Non-iterative Solution to Robust Anisotropy-based Analysis and Control Problems for Uncertain Descriptor Systems

Andrianova Olga; Белов Алексей Анатольевич

doi:10.1109/ICSTCC.2019.8885575

Publications

Book chapter

Non-iterative Solution to Robust Anisotropy-based Analysis and Control Problems for Uncertain Descriptor Systems

P. 455-460.

Andrianova O., Белов А. А.

The problem of robust admissibilization with guar-
anteed random disturbance attenuation level for discrete-time
time-invariant (LDTI) descriptor systems with norm-bounded
uncertainties is considered. The input disturbance is supposed
to be a stationary Gaussian sequence with bounded mean
anisotropy level. The solutions to analysis and robust state-
feedback control problems are formulated in terms of matrix
inequalities. The obtained conditions are convex over all decision
variables and do not require inverse matrix searching. Compar-
ison between iterative [1], [2] and non-iterative methods is given.

Language: English

Full text (PDF, 411 Kb)

DOI

Keywords: descriptor systems suboptimal control colored noise Stochastic control uncertain linear systems robust performance robust control state-feedback control

In book

2019 23rd International Conference on System Theory, Control and Computing (ICSTCC)

IEEE, 2019.

Синтез P и PI-регуляторов для нелинейных систем с использованием окружностей Холла и диаграмм Никольса

Капалин В. И., Ведяшкина Наталья Евгеньевна Промышленные АСУ и контроллеры. 2015. № 6. С. 41-47.

A simple technique for the design of P and PI-regulators for nonlinear control systems, which is based on the theory of minimax approximations, is proposed. Unlike the widely known methods of harmonic and statistic linearization, the minimax linearization method used in the present paper does not require special suppositions concerning the input signal of the nonlinear element. And unlike the classical method of Taylor series it does not require the small intervals of approximation. The main idea of the proposed method consists in substitution of the nonlinear element of the system by a family of its linear models obtained by minimax technique. For the design of the feedback system after this substitution the simple methods of Hall circles for zero order regulators and Nichols diagram for fi rst order regulators is used. This approach may prove out to be preferable for practice than robust control methods which usually give the high order regulators. For the check of the robust properties as to the nonlinear element all the computations are performed for two kinds of nonlinear elements – piecewise linear and polynomial. The simulation for the linear models is performed in toolbox Control System Toolbox of MATLAB. The design of the nonlinear feedback systems is carried out in Simulink. The results of simulation for different levels of input signals for the nonlinear element corroborated the robustness of the designed nonlinear feedback system concerning the uncertain nonlinear elements. The simulation was performed for the case of satur ation nonlinear elements but the suggested approach applicable for every continuous nonlinear elements in the system.

Added: Nov 29, 2015

On Anisotropy-Based Control Problem with Regional Pole Assignment for Descriptor Systems

Belov A., Andrianova O. In bk.: Proceedings of the 2017 21st International Conference on Process Control, PC 2017. IEEE, 2017. P. 12-17.

In this paper, anisotropy-based control problem with regional pole assignment for descriptor systems is investigated. The purpose is to find a state-feedback control law, which guar- antees desirable disturbance attenuation level from stochastic input with unknown covariance to controllable output of the closed-loop system, and ensures, that all finite eigenvalues of the closed-loop system belong to the given region inside the unit disk. The proposed control design procedure is based on solving convex optimization problem with strict constraints. The numerical effectiveness is illustrated by numerical example.

Added: Feb 6, 2018

Управление нелинейными объектами с параметрами, зависящими от состояния

Афанасьев В. Н. Автоматика и телемеханика. 2011. № 4. С. 43-56.

The theoretical fundamentals for solving the linear quadratic problems may be some times used to design the optimal control actions for the nonlinear systems. The method relying on the Riccati equation with state-dependent coefficients is promising and rapidly developing tools for design of the nonlinear controllers. The set of possible suboptimal solutions is generated by ambiguous representation of the nonlinear system as a linearly structured system with state-depended coefficients and the lack of sufficiently universal algorithms to solve the Riccati equation also having state-depended coefficients. The paper proposed a method to design a guaranteed control for the uncertain nonlinear plant with state-depended parameters. An example of design the controller for an uncertain nonlinear system was presented.

Added: Apr 13, 2012

Субоптимальное управление нелинейным объектом, линеаризуемым обратной связью

Афанасьев В. Н., Орлов П. В. Известия РАН. Теория и системы управления. 2011. Т. 50. № 3. С. 13-22.

An optimal control problem is formulated for a class of nonlinear systems for which there exists a coordinate representation (diffeomorphism) transforming the original system into a system with a linear main part and a nonlinear feedback. In this case the coordinate transformation significantly changes the form of original quadratic functional. The penalty matrices become dependent on the system state. The linearity of the structure of the transformed system and the quadratic functional make it possible to pass over from the Hamilton–Jacoby–Bellman equation to the Riccati type equation with state-dependent parameters upon the control synthesis. Note that it is impossible to solve the obtained form of Riccati equation analytically in the general case. It is necessary to approximate the solution; this approximation is realized by numerical methods using symbolic computer packages or interpolation methods. In the latter case, it is possible to obtain the suboptimal control. The presented example illustrates the application of the proposed control method for the feedback linearizable nonlinear system.

Added: Apr 13, 2012

On Optimal Anisotropy-Based Control Problem for Discrete-Time Descriptor Systems

Belov A. A., Andrianova O. In bk.: . P. 661-666.

This paper is dedicated to optimal state-feedback control problem for discrete-time descriptor systems in presence of “colored” noise with known mean anisotropy level. Here “colored” noise stands for a stationary Gaussian sequence, generated by a linear shaping filter from the Gaussian white noise sequence. The control goal is to find a state feedback control law which makes the closed-loop system admissible and minimizes its a-anisotropic norm (mean anisotropy level a is known).

Added: Jul 16, 2018

Anisotropy-based Analysis for Descriptor Systems with Norm-Bounded Parametric Uncertainties

Belov A. A., Olga G. Andrianova. In bk.: PROCEEDINGS OF 2016 INTERNATIONAL CONFERENCE “STABILITY AND OSCILLATIONS OF NONLINEAR CONTROL SYSTEMS” (PYATNITSKIY’S CONFERENCE). IEEE, 2016. P. 1-4.

In this paper, linear discrete-time descriptor systems with norm-bounded parametric uncertainties are under consider- ation. The input signal is supposed to be a “colored” noise with bounded mean anisotropy. Sufficient conditions of anisotropic norm boundedness for such class of systems are given.

Added: Feb 6, 2018