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A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 8 Issue 3
Mar.  2021

IEEE/CAA Journal of Automatica Sinica

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F. Wang, J. Gong, Z. Liu, and F. Chen, “Fixed-time stability of random nonlinear systems,” IEEE/CAA J. Autom. Sinica, 2024. doi: 10.1109/JAS.2024.124353
Citation: Xuejing Lan, Wenbiao Xu, Zhijia Zhao and Guiyun Liu, "Autonomous Control Strategy of a Swarm System Under Attack Based on Projected View and Light Transmittance," IEEE/CAA J. Autom. Sinica, vol. 8, no. 3, pp. 648-655, Mar. 2021. doi: 10.1109/JAS.2021.1003880

Autonomous Control Strategy of a Swarm System Under Attack Based on Projected View and Light Transmittance

doi: 10.1109/JAS.2021.1003880
Funds:  This work was supported in part by the National Natural Science Foundation of China (61803111, 61803109), in part by the Innovative School Project of Education Department of Guangdong (2017KQNCX153), in part by the Science and Technology Planning Project of Guangzhou City (201904010494), in part by the Scientific Research Projects of Guangzhou Education Bureau (201831805, 202032793)
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  • In the study of a visual projection field with swarm movements, an autonomous control strategy is presented in this paper for a swarm system under attack. To ensure a fast swarm dynamic response and stable spatial cohesion in a complex environment, a new hybrid swarm motion model is proposed by introducing global visual projection information to a traditional local interaction mechanism. In the face of attackers, individuals move towards the largest free space according to the projected view of the environment, rather than directly in the opposite direction of the attacker. Moreover, swarm individuals can certainly regroup without dispersion after the attacker leaves. On the other hand, the light transmittance of each individual is defined based on global visual projection information to represent its spatial freedom and relative position in the swarm. Then, an autonomous control strategy with adaptive parameters is proposed according to light transmittance to guide the movement of swarm individuals. The simulation results demonstrate in detail how individuals can avoid attackers safely and reconstruct ordered states of swarm motion.

     

  • Dear Editor,

    This letter embarks on an examination of fixed-time stability (FxTS) for random nonlinear systems (RNSs) governed by random differential equations. This endeavor encompasses a multifaceted analysis of FxTS, commencing with its rigorous definition and its integration with Lyapunov theory, along which a consequential corollary emerges. Particularly, the positive definiteness of the expectation of settling time is established, and a less conservative upper bound is derived. The effectiveness of the proposed fixed-time theorem is verified by an example.

    In numerous instances, physical systems necessitate operation within stochastic environments to attain the desired level of performance. Depending on the manner in which stochastic disturbances are characterized, they can be broadly categorized into two distinct classes: stochastic nonlinear systems (SNSs) featuring white noise and RNSs characterized by colored noise. However, SNSs face limitations, primarily stemming from the ambiguity surrounding the physical interpretation of the Hessian term in Ito integrals and the non-differentiability of white noise at all points, rendering them less suitable for modeling a diverse spectrum of practical engineering systems. Conversely, RNSs are defined as random differential equations entailing colored noise, characterized by an uneven spectral density. This framework finds extensive application in both theoretical and practical domains [1]–[4], owing to its versatility and capacity to accurately model a wide range of real-world engineering systems.

    Within the framework of RNSs, stability theory stands out as a pivotal and ever-evolving area of focus. A seminal milestone in this pursuit was marked by the seminal work in [5], which introduced the definitions of asymptotic stability and noise-to-state stability in probability, along with the corresponding Lyapunov criterion. This foundational work laid the groundwork for subsequent research endeavors, resulting in a wealth of outstanding contributions [6]–[8]. It is worth noting that the predominant focus of current research within this domain revolves around asymptotic stability. However, recognizing the need for expedited convergence rates, recent efforts have turned toward investigating finite-time stability in the context of RNSs. Notably, in [9], the Lyapunov criteria for noise-to-state practically finite-time stability in RNSs was introduced. Furthermore, the study presented in [10] delves into event-triggered finite-time control strategies for a specific class of high-order RNSs.

