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Discusses a goal-oriented project, focused on open learning environments using computer networks, called Distance Learning in Multimedia Networks that was part of the Finnish Multimedia Program. Describes the combined efforts of Finnish telecommunications companies, content providers, publishing houses, hardware companies, and educational institutions in the field of distance learning. (Author/LRW)

It is well known that a low-gain controller of the form [C.sub.[epsilon]](s) = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] = -n [epsilon][K.sub.[kappa]](s - i[[omega].sub.[kappa]]) is able to track and reject constants and finite linear combinations of sinusoidal reference and disturbance signals with known frequencies [[omega].sub.[kappa]]. In this note, we investigate the optimal tuning of the matrix gains [K.sub.[kappa]] of the controller [C.sub.[epsilon]](s) as the positive scalar gain [epsilon] [right arrow] [0.sup.+] for exponentially stable plants with transfer function P [member of] [H.sup.[[infinity]. The cost function is taken to be the [H.sup.2]-norm of the error between the reference signal and the measured output signal. It is shown that as [epsilon] [right arrow] [0.sup.+] the cost function decomposes into a sum of simpler cost functions, each depending only on [K.sub.[kappa]] and P(i[[omega].sub.[kappa]]). Using this decomposition closed form solutions for the subproblems are found in certain special cases, and upper and lower bounds are given in the general case. No plant model is necessary since only the values P(i[[omega].sub.[kappa]]) are needed, and it is shown that these can be measured from the open-loop plant with suitable input--output experiments. Index Terms--Distributed parameter systems, low-gain control, optimal control, tracking.

In this note, we consider output regulation and disturbance rejection of periodic signals via state feedback in the setting of exponentially stabilizable linear infinite-dimensional systems. We show that if an infinite-dimensional exogenous system is generating periodic reference signals, solvability of the state feedback regulation problem is equivalent to solvability of the so called equations. This result allows us to consider asymptotic tracking of periodic reference signals which only have absolutely summable Fourier coefficients, while in related existing work the reference signals are confined to be infinitely smooth. We also discuss solution of the regulator equations and construct the actual feedback law to achieve output regulation in the single-input--single-output (SISO) case: The output regulation problem is solvable if the transfer function of the stabilized plant does not have zeros at the frequencies i[[omega].sub.n] of the periodic reference signals and if the sequence ([[CR(i[[omega].sub.n], A + BK) B].sup.-1] x [(Q[[phi].sub.n] - CR(i[[omega].sub.n], A + BK) P [[phi].sub.n])). [sub.n][[member of]Z] [member of] [l.sup.2] A one-dimensional heat equation is used as an illustrative example. Index Terms--Asymptotic tracking, Fourier series, heat equation, infinite-dimensional systems, output regulation, periodic signals, regulator equations, state feedback.

In a previous paper, the authors have shown that a low-gain controller of the form [C.sub.[epsilon]] (s) -- [[summation of].sup.n.sub.k=-n] [epsilon] [K.sub.k]/(s - i[[omega].sub.k] is able to track and reject constant and sinusoidal reference and disturbance signal for a stable plant in the Callier-Desoer (CD) algebra. In this note, we investigate the optimal tuning of the matrix gains [K.sub.k] of the controller [C.sub.[epsilon]] (s) as the scalar gain [epsilon] [down arrow] 0. The cost function is the maximum error between the reference signal and the measured output signal over all frequencies and bounded reference and disturbance signal amplitudes. Closed forms for asymptotically globally optimal solutions are given. The optimal matrix gains [K.sub.k] are expressed in terms of the values of the plant transfer matrix at the reference and disturbance signal frequencies. Thus the matrices [K.sub.k] can be tuned with input-output measurements made from the open loop plant without knowledge of the plant model. Although the analysis is in the CD-algebra, to the authors' knowledge the main results are new even for finite-dimensional systems. Index Terms--Low-gain control, distributed parameter systems, Callier-Desoer (CD)-algebra, tracking, optimal control.

Byline: Seppo Pohjolainen, Martti Ala-Rantala, Ossi Nykanen, Heli Ruokamo The purpose of the paper is to discuss and clarify the design and evaluation principles of open learning environments. By an open learning environment we mean a virtual environment that can be used over computer networks, especially over the Internet, to support self-paced and collaborative learning. To make the environment useful, the design should be based on modern learning theories. These emphasise the learner's active role, collaboration and reflection in the construction of new knowledge. The main metaphors for learning environment consist of a state model of a classroom that can be reached from the students' or teachers' study. The system architecture consists of data management facilities including data acquisition, tools for communication and collaboration, course-dependent cognitive tools, and authoring tools for producing hypermedia courseware.

Byline: Seppo Pohjolainen, Sami Hautakangas, Pekka Ranta, Jarkko Levasma, Katja Pesonen This article describes a learning experiment in mathematics carried out at Tampere University of Technology. The students studied matrix algebra for four weeks time using A&O learning environment. The environment contained hypermedia material and communication- , collaboration- and cognitive tools. Pedagogical design of web-based curriculum and pedagogically efficient use of the tools as well as their usability was investigated.

In this paper, the output regulation problem is addressed for a class of linear hyperbolic infinite-dimensional systems with spatially varying coefficients modelling a large class of convection-dominated transport reaction systems. In particular, distributed parameter systems with bounded input and unbounded output operators are considered. First, we demonstrate a general conclusion about the exponential stability of the considered system by relating the stability to the solution of an associated differential equation. Based on the assumption that the hyperbolic system satisfies the exponential stability conditions, the main manuscript contribution is the development of two novel finite-dimensional regulators, output and error feedback regulators, such that the controlled output of the plant tracks a reference signal generated by a known signal process (exosystem). In order to guarantee the feasibility of the proposed regulators, the solvability of the corresponding Sylvester equations is discussed and the solvability conditions are provided. Finally, simulations of output regulation of an axial dispersion reactor and a relevant numerical example illustrate the main results and performance of the proposed regulators synthesis. [ABSTRACT FROM AUTHOR]

In this paper, robust multivariable controllers for stable infinite-dimensional systems in the Callier-Desoer algebra (CD-algebra) will be discussed. In particular, the following robust regulation problem will be solved. Given reference and disturbance signals, which are linear combinations of signals of the form [t.sup.j] sin([w.sub.k]t + [[Phi].sub.k]), j [is greater than or equal to] 0, k = 0, ..., n, find a low-order finite-dimensional controller so that the outputs asymptotically track the reference signals, asymptotically reject the disturbance signals, and the closed-loop system is stable and robust with respect to a class of perturbations in the plant. The proposed controller consists of a positive scalar gain [Epsilon] and certain polynomial matrices [K.sub.k](s) for k = 0, ..., n. The main result of the paper shows that the matrices [K.sub.k](s) must satisfy certain stability conditions involving the values of the plant transfer function only at the reference and disturbance signal frequencies [w.sub.k] for k = 0, ..., n. Thus, the matrices [K.sub.k](s) can be tuned with input-output measurements made from the open-loop plant without knowledge of the plant parameters. The scalar gain [Epsilon] will be tuned experimentally. Because of the internal model principle, the controller has unstable poles on the imaginary axis. When the control loop is closed, these unstable poles will move into the left half-plane. The behavior of these poles as a function of the scalar parameter [Epsilon] in the form of a Puiseux series will be given. The results extend our previous results to a larger class of plants and reference and disturbance signals. We also give a generalization of Davison's tuning algorithm, even for finite-dimensional plants. In the case of constant reference and disturbance signals, the controller reduces to the we!l-known multivariable I-controller.