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No 11 (2023)
Articles
Interval Observers for Continuous-Time Systems with Parametric Uncertainties
Abstract
In this paper, interval observers are designed for linear dynamic systems described by continuous-time models with exogenous disturbances, measurement noises, and parametric uncertainties.
Jordan canonical form-based relations are presented for an interval observer that estimates the set of admissible values of a given linear function of the system state vector. The theoretical results are
illustrated by a practical example.
3-16
Robust Stability of Differential-Algebraic Equations under Parametric Uncertainty
Abstract
This paper considers linear differential-algebraic equations (DAEs) representing a system of ordinary differential equations with an identically singular matrix at the derivative in the domain of its
definition. The matrix coefficients of DAEs are assumed to depend on the uncertain parameters belonging to a given admissible set. For the parametric family under consideration, structural forms with separate differential and algebraic parts are built. As is demonstrated below, the robust stability of the DAE family is equivalent to the robust stability of its differential subsystem. For the structure of perturbations, sufficient conditions are established under which the separation of DAEs into the algebraic and differential components preserves the original type of functional dependence on the uncertain parameters. Sufficient conditions for robust stability are obtained by constructing a quadratic Lyapunov function.
17-35
Pattern Bifurcation in a Nonlocal Erosion Equation
Abstract
This paper considers a periodic boundary value problem for a nonlinear partial differential equation with a deviating spatial variable. It is called the nonlocal erosion equation and was proposed as a model for the formation of dynamic patterns on the semiconductor surface. As is demonstrated below, the formation of a spatially inhomogeneous relief is a self-organization process. An inhomogeneous relief appears due to local bifurcations in the neighborhood of homogeneous equilibria when they change their stability. The analysis of this problem is based on modern methods of the theory of infinite-dimensional dynamic systems, including such branches as the theory of invariant manifolds, the apparatus of normal forms, and asymptotic methods for studying dynamic systems.
36-54
Density Systems: Analysis and Control
Abstract
This paper considers a class of systems called density systems. For such systems, the derivative of a quadratic function depends on some function termed the density function. The latter function is used to define the properties of the space affecting the behavior of the systems under consideration. The role of density systems in control law design is shown. Control systems are constructed for plants with known and unknown parameters. The theoretical results are illustrated by numerical simulation.
55-76
Analiz veroyatnosti svyaznosti telekommunikatsionnoy seti na osnove matritsy nezavisimykh sobytiy
Abstract
77-92
Approximate Method for Estimating Characteristics of Joint Service of Real-time Traffic and Elastic Data Traffic in Multiservice Access Nodes
Abstract
A mathematical model of joint servicing of priority real-time traffic and elastic data traffic in multiservice access nodes has been constructed and studied. Definitions of quality indicators for
joint servicing of incoming requests for information services are provided. A system of statistical equilibrium equations is formed and its use for calculating the exact values of the introduced characteristics is considered. A method for approximate calculation of characteristics is proposed, based on the construction of a system of simplified equilibrium equations. It has been established that the obtained estimates of customer service indicators are asymptotically accurate in the region of large and small losses. The use of the developed method is shown to solve the problem of estimating the volume of traffic offloaded in an overload situation to other access nodes or to other frequency ranges in order to achieve values of specified QoS indicators and to solve the problem of planning the volume of required transmission resource of a multiservice access node.
93-114
Adaptive Observer of State and Disturbances for Linear Overparameterized Systems
Abstract
The problem of state reconstruction is considered for a class of linear systems with timeinvariant unknown parameters and overparameterization that are affected by external perturbations
generated by a known exosystem with unknown initial conditions. An extended adaptive observer is proposed, which, in contrast to existing approaches, solves state and perturbation adaptive estimation problems for systems that are not represented in the observer canonical form. The obtained theoretical results are validated via mathematical modeling.
115-146
Exponentially Stable Adaptive Control. Part III. Time-Varying Plants
Abstract
A state-feedback adaptive control system is proposed for a class of linear systems in the controllable canonical form with time-varying unknown parameters described by known nonstationary exosystems with unknown initial conditions. The solution ensures global exponential stability of the closed-loop system in case a regressor is finitely exciting, and also does not require a priori information
about the sign of the high-frequency gain (control direction). The obtained theoretical results are validated via mathematical modeling.
147-168