    Nevertheless, finite-time stability, despite its advantages, exhibits a limitation tied to the dependence of its settling time on the initial state, a constraint that hinders its practical utility, particularly in scenarios where critical information like the initial value remains unknown. To address this issue, the concept of FxTS was introduced in [11], offering the invaluable attribute of a finite settling time without being contingent on knowledge of the initial conditions. Subsequently, the field witnessed remarkable advancements in the theory of FxTS for deterministic systems [12]–[14]. It’s essential to note that when dealing with the non-deterministic counterpart, a fundamental distinction arises, namely, the settling time of these systems becomes a random variable. The fixed-time stable theorem for SNSs is studied in [15], and the fixed-time control for SNSs is implemented in [16]–[18]. However, to the best of our knowledge, no systematic proposal has been made for the FxTS of RNSs. This compels us to put forth a fixed-time theorem for RNSs in order to enable the implementation of subsequent fixed-time observation and control. On the other hand, as inspired by [19], the characteristic of random settling time piques our curiosity, driving us to explore and analyze the nuanced properties of the settling time within the context of RNSs.

    In this letter, the FxTS for RNSs is proposed. In particular, the following problems are mainly solved.

    1) How to provide the fixed-time theorem of RNSs for stability analysis?

    2) What are the sufficient conditions for ensuring that the expectation of settling time is bounded and positive definite?

    3) How to estimate the upper bound of settling time with reduced conservatism?

    Drawing inspiration from the aforementioned studies, this letter introduces, for the first time, both the definition and theorem pertaining to FxTS in the context of RNSs. Notably, it is rigorously established that the expectation of settling time is unequivocally positive definite, while concurrently presenting an explicit upper bound that exhibits reduced conservatism.

    Notation: Let K denote a class of continuous and strictly increasing function satisfying limty(t)= and y(0)=0. Let C2 be the set of twice continuously differentiable functions. ab=min{a,b}. I{} denotes the indicator function.

    Problem Formulation: Consider a RNS described by

    ˙x=f(x,t)+ϕ(x,t)ξ(t),x(t0)=x0, (1)

    where xRn is the state, ξRl is a Ft-adapted and piecewise continuous stationary process defined on a complete probability space (Ω,F,Ft,P), and f:Rn×R+Rn and ϕ:Rn×R+Rn×l are piecewise continuous and locally Lipschitz in x for each t[t0,T].

    Assumption 1: There exists a positive constant ϖ such that suptt0E{|ξ|2}<ϖ.

    Lemma 1 [5]: If Assumption 1 holds and |f(0,t)|=, \forall t \in [t_0, \infty) , then (1) has a pathwise strong unique solution.

    Assumption 2: Suppose |\xi(t)|^2 satisfies the week law of large numbers, i.e., for sufficiently small positive constants \epsilon, \sigma , there exists T>t_0 such that for any t \ge T ,

    P\left\{\left\lvert \frac{1}{t-t_0} \int_{t_0}^t |\xi(s)|^2ds-E|\xi(t)|^2 \right\rvert \ge \sigma \right\} \le \epsilon.

    Definition 1: If system (1) admits a solution x(t; x_0) for any initial value x_0 \in \mathrm{R}^n , and the following conditions hold:

    {\rm{i}}) for \epsilon \in (0, 1) and r > 0 , there exists a constant \delta(\epsilon, r) > 0 such that P\{|x(t, x_0)| < r\} \ge 1-\epsilon for any t>0 whenever |x_0| < \delta ,

    {\rm{ii}}) and the first hitting time \tau = \inf\{t \ge 0 : x(t, x_0) = 0\} , which called random settling time, is bounded almost surely. That is P(\tau< \infty) = 1 and satisfies E\tau\le T with a constant T>0 ,

    then the trivial zero solution of (1) is said to be fixed-time stable in probability.

