Some Results in the Mathematical Modeling of the Dynamics of Not Completely Observable Spatially Distributed Systems
- PDF / 193,656 Bytes
- 15 Pages / 594 x 792 pts Page_size
- 29 Downloads / 212 Views
SYSTEMS ANALYSIS SOME RESULTS IN THE MATHEMATICAL MODELING OF THE DYNAMICS OF NOT COMPLETELY OBSERVABLE SPATIALLY DISTRIBUTED SYSTEMS UDC 517.95:519.86
V. A. Stoyan
Abstract. An analytical summary of author’s research in the mathematical modeling of the dynamics of linear spatially distributed systems under limited information about their initial–boundary-value state is presented. The solutions to problems of control of such systems using an arbitrary combination of external-dynamic disturbing factors are given. The problems are solved for continuously and discretely defined observations of the initial–boundary-value disturbances of the system and its desired state. Keywords: modeling, distributed parameter systems, dynamic systems, initial–boundary-value problems, control. INTRODUCTION The development of science and engineering caused by the necessity of improving new hydro-, aero-, and space technologies in the second half of the last century has made new demands to their engineering and mathematical fundamentals as well. In particular, it became necessary to modify and develop the reliable and classically simple physicomechanical models [1, 2] of elastic hydrodynamic processes, classically adjusted mathematical methods of the analysis of these models. New mathematical models of classically old dynamic processes [3–5] and processes related to the newest physicomechanical systems [6] were complicated so that it was not always possible to mathematically correctly formulate the problem of their analysis and hence, to obtain its correct, exact, and mathematically justified solution. Even in the presence of practically observable mathematical methods, the problem of the analysis of modern models of physicomechanical and engineering systems is complicated because of incomplete information about the initial–boundary external-dynamic perturbations, which cannot always be obtained in practice in the volume and quality required by the mathematical model. An example of such systems can be both complex spatially distributed buildings [7] and nonclassical elements of mechanical structures [3, 4] and modern physicomechanical systems [8]. In the present paper, we will consider one of the possible approaches to the analysis of differentially described space–time processes and phenomena under incomplete information about their initial–boundary state. A feature of the approach is that it allows obtaining an exact solution to the linear differential model of the process, consistent with its external-dynamic (initial, boundary, current) observations with respect to the root mean square criterion even for their small number and bad quality (continuous, discrete). The same criteria are used to successfully solve control problems for such processes for an arbitrary combination of external-dynamic control factors (initial, boundary, and distributed in a domain). A technique to solve the above-mentioned problems was proposed in [9] and developed in [10] by the author in a close cooperation with Prof. Kirichenko [11] and Corresponding M
Data Loading...
