A distributed leader‐following tracking controller using delayed control input information from neighbors

Abstract

Summary In this paper, we propose a simple, continuous, and distributed controller for the second‐order multiagent system to achieve leader‐following trajectory tracking, by exploiting the control input information of neighbors (CIIN) and using proportional‐derivative (PD) control in terms of local neighborhood synchronization error. A constant time delay is introduced in the CIIN as a design parameter to avoid the algebraic loop issue arising from the control input coupling. We develop an easily testable condition on the PD gains to ensure that the resulting neutral‐type error system is input‐to‐state stable for an arbitrary bounded delay, and prove that when the leader's acceleration is a Lipschitz continuous function with respect to time, the ultimate bound of tracking errors is strictly increasing with respect to the introduced time delay. Moreover, we analyze the robustness of the controller with respect to model uncertainties and show its potential advantages over two existing controllers in balancing the steady‐state tracking precision, the communication cost, and the continuity of controller signal. Finally, extensive simulations are conducted to show the effect of the delay on system stability, to verify the condition on PD gains, to confirm the robustness of the controller, and to demonstrate the detailed advantages.

Enhanced affine formation maneuver control using historical acceleration command

“…Note that 𝜇 i and 𝜇 j can be viewed as the acceleration information in a second-order system, it triggers the algebraic loop while introducing it directly. Inspired by the work of Zhu et al, 29 we can readily repalce 𝜇 i and 𝜇 j with HAC 𝜇 i (t − 𝜏) and 𝜇 j (t − 𝜏) to avoid the algebraic loop, and we define 𝜇 i (𝜓) = 0 for 𝜓 ∈ (−𝜏, 0), i ∈  f . Motivated by Devasia's work, 30 𝜇 i (t − 𝜏), HAC from node i itself, is considered to improve the system performance without changing the network connectivity.…”

“…28 Recently, Zhu et al improved the tracking performance by introducing the delayed control input information from neighbors in second-order MAS. 29 Devasia proposed a delayed self-reinforcement (DSR) method to maintain the cohesion of MAS and simultaneously speed up the convergence rate of the network. 30 For consensus and synchronized tracking algorithms, the performance improvement design has received considerable attention.…”

“…Compared with the recent works on affine formation maneuver control, [17][18][19][20][21] this work places emphasis on the control design for performance tuning rather than being limited to stability or convergence analysis. Meanwhile, compared with consensus control studies employing the derivative information, 25 delayed-control-input, 29 or DSR, 30 this paper introduces the HAC to deal with the comprehensive performance-tuning problem in affine formation control. In addition to the aforementioned theoretical analysis, we design seven simulation cases to verify our findings and the effectiveness of the proposed controller.…”

“…Liu et al proposed a protocol with delayed control input information of neighbors, demonstrating its effectiveness in achieving the containment tracking 28 . Recently, Zhu et al improved the tracking performance by introducing the delayed control input information from neighbors in second‐order MAS 29 . Devasia proposed a delayed self‐reinforcement (DSR) method to maintain the cohesion of MAS and simultaneously speed up the convergence rate of the network 30 .…”

“…The proof contains two aspects. (1) By a theory tool of neutral functional differential equations,29,31 we derive a brief condition to guarantee the robustness of system stability. (2) By the theory of input-to-state (ISS) stability, we derive an inequality to describe the relationship between the ultimate bounds of tracking errors and the delay parameter.…”