    Main results: A novel criteria of FxTS for (1) in this section.

    Theorem 1: If there exists \mathrm{K}_{\infty} class functions \nu_1 , \nu_2 , real numbers h_1,h_2 > 0 , and a \mathrm{C}^2 function V : \mathrm{R}^n \to \mathrm{R}_{+} such that for any x \in \mathrm{R}^n ,

    \nu_1(|x|) \le V(x) \le \nu_2(|x|), \qquad\qquad\qquad\qquad\;\; \;\;\; (2)
    V_xf(x,t) < -h_1 r(V(x)), |V_x \phi(x,t)| \le h_2 r(V(x)), (3)

    where r:\mathrm{R}_{+} \to \mathrm{R}_{+} is continuous differentiable with the derivative r^{\prime}(s) \ge 0 , r(s) >0 for any s>0 and \int_{0}^{\epsilon}\frac{ds}{r(s)} < M, \quad \forall \epsilon >0, and if the parameters satisfy then

    {\rm{i}}) the trivial solution of (1) is fixed-time stable in probability,

    {\rm{ii}}) and random settling time is bounded by E\tau \le M/(h_1-2h_2\sqrt{\varpi}) , and its expectation is positive definite.

    Proof. Let 0<\epsilon<1, s>0 be arbitrary constants. Define stopping time \gamma_s = \inf\{t;|x(t;x_0)|>s\} , which gives

    EV(x(t \wedge \gamma_s)) \le V(x_0). (4)

    By (2), we have

    \begin{split} P\{\gamma_s \le t\} \nu_1(s) & \le E[I_{\{\gamma_s \le t\}}V(x(\gamma_s))] \\ & \le EV(x(\gamma_s)) \le V(x_0)\le \nu_2(|x_0|), \end{split} (5)

    Taking \vartheta = \nu_2^{-1}(\mu_1(s)\epsilon) , it follows from (1) that P(\gamma_s \le t) \le \epsilon whenever |x_0| \le \vartheta . When t \to \infty , it follows that P(\gamma_s < \infty) \le \epsilon , leading to P(\sup_{t \ge 0}|x(t;x_0)|\le s)\ge 1-\epsilon. Hence, stability in probability is guaranteed. Next, we concentrate on proving FxTS in probability.

    From (3), \dot{V}(x) is given by

    \dot{V}(x) = V_x f(x,t)+ V_x \phi(x,t)\xi(t) \le (-h_1+h_2|\xi|)r(V(x)). (6)

    We only need to be proved the case x_0 \in \mathrm{R}^n \setminus \{0\} . Because the assertion holds evidently for x_0 = 0 , since x(t; x_0) \equiv 0 . Let the function {\cal{R}}(x) = \int_{0}^{V(x)} \frac{ds}{r(s)}, which is twice continuously differentiable in \mathrm{R}^n \setminus\{0\} . Define the first hitting time \tau = \inf\{t \ge 0; |x(t;x_0)| = 0\}. Then,

    \begin{split} {\cal{R}}(x(t \wedge \tau);x_0) & = {\cal{R}}(x_0)+\int_{0}^{t\wedge \tau} \frac{\dot{V}(s)}{r(s)} ds \\ &\le {\cal{R}}(x_0)+\int_{0}^{t\wedge \tau} (-h_1+h_2|\xi(s)|)ds. \end{split} (7)

    According to Assumption 2, there exists a T>0 such that for each sufficiently small \epsilon >0 and \sigma \in (0,3\varpi ) ,

    P \left\{ \left\lvert \frac{1}{t-t_0}\int_{t_0}^{t} |\xi(s)|^2ds-E[|\xi(t)|^2] \right\rvert \le \sigma \right\} \ge 1-\epsilon.

