solutions of the LQ optimal control problem for 2D systems , 1991, Kybernetika.

[12]  Two-dimensional minimum variance and self-tuning controllers , 1990 .

[13]  Heikki N. Koivo,et al.  A multivariable self-tuning controller , 1980, Autom..

[14]  T. Kasami,et al.  Positive Real Functions of Several Variables and Their Applications to Variable Networks , 1960 .

[15]  B. Wittenmark.  A self-tuning predictor , 1974 .

[16]  Extended self-tuning predictors, smoothers and filters for two-dimensional data fields , 1990 .

[17]  W. Fulton.  Algebraic curves , 1969 .

[18]  K. Åström.  Introduction to Stochastic Control Theory , 1970 .

[19]  William P. Heath,et al.  Self-tuning prediction and control for two-dimensional processes. Part 2: parameter estimation, set-point tracking and offset handling , 1995 .

[20]  H. Ansell.  On Certain Two-Variable Generalizations of Circuit Theory, with Applications to Networks of Transmission Lines and Lumped Reactances , 1964 .