2D Systems Theory Research Articles

Relaxed pass profile controllability of discrete linear repetitive processes

Repetitive processes are a distinct class of 2D systems (i.e. information propagation in two independent directions) of both systems theoretic and applications interest. They cannot be controlled by direct extension of existing techniques from either standard (termed 1D here) or 2D systems theory. In this paper we develop significant new results on controllability of so-called discrete linear repetitive processes. The end result is necessary and sufficient conditions for this property in terms of matrix rank based tests. The application of these tests is illustrated by a numerical example.

Stabilization of Discrete Linear Repetitive Processes with Switched Dynamics

Repetitive processes are a distinct class of 2D systems (i.e. information propagation in two independent directions) of both systems theoretic and applications interest. They cannot be controlled by direct extension of existing techniques from either standard (termed 1D here) or 2D systems theory. Here we give new results on the relatively open problem of the design of physically based control laws. These results are for a sub-class of discrete linear repetitive processes with switched dynamics in both independent directions of information propagation.

PI control of discrete linear repetitive processes

Repetitive processes are a distinct class of 2D systems (i.e. information propagation in two independent directions) of both systems theoretic and applications interest. They cannot be controlled by direct extension of existing techniques from either standard (termed 1D here) or 2D systems theory. In this paper, we exploit their unique physical structure to show how two term, i.e. proportional plus integral (or PI) action, can be used to control these processes to produce desired behavior (as opposed to just stability).

H/sub /spl infin// control of differential linear repetitive processes

Repetitive processes are a distinct class of two-dimensional systems (i.e., information propagation in two independent directions) of both systems theoretic and applications interest. They cannot be controlled by direct extension of existing techniques from either standard (termed 1D here) or two-dimensional (2D) systems theory. Here, we give new results on the relatively open problem of the design of physically based control laws using an H/sub /spl infin// setting. These results are for the sub-class of so-called differential linear repetitive processes, which arise in application areas such as iterative learning control.

Formula omitted] and guaranteed cost control of discrete linear repetitive processes

Repetitive processes are a distinct class of 2D systems (i.e. information propagation in two independent directions) of both systems theoretic and applications interest. In general, they cannot be controlled by direct extension of existing techniques from either standard (termed 1D here) or 2D systems theory. Here first we give major new results on the design of control laws using an H ∞ setting and including the possibility of uncertainty in the process model. Then we give the first ever results on guaranteed cost control, i.e. including a performance criterion in the design. The designs in both cases can be computed using linear matrix inequalities. These results are for so-called discrete linear repetitive processes which arise in applications areas such as iterative learning control.

CONTROLLABILITY AND QUADRATIC STABILIZATION OF A CLASS OF DISCRETE LINEAR REPETITIVE PROCESSES

Repetitive processes are a distinct class of two-dimensional systems (i.e. information propagation in two independent directions) of both systems theoretic and applications interest. They cannot be controlled by direct extension of existing techniques from either standard (termed 1D here) or two-dimensional (2D) systems theory. In this paper we define a new model for these processes necessary to represent dynamics which arise in some applications areas and which are not included in the currently used model. Then we proceed to define quadratic stability for this case and develop the first results on a control theory in the form of pass controllability and the design of physically based control laws.

H2 CONTROL OF DIFFERENTIAL LINEAR REPETITIVE PROCESSES

Repetitive processes are a distinct class of two-dimensional systems (i.e. information propagation in two independent directions) of both systems theoretic and applications interest. They cannot be controlled by direct extension of existing techniques from either standard (termed 1D here) or two-dimensional (2D) systems theory. Here we give new results on the design of physically based control laws using an H2 setting. These results are for the sub-class of so-called differential linear repetitive processes which arise in applications areas such as iterative learning control.

Output feedback control of discrete linear repetitive processes

Repetitive processes are a distinct class of 2D systems (i.e. information propagation in two independent directions) of both systems theoretic and applications interest. They cannot be controlled by direct extension of existing techniques from either standard (termed 1D here) or 2D systems theory. Here, we give new results on the relatively open problem of the design of physically based control laws using an LMI setting. These results are for the sub-class of the so-called discrete linear repetitive processes which arise in applications areas such as iterative learning control.

Iterative learning control — 2D control systems from theory to application

It has long been recognized that iterative learning control is a 2D system, i.e. information propagation occurs in two independent directions. In this paper, the application of so-called norm optimal iterative learning control, which has its origins in the theory of the class of 2D systems known as linear repetitive processes to an experimental testbed in the form of a chain conveyor system is reported. This includes the motivation for applying iterative learning control to such systems, the design and construction of the testbed, and its use to demonstrate that norm optimal iterative learning control gives superior performance over alternatives. As such, it provides an application for 2D systems theory where distinct advantages arise from using such a setting for modelling and control.

Z - Transform and Volterra-Operator Based Approaches to Controllability and Observability Analysis for Discrete Linear Repetitive Processes

Linear repetitive processes are a distinct class of 2D systems of both systems theoretic and applications interest. They are distinct from other classes of such systems by the fact that information propagation in one of the two separate directions only occurs over a finite duration. This, in turn, means that existing 2D systems theory either cannot be applied at all or only in substantially modified form. Hence a distinct systems theory must be developed for them with onward translation (where appropriate) into reliable routinely applicable analysis and design tools. This paper contributes substantial news results to this general task in the areas of controllability and observability for the sub-class of so-called discrete linear repetitive processes which arise in key applications areas and, in particular, iterative learning control.

Internal Model Control using Recurrent Neural Networks for Nonlinear Dynamic Systems

This paper presents a control method using Recurrent Neural Networks (RNNs) in an Internal Model Control (IMC) framwork. and demonstrates their effectiveness of modelling and control for nonlinear dynamic systems. Unlike existing neural IMC design methods, the proposed control scheme consists of two stages. The first stage is that using two same structure of RNNs through iterative learning techniques to obtain a desired control signal to the unknown nonlinear systems. Then a RNN is used to generate the desired control signal within IMC structure. The algorithm for the RNNs is a real time iterative learning algorithm based on two-dimensional (2D) system theory. The simulation results demonstrate the proposed control method can drive unknown systems to follow the desired trajectories very well.

Causal Input/Output Representation of 2D Systems in the Behavioral Approach

In this paper the concept of causal input/output representation of two-dimensional (2D) systems in the behavioral approach is introduced. These representations provide an interesting connection between classical 2D systems theory and 2D systems theory in the behavioral approach. Some characterizations of such representations are presented. Finally, a technique that allows us to obtain causal input/output representations is proposed.

Convergence Rates for Learning Control Algorithms-A Repetitive Process Theory Approach

This paper presents significant new results on the stability and convergence properties of a general class of iterative learning control schemes derived using two-dimensional(2D) systems theory. These results apply for a general learning law which (explicitly) uses information from previous iterations or trials. A key feature of these results is that they are expressed in terms of standard linear systems theoretic properties, such as relative degree and the location of the zeros.

New 2D Systems Models for Repetitive Processes

This paper develops new 2D systems state space models for discrete linear repetitive processes. The overall aim is to use these models and well established 2D systems theory to address basic systems theoretic questions for this subclass of repetitive processes. To this end, it is shown that the stability theories are equivalent and a state transition matrix is developed and used to present some basic results on reachability.