    Combining with Assumption 1 and Cauthy-Schitz inequation, it follows that

    \int_{0}^{t\wedge \tau} |\xi(s)|^2ds \le 4\varpi(t\wedge \tau). \;\; (8)
    \int_{0}^{t\wedge \tau} |\xi(s)|ds \le 2 \sqrt{\varpi } (t\wedge \tau). (9)

    Hence, (7) can be rewritten to

    E[{\cal{R}}(x(t \wedge \tau))]\le {\cal{R}}(x_0)+(2h_2\sqrt{\varpi }-h_1)E(t\wedge \tau). (10)

    Combining (10) and {\cal{R}}(s) \ge 0 leads to E(t\wedge \tau) \le {{\cal{R}}(x_0)}/(h_1- 2h_2\sqrt{\varpi}). Letting t \to \infty and using Fatou lemma, one has E\tau \le {{\cal{R}}(x_0)}/({h_1-2h_2\sqrt{\varpi }})<{M}/({h_1-2h_2\sqrt{\varpi}}), which implies that P(\tau_r< \infty) = 1 . Hence, FxTS is guaranteed.

    Then, we prove that the settling time E\tau is positive definite. Because (1) is stable in probability, there exists a 0<\delta = \delta(s)\le 1 and an open neighborhood \Omega_\delta = \{x\in \mathrm{R}^n: |x|<\delta \} such that

    P \left\{\sup\limits_{t\ge 0} |x(t,x_0)|\le s \right\}\ge \frac{1}{2}, \quad \forall x_0 \in \Omega_\delta \setminus \{0\}. (11)

    Due to the continuity of functions f(x,t), and \phi(x,t) , there exists an s = s(z)>0 for z>0 such that

    \sup\limits_{|x|\le s} \{|f(x,t)| \vee \|\phi(x,t) \| \} \le z. (12)

    It is clear that \{\gamma_s = \infty\} = \{\sup\limits_{t\ge 0} |x(t)|\le s\} . Because x(\tau) = 0 , one has |x_0|I_{\gamma_s = \infty}\le I_{\gamma_s = \infty} \int_0^{\tau} (|f(x,t)|+\rho_1|\phi(x,t)|^2 + \rho_2 |\xi(t)|^2)dt, where \rho_1, \rho_2 are positive constants. It follows from (11) and (12) that

    \frac{1}{2}|x_0| \le P\{\gamma_s = \infty\}|x_0| \le (z+4\rho_1 z^2+\rho_2 \varpi )E \tau, (13)

    which implies that

    E \tau \ge \frac{|x_0|}{2(z+4\rho_1 z^2+\rho_2 \varpi )} = :c|x_0|, (14)

    where c > 0 is an arbitrary constant. The proof is complete.

    A corollary is provided next.

    Corollary 1: If there exists functions \nu_1, \nu_2 \in \mathrm{K}_{\infty} , positive real numbers h_1, h_2 , and a \mathrm{C}^2 positive definite function V : \mathrm{R}^n \to \mathrm{R}_+ such that

    \nu_1(|x|) \le V(x) \le \nu_2(|x|),\qquad\qquad\qquad (15)
    \dot{V}(x) \le (-h_1+h_2|\xi|)(\alpha V^{\varrho_1}(x)+\beta V^{\varrho_2}(x)), (16)

    where 0<{\varrho_1}<1<{\varrho_2} , and if h_1 >2h_2\sqrt{\varpi} , then the trivial solution of (1) is fixed-time stable in probability, and the random settling time is upper bounded by E\tau \le {M}/{(h_1-2h_2\sqrt{\varpi})}.

    Proof. Let r(s) = \alpha s^{\varrho_1} +\beta s^{\varrho_2} , (6) is rewritten as

    \dot{V}(x) \le (-h_1+h_2|\xi|)(\alpha V^{\varrho_1}(x)+\beta V^{\varrho_2}(x)).

    Similar to the proof of Theorem 1, Corollary 1 can be proved.

