Structure Preserving Uncertainty Modelling and Robustness Analysis for Spatially Distributed Dissipative Dynamical Systems

Abstract

The paper deals with uncertainty modelling, robust stability and performance analysis of multi-input multi-output (MIMO) reduced order spatially distributed dissipative dynamical systems. While researching the topic of modern robust control of such systems, two key findings were discovered: (i) systematic modelling of the uncertainty and model order reduction (MOR) at the level of a subsystem gives both modelling freedom and the ability for obtaining less conservative uncertainties on the level of a subsystem; (ii) for a special class of interconnected dissipative dynamical systems, uncertainty conservatism at the subsystem level can be reduced—a novel, structure preserving algorithm employing subsystem partitioning and subsystem MOR by means of balanced truncation method (BTM) is used to obtain low-order robustly stable interconnected systems. Such systems are suitable for practical decentralized and distributed robust controller synthesis. Built upon a powerful framework of integral quadratic constraints (IQCs), this approach gives uncertainty modelling flexibility to perform robustness analysis of real world interconnected systems that are usually affected by multiple types of uncertainties at once. The proposed uncertainty modelling procedure and its practical application are presented on the numerical example. A spatially discretized vibration dynamical system comprised of a series of simply supported Euler beams mutually interconnected by springs and dampers is examined. Spatial discretization of the mathematical model is carried out using the finite element method (FEM).

A Combinatorial Model for Determining Information Loss in Organizational and Technical Systems

“…This behavior of the system is close to the phenomena of systemic hysteresis described in the literature [20][21][22]. The use of the combinatorial model given in the article, in contrast to the models described in [1][2][3][4][5][6][7] and others, develops a set-theoretic representation of systems for solving problems related to the study of the functioning of systems under destructive conditions and external influences, namely with the minimization of information losses in the system. The presented model, in our opinion, is invariant to the subject area, since it uses only a multiple representation of the structure, which is not directly related to the functionality of the system.…”

“…A complex dynamic system cannot be represented by a single model-an entire hierarchy of models is needed, which will differ in the level of displayed events. As a rule, four main gradations of levels are used [1,2]:…”

“…The approaches presented in [1][2][3][4][5][6][7]for constructing models of complex dynamical systems have a number of disadvantages. For example, in [4,7], the presented approach to building a model is applicable only in the case of the availability of statistical data on the functioning of the system and does not take into account the information component of the processes in the system.…”

“…For example, in [4,7], the presented approach to building a model is applicable only in the case of the availability of statistical data on the functioning of the system and does not take into account the information component of the processes in the system. The papers [1][2][3]5,6] also do not consider issues related to the assessment of information losses in the system due to external destructive influences. Therefore, we proposed an informational approach for the construction of the combinatorial model for determining information loss in organizational and technical systems.…”