Global Adaptive Stabilization and Tracking Control for High-Order Stochastic Nonlinear Systems With Time-Varying Delays

Xue, Lingrong; Zhang, Tianliang; Zhang, Weihai; Xie, Xue‐Jun

doi:10.1109/tac.2018.2797169

Cited by 73 publications

(29 citation statements)

References 49 publications

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“…где ( ) 14, получим дискретную модель группы в виде уравнения в изображениях (10) и уравнение замкнутой системы (18). Передаточные матрицы в уравнении (10) для компактности представим следующим образом:…”

Section: решение задачи синтеза сгуunclassified

“…Как известно, временная задержка в системах управления оказывает существенное влияние на их свойства, в частности на устойчивость [16][17][18][19][20][21]. Наибольшие трудности в обеспечении устойчивости замкнутых систем управления возникают в тех случаях, когда запаздывание является неопределенным [18,19,21]. Для преодоления этой трудности представляется целесообразным использование робастных систем управления с запаздыванием [22][23][24][25].…”

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Control of the UAV group at uncertain delays in communication channels

Gaiduk¹,

Kapustyan²,

Plaksienko³

et al. 2020

Science Bulletin of the NSTU

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The UAV groups and other unmanned robots are more and more widely used to solve production and special problems in view of their bigger efficiency in comparison with single robots. The efficiency of a group in many respects is defined by the opportunities of the communications means between members of the group and its leader, which influences the efficiency of the decisions made. The control of the UAV group is often exercised by a multivariable control system whose algorithms are implemented by a computer complex of the group UAV leader. The problem here is that in individual channels of information exchanges between the UAV-leader and other UAVs of the group there is a time delay. Any space distributions of the UAV in the neighborhood of the leader cause significantly different, uncertain delays in channels of its contact with the UAV group that can lead to a loss of control stability. It is proposed to apply a multivariable, robust to delay control system to overcome this difficulty. The design of this system is carried out on the basis of the matrix decoupling control and the method of an analytical design of systems with control on output and impact (ADSCOI) taking into account conditions of feasibility of controls on digital computing elements. Analytical expressions including the solution to the linear system algebraic equations and the creation procedure of the digital control algorithms are found in the article. This control provides robustness of the system to delays in communication channels. The efficiency of the proposed approach is illustrated by a numerical design example of the multivariable group control system of the UAV. The results obtained can be applied to create digital control systems by both single input-single-output and multi-input-multi-output objects with an uncertain delay in agricultural, food, power, machine-building and other industries.

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Section: решение задачи синтеза сгуunclassified

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Control of the UAV group at uncertain delays in communication channels

Gaiduk¹,

Kapustyan²,

Plaksienko³

et al. 2020

Science Bulletin of the NSTU

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“…Proof. It is easy to see that condition (18) for ∈ Π 0 is a special case of condition (19) for ∈ Π 1 . Without loss of generality, in the following, the proof of the more complex case ∈ Π 1 is to be considered.…”

Section: Piecewise Affine Nonfragile Controller Analysis and Designmentioning

confidence: 99%

“…In recent years, many valuable references on the systematic analysis and synthesis for the PWA systems have been published [12][13][14][15][16][17][18][19][20][21][22]. In [12], the stability of continuous-time PWA systems was analyzed by utilizing discontinuous piecewise Lyapunov functions (PLFs).…”

Section: Introductionmentioning

confidence: 99%

A New Robust Nonfragile Controller Design Scheme for a Class of Hybrid Systems through Piecewise Affine Models

Chen

Pang

Zhao

et al. 2018

Mathematical Problems in Engineering

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This paper investigates the robust H∞ nonfragile control problem for a class of discrete-time hybrid systems based on piecewise affine models. The objective is to develop an admissible piecewise affine nonfragile controller such that the resulting closed-loop system is asymptotically stable with robust H∞ performance γ. By employing a state-control augmentation methodology, some new sufficient conditions for the controller synthesis are formulated based on piecewise Lyapunov functions (PLFs). The controller gains can be obtained via solving a set of linear matrix inequalities. Simulation examples are finally presented to demonstrate the feasibility and effectiveness of the proposed approaches.

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“…Based on these powerful methods, numerous interesting results on the control problem of SNSs are obtained. For instance, Chen et al [8] solved the state feedback stabilisation of a class of high‐order stochastic lower‐triangular systems with time delays; Xie and Tian [9] investigated the adaptive control of high‐order stochastic parameterised systems; the authors in [10] studied the output feedback stabilisation of high‐order SNSs under weaker non‐linear growth conditions; the latest paper [11] addressed the adaptive control of high‐order stochastic non‐linear systems with time‐varying delays. Our previous work [12] considered the problem of the state feedback stabilisation of high‐order SNSs and weakened the assumptions on systems' non‐linear terms by utilising the concept of homogeneity with monotone degrees (HWMD).…”

Section: Introductionmentioning

confidence: 99%