    Then, we give an estimate of settling time with reduced conservatism. The function {\cal{R}}(x) satisfies

    \begin{split} {\cal{R}}(x) &\le \int_{0}^{\theta} \frac{ds}{\alpha V^{\varrho_1}+\beta V^{\varrho_2}} +\int_{\theta}^{\infty} \frac{ds}{\alpha V^{\varrho_1}+\beta V^{\varrho_2}} \\ &\le \frac{\theta^{1-\varrho_1}}{\alpha(1-\varrho_2)}+\frac{\theta^{1-\varrho_1}}{\beta(\varrho_2-1)}: = {\Theta}(\theta). \end{split} (17)

    Though mathematical analysis, when the parameter is taken as \theta^* = {(\alpha/\beta)}^{\varrho_1-\varrho_2} , the minimum value of function {\Theta}(\theta) is given by

    M = \frac{(\alpha/\beta)^{(1-\varrho_1)/(\varrho_2-\varrho_1)}}{\alpha(1-\varrho_1)}+\frac{(\alpha/\beta)^{(1-\varrho_1)/(\varrho_2-\varrho_1)}}{\beta(\varrho_2-1)}. (18)

    Furthermore, the random settling time is given by E\tau \le \frac{M}{h_1-2h_2\sqrt{\varpi}}. This implies that FxTS is achieved.

    Remark 1: Similar to Lemma 1 in the deterministic systems [12], by selecting parameter \theta = 1 , the settling time E \tau_n = {1}/\alpha(1- \varrho_1)(h_1- 2h_2\sqrt{\varpi})+{1}/{\beta(\varrho_2-1)(h_1-2h_2\sqrt{\varpi})} can be obtained. In contrast, E \tau has less conservatism in estimating the settling time because E \tau < E \tau_n . It is also worth noting that the parameter selections for α and β. One is that the function {\cal{R}}(s) \le M must be guaranteed, which removes the reliance on initial values for the trivial solution of (1). The other is that the settling time should not be overestimated, i.e., if the parameters are \alpha = \rho , \beta = 1/\rho , E \tau \to \infty as \rho \to \infty .

    Numerical example: This section presents an example illustrating the validity of the FxTS results. Consider the RNS

    \dot{x} = -2x^{\frac{2}{3} }-2x^3+\frac{1}{4}x^{\frac{2}{3} }\xi(t). (19)

    According to [5], we consider \xi(t) as a stationary process generated by \kappa \dot{\xi}(t) = -\xi(t)+\pi(t), \xi(0) = 0, where \kappa>0 . Let \pi \in R represent a zero-mean bandlimited white noise with power spectrum satisfying F_{\omega}(j\mathfrak{b}) = \Xi, |\mathfrak{b}| \le \mathfrak{b}_w, otherwise, F_{\omega}(j\mathfrak{b}) = 0, where \mathfrak{b}_w > 0 is bandwidth and Ξ is noise power. Fig. 1 depicts the random noise variation curve of \xi(t) .

    Figure  1.  Random noise variation curve.

    Select Lyapunov function V(x) = \frac{1}{2}x^2 . It follows that

    \left\{ \begin{aligned} & V_x f(x,t) = -x^{\frac{5}{3} }-x^4 \le -4V^\frac{5}{6}-8V^2, \\ & |V_x \phi(x,t)| = \frac{1}{4}x^{\frac{5}{3} } \le -V^\frac{5}{6}-2V^2, \end{aligned} \right.

    where h_1 = 3/2 and h_2 = 1/2 . Then initial values are given by x_0 = 3, x_0 = 1 , and x_0 = -2 . It is shown in Fig. 2 that the state responses can converge to zero after 2.75 s regardless of how the initial value is determined. Due to the possible errors in the simulation, we think that the order of magnitude is in the range of 10^{-6} , which can be regarded as states converging to zero. Therefore, the validity of the proposed fixed-time stability theorem is verified.

    Figure  2.  The state responses of system (19).

