KERNEL RECURSIVE DUAL CONTROL ALGORITHM FOR NONLINEAR DYNAMIC PROCESSES

В работе рассматривается задача адаптивной идентификации и управления нелинейными динамическими объектами. Предлагается новый рекуррентный ядерный алгоритм дуального управления с использованием идентификатора. Приводятся результаты численного исследования, подтверждающие эффективность предложенного алгоритма. The paper considers adaptive identification and control problem of nonlinear dynamic processes. For solution of the problem new recursive identification and control algorithms are proposed. The paper presents the results of a numerical study illustrating the performance of the proposed recursive identification and control algorithms.

Near-Epoch Dependence

Near‐epoch dependence (NED) is a generalized dependence concept for functions of mixing processes. This chapter gives definitions and examples, and considers the application to nonlinear dynamic processes. The relation to mixingales is the key theoretical result. Results on the preservation of NED under various transformations and a special result for the adapted sequence case are considered next. Finally, the related concept of approximability is defined which, unlike NED, can hold in the absence of integer moments.

Nonlinear Measure for Nonlinear Dynamic Processes Using Convergence Area: Typical Case Studies

Several industrial chemical processes exhibit severe nonlinearity. This paper addresses the computational and nonlinear issues occurring in many typical industrial problems in aspects of its stability, strength of nonlinearity and input output dynamics. In this article, initially, a prospective investigation is conducted on various nonlinear processes through phase portrait analysis to understand their stability status at different initial conditions about the vicinity of the operating point of the process. To estimate the degree of nonlinearity, for input perturbations from its nominal value, a novel nonlinear measure is put forward, that anticipates on the converging area between the nonlinear and their linearized responses. The nonlinearity strength is fixed between 0 and 1 to classify processes to be mild, medium or highly nonlinear. The most suitable operating point, for which the system remains asymptotically stable is clearly identified from the phase portrait. The metric can be contemplated as a promising tool to measure the nonlinearity of Industrial case studies at different linear approximations. Numerical simulations are executed in Matlab to compute , which conveys that the nonlinear dynamics of each Industrial example is very sensitive to input perturbations at different linear approximations. In addition to the identified metric, nonlinear lemmas are framed to select appropriate control schemes for the processes based on its numerical value of nonlinearity..

The Role of Nonlinear Dynamics in Musicians' Interactions with Digital and Acoustic Musical Instruments

Nonlinear dynamic processes are fundamental to the behavior of acoustic musical instruments, as is well explored in the case of sound production. Such processes may have profound and under-explored implications for how musicians interact with instruments, however. Although nonlinear dynamic processes are ubiquitous in acoustic instruments, they are present in digital musical tools only if explicitly implemented. Thus, an important resource with potentially major effects on how musicians interact with acoustic instruments is typically absent in the way musicians interact with digital instruments. Twenty-four interviews with free-improvising musicians were conducted to explore the role that nonlinear dynamics play in the participants' musical practices and to understand how such processes can afford distinctive methods of creative exploration. Thematic analysis of the interview data is used to demonstrate the potential for nonlinear dynamic processes to provide repeatable, learnable, controllable, and explorable interactions, and to establish a vocabulary for exploring nonlinear dynamic interactions. Two related approaches to engaging with nonlinear dynamic behaviors are elaborated: edge-like interaction, which involves the creative use of critical thresholds; and deep exploration, which involves exploring the virtually unlimited subtleties of a small control region. The elaboration of these approaches provides an important bridge that connects the concrete descriptions of interaction in musical practices, on the one hand, to the more-abstract mathematical formulation of nonlinear dynamic systems, on the other.

Nonlinear dynamic processes control system for a DC converter of the first kind

In the paper a composite nonlinear dynamic processes control system for DC switching converters of the first kind is being considered. The proposed control system is based on two methods: time-delayed feedback method and target-oriented control. The advantage of the composite control system is the absence of the weak points specific to the two mentioned methods utilized on a standalone basis, such as possibility of occurrence of multistability domains, which is characteristic of time-delayed feedback method, and addition of static error when using the target-oriented control. The mathematical simulation of a closed-loop composite automatic control system for manipulating nonlinear dynamic processes has been implemented. The simulation results have proved the efficiency of the control system under consideration. The proposed solution can be realized with the use of a great variety of existing microcontrollers.