Robust consensus control of uncertain multi‐agent systems with input delay: a model reduction method

Abstract:In this paper, we propose a control structure for a class of systems with Lipschitz nonlinearity and unknown time-varying input delay. This scheme considers the worst case scenario in control design with Truncated Prediction Feedback (TPF) approach, and takes into account the information of the lower bound of delay in the stability analysis. A finite-dimensional controller is constructed, requiring neither the nonlinear function nor the exact delay function. The truncated prediction deviation is minimized by employing the delay range, and then bounded by integral construction and related techniques. Within the framework of LyapunovKrasovskii functionals, sufficient delay-range-dependent conditions are derived for the closed-loop system to guarantee the global stability. Two numerical examples are given to validate the proposed control design. IntroductionIn Note that all the results above are built based on the assumption that the exact delay information is known, which may be irrealizable in many circumstances. The predictor-based feedback control methods suffer from a difficulty in practical implementation when the delay function is unknown. A Lyapunov-based adaptive control design is presented in [25] to deal with unknown constant delay for a class of linear systems. However, few results are available on stabilization for nonlinear systems with unknown time-varying input delay. The TPF control also encounters the same barrier since the prediction is based on the exact knowledge of the delay function [19]-[24].Inspired by the above observation and based on our previous results [26]-[30], in this paper, we propose a control scheme for a class of systems with unknown time-varying input delay and Lipschitz nonlinearity. The key contributions include: (i) in contrast to [13,16,[21][22][23], we propose a new control structure by merely using the delay upper bound, which greatly reduces the computation burden and improves the practical implementation; (ii) we extend the results on the truncated predictor feedback for linear systems to a class of Lipschitz nonlinear systems with unknown time-varying input delay and the derived conditions are less conservative with respect to the existing results [24]; (iii) the information of the lower bound of delay is taken into account in the stability analysis, which benefits the derived conditions. The remainder of this paper is organized as follows. Section 2 presents the problem formulation and a few preliminary results for the stability analysis. Section 3 presents the main results on the controller design and stability analysis. Simulation results are given in Section 4. Section 5 concludes the paper. Problem statement and preliminariesWe consider the systeṁwhere x(t) ∈ R n is the state, u(t) ∈ R p is the input, A ∈ R n×n and B ∈ R n×p are constant matrices with (A, B) being controllable, ζ(t) is a continuously differentiable function that incorporates the actuator delay, and ϕ : R n → R n , ϕ(0) = 0, is a Lipschitz nonlinear function with a Lipschitz constant γ. Fo...

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“…[24] and [26]- [29] as a special case withζ(t) ≡ 1. Furthermore, if d(t) ≡ 0, condition (28) in [24] degenerates to…”

Section: Stability Analysismentioning

confidence: 99%

Control scheme for LTI systems with Lipschitz non‐linearity and unknown time‐varying input delay

Wang

Ding

2017

IET Control Theory & Applications

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“…Ren addressed formation control problems by implementing the consensus‐based approach and showed that the above‐mentioned classical methodologies could be unified in the framework of the consensus‐based formation control. Inspired by the development of the consensus theory in the control community, the newly developed consensus‐based formation control strategies were reported in many application fields including mobile robots, intelligent ground vehicles, and unmanned aerial vehicles (see References and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Robust time‐varying formation design for multiagent systems with disturbances: Extended‐state‐observer method

Wang

et al. 2020

Intl J Robust & Nonlinear

107

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Robust time-varying formation design problems for second-order multiagent systems subjected to external disturbances are investigated. First, by constructing an extended state observer, the disturbance compensation is estimated, which is a critical term in the proposed robust time-varying formation control protocol. Then, an explicit expression of the formation center function is determined and impacts of disturbance compensations on the formation center function are presented. With the formation feasibility conditions, robust time-varying formation design criteria are derived to determine the gain matrix of the formation control protocol by utilizing the algebraic Riccati equation technique. Furthermore, the tracking performance and the robustness property of multiagent systems are analyzed. Finally, the numerical simulation is provided to illustrate the effectiveness of theoretical results. K E Y W O R D S algebraic Riccati equation, extended state observer, external disturbance, multiagent system, robust time-varying formation 2796

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“…In previous works, robust controllers are necessary to compensate for the effects of model uncertainties. Some strategies have been given to deal with uncertainties in multiagent systems, eg, independent of the state uncertainties, known bounded uncertainties, and Lipschitz condition uncertainties . Thus, the state‐dependent uncertainties cannot satisfy these conditions.…”

Section: Introductionmentioning

confidence: 99%

Adaptive fault‐tolerant time‐varying formation tracking for multiagent systems with multiple leaders

Wang

et al. 2019

Intl J Robust & Nonlinear

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Summary In this paper, an adaptive fault‐tolerant time‐varying formation control problem for nonlinear multiagent systems with multiple leaders is studied against actuator faults and state‐dependent uncertainties. Simultaneously, the followers form a predefined formation while tracking reference signal determined by the convex combination of the multiple leaders. Based on the neighboring relative information, an adaptive fault‐tolerant formation time‐varying control protocol is constructed to compensate for the influences of actuator faults and model uncertainties. In addition, the updating laws can be adjusted online through the adaptive mechanism, and the proposed control protocol can guarantee that all the signals in the closed‐loop systems are bounded. Lyapunov‐like functions are addressed to prove the stability of multiagent systems. Finally, two examples are provided to demonstrate the effectiveness of the theoretical results.

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Robust consensus control of uncertain multi‐agent systems with input delay: a model reduction method

Cited by 52 publications

References 31 publications

Control scheme for LTI systems with Lipschitz non‐linearity and unknown time‐varying input delay

Control scheme for LTI systems with Lipschitz non‐linearity and unknown time‐varying input delay

Robust time‐varying formation design for multiagent systems with disturbances: Extended‐state‐observer method

Adaptive fault‐tolerant time‐varying formation tracking for multiagent systems with multiple leaders

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