    Conclusion: In this letter, we have introduced both the definition and Lyapunov criterion pertaining to FxTS for RNSs. Additionally, we have contributed a valuable corollary, which facilitates the practical implementation of Lyapunov functions in various applications. Furthermore, we have rigorously established the positive definiteness of the expectation associated with settling time while presenting a more refined upper-bound estimate that mitigates conservatism.

  • [1]
    O. Feinerman, I. Pinkoviezky, A. Gelblum, E. Fonio, and N. S. Gov, “The physics of cooperative transport in groups of ants,” Nature Physics, vol. 14, pp. 683–693, Jul. 2018.
    [2]
    A. M. Calvão and E. Brigatti, “Collective movement in alarmed animals groups: A simple model with positional forces and a limited attention field,” Physica A, vol. 520, pp. 450–457, Apr. 2019. doi: 10.1016/j.physa.2019.01.029
    [3]
    H. Ling, G. E. Mclvor, J. Westley, K. Vaart, R. T. Vaughan, A. Thornton, and N. T. Ouellette, “Behavioural plasticity and the transition to order in jackdaw flocks,” Nature Communications, vol. 10, no. 1, pp. 1–7, Nov. 2019.
    [4]
    H. Ling, G. E. Mclvor, K. van der Vaart, R. T. Vaughan, A. Thornton, and N. T. Ouellette, “Local interactions and their group-level consequences in flocking jackdaws,” Proc. the Royal Society B:Biological Sciences, vol. 286, no. 1906, pp. 1–10, Jul. 2019. doi: 10.1098/rspb.2019.0865
    [5]
    I. L. Bajec and F. H. Heppner, “Organized flight in birds,” Animal Behaviour, vol. 78, no. 4, pp. 777–789, Oct. 2009. doi: 10.1016/j.anbehav.2009.07.007
    [6]
    S. D. Algar, T. Lymburn, T. Stemler, M. Small, and T. Jüngling, “Learned emergence in selfish collective motion,” Chaos:An Interdisciplinary Journal of Nonlinear Science, vol. 29, no. 12, pp. 1–11, Dec. 2019. doi: 10.1063/1.5120776
    [7]
    B. Zhu, L. Xie, D. Han, X. Meng, and R. Teo, “A survey on recent progress in control of swarm systems,” Science China Information Sciences, vol. 60, no. 7, pp. 1–24, Jun. 2017.
    [8]
    P. Rahmani, F. Peruani, and P. Romanczuk, “Flocking in complex environments—Attention trade-offs in collective information processing,” PLOS Computational Biology, vol. 16, no. 4, pp. 1–18, Apr. 2020.
    [9]
    W. Zha, J. Chen, and Z. Peng, “Dynamic multi-team antagonistic games model with incomplete information and its application to multi-UAV,” IEEE/CAA Journal of Automatica Sinica, vol. 2, no. 1, pp. 74–84, 2015. doi: 10.1109/JAS.2015.7032908
    [10]
    H. Oh, A. R. Shirazi, C. Sun, and Y. Jin, “Bio-inspired self-organising multi-robot pattern formation: A review,” Robotics and Autonomous Systems, vol. 2017, no. 91, pp. 83–100, Jan. 2017.
    [11]
    X. Huang and J. Dong, “Reliable leader-to-follower formation control of multiagent systems under communication quantization and attacks,” IEEE Trans. Systems,Man,and Cybernetics:Systems, vol. 50, no. 1, pp. 1–11, Jan. 2020.
    [12]
    L. Huang, M. C. Zhou, K. Hao, and E. Hou, “A survey of multi-robot regular and adversarial patrolling,” IEEE/CAA Journal of Automatica Sinica, vol. 6, pp. 894–903, 2019. doi: 10.1109/JAS.2019.1911537
    [13]
    A. Yang, W. Naeem, and M. Fei, “Decentralised formation control and stability analysis for multi vehicle cooperative manoeuvre,” IEEE/CAA Journal of Automatica Sinica, vol. 1, no. 1, pp. 92–100, 2014.
    [14]
    L. Bayindir, “A review of swarm robotics tasks,” Neurocomputing, vol. 172, no. C, pp. 292–321, Jan. 2016.
    [15]
    X. Huang and J. Dong, “ADP-Based Robust Resilient Control of Partially Unknown Nonlinear Systems via Cooperative Interaction Design,” IEEE Trans. Systems,Man,and Cybernetics:Systems, pp. 1–9, Feb. 2020.
    [16]
    C. W. Reynolds, “Flocks, herds and schools – A distributed behavioral model,” SIGGRAPH, vol. 1987, no. 21, pp. 25–34, 1987.
    [17]
    T. Vicsek, A. Czirok, E. Ben-Jacob, I. Cohen, and O. Shochet, “Novel type of phase transition in a system of self-driven particles,” Physical Review Letters, vol. 75, pp. 1226–1229, Aug. 1995. doi: 10.1103/PhysRevLett.75.1226
    [18]
    I. D. Couzin, J. Krause, R. James, G. D. Ruxton, and N. R. Franks, “Collective memory and spatial sorting in animal groups,” Journal of Theoretical Biology, vol. 218, pp. 1–11, Sep. 2002. doi: 10.1006/jtbi.2002.3065
    [19]
    F. Cucker and S. Smale, “Emergent behavior in flocks,” IEEE Trans. Automatic Control, vol. 52, no. 5, pp. 852–862, May 2007. doi: 10.1109/TAC.2007.895842
    [20]
    A. Attanasi, A. Cavagna, L. Del Castello, I. Giardina, T. S. Grigera, A. Jelic, S. Melillo, L. Parisi, O. Pohl, E. Shen, and M. Viale, “Information transfer and behavioural inertia in starling flocks,” Nature Physics, vol. 10, no. 9, pp. 691–696, Jul. 2014. doi: 10.1038/nphys3035
    [21]
    B. Li, Z. X. Wu, and J. Y. Guan, “Collective motion patterns of selfpropelled agents with both velocity alignment and aggregation interactions,” Physical Review E, vol. 99, no. 2, pp. 1–10, Feb. 2019.
    [22]
    R. Olfati-Saber, “Flocking for multi-agent dynamic systems – algorithms and theory,” IEEE Trans. Automatic Control, vol. 51, no. 3, pp. 401–420, 2006. doi: 10.1109/TAC.2005.864190
    [23]
    X. Lan, L. Liu, and Y. Wang, “ADP-based intelligent decentralized control for multi-agent systems moving in obstacle environment,” IEEE Access, vol. 7, pp. 59 624–59 630, May 2019. doi: 10.1109/ACCESS.2019.2914669
    [24]
    X. Lan, Y. Liu, and Z. Zhao, “Cooperative control for swarming systems based on reinforcement learning in unknown dynamic environment,” Neurocomputing, vol. 410, pp. 410–418, Oct. 2020. doi: 10.1016/j.neucom.2020.06.038
    [25]
    C. C. Cheah, S. P. Hou, and J. J. E. Slotine, “Region-based shape control for a swarm of robots,” Automatica, vol. 45, no. 10, pp. 2406–2411, Oct. 2009. doi: 10.1016/j.automatica.2009.06.026
    [26]
    X. Lan, Z. Wu, W. Xu, and G. Liu, “Adaptive-neural-network-based shape control for a swarm of robots,” Complexity, vol. 2018, pp. 1–8, Dec. 2018.
    [27]
    A. Cavagna, A. Cimarelli, I. Giardina, G. Parisi, R. Santagati, F. Stefanini, and M. Viale, “Scale-free correlations in starling flocks,” Proc. the National Academy of Sciences, vol. 107, no. 26, pp. 11865–11 870, 2010. doi: 10.1073/pnas.1005766107
    [28]
    M. Zumaya, H. Larralde, and M. Aldana, “Delay in the dispersal of flocks moving in unbounded space using long-range interactions,” Scientific Reports, vol. 8, pp. 1–9, Oct. 2018. doi: 10.1038/s41598-017-17765-5
    [29]
    J. Ren, W. Sun, D. Manocha, A. Li, and X. Jin, “Stable information transfer network facilitates the emergence of collective behavior of bird flocks,” Physical Review E, vol. 98, no. 5, pp. 1–10, Nov. 2018.
    [30]
    H. Ling, G. E. Mclvor, J. Westley, K. van der Vaart, J. Yin, R. T. Vaughan, A. Thornton, and N. T. Ouellette, “Collective turns in jackdaw flocks: kinematics and information transfer,” Journal of The Royal Society Interface, vol. 16, no. 159, pp. 1–10, Oct. 2019. doi: 10.1098/rsif.2019.0450
    [31]
    A. Cavagna, I. Giardina, T. S. Grigera, A. Jelic, D. Levine, S. Ramaswamy, and M. Viale, “Silent Flocks: Constraints on Signal Propagation Across Biological Groups,” Physical Review Letters, vol. 114, no. 21, pp. 1–5, May 2015.
    [32]
    A. Strandburg-Peshkin, C. R. Twomey, N. W. F. Bode, A. B. Kao, Y. Katz, C. C. Ioannou, S. B. Rosenthal, C. J. Torney, H. S. Wu, S. A. Levin, and I. D. Couzin, “Visual sensory networks and effective information transfer in animal groups,” Current Biology, vol. 23, no. 17, pp. R709–R711, Sep. 2013. doi: 10.1016/j.cub.2013.07.059
    [33]
    D. J. G. Pearce, A. M. Miller, G. Rowlands, and M. S. Turner, “Role of projection in the control of bird flocks,” Proc. the National Academy of Sciences, vol. 111, no. 29, pp. 10422–10426, Jul. 2014. doi: 10.1073/pnas.1402202111
    [34]
    B. Collignon, A. Sguret, and J. Halloy, “A stochastic vision-based model inspired by zebrafish collective behaviour in heterogeneous environments,” Royal Society Open Science, vol. 3, no. 1, Article no. 150473, 2016.
    [35]
    H. J. Charlesworth and M. S. Turner, “Intrinsically motivated collective motion,” Proc. the National Academy of Sciences, vol. 116, no. 31, pp. 15 362–15 367, 2019. doi: 10.1073/pnas.1822069116
    [36]
    L. Barberis and F. Peruani, “Large-scale patterns in a minimal cognitive flocking model: incidental leaders, nematic patterns, and aggregates,” Physical Review Letters, vol. 117, no. 24, pp. 248001–248006, Dec. 2016. doi: 10.1103/PhysRevLett.117.248001
    [37]
    T. Bagarti and S. N. Menon, “Milling and meandering: Flocking dynamics of stochastically interacting agents with a field of view,” Physical Review E, vol. 100, no. 1, pp. 1–6, Jul. 2019.
    [38]
    F. A. Lavergne, H. Wendehenne, T. Bauerle, and C. Bechinger, “Group formation and cohesion of active particles with visual perceptiondependent motility,” Science, vol. 364, pp. 70–74, Apr. 2019. doi: 10.1126/science.aau5347
    [39]
    R. Bastien and P. Romanczuk, “A model of collective behavior based purely on vision,” Science Advances, vol. 6, pp. 1–9, Feb. 2020.
    [40]
    M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I. Giardina, V. Lecomte, A. Orlandi, G. Parisi, A. Procaccini, M. Viale, and V. Zdravkovic, “Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study,” Proc. the National Academy of Sciences, vol. 105, no. 4, pp. 1232–1237, 2008. doi: 10.1073/pnas.0711437105
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    Highlights

    • A hybrid swarm motion model is proposed with the visual projection information.
    • The light transmittance of each individual is defined based on the projected view.
    • An autonomous control strategy is presented according to the light transmittance.

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