Active Vibration Suppression of Uncertain Hose and Drogue Systems in the Presence of Actuator Nonlinearities

This paper investigates vibration suppression of uncertain hose and drogue systems in the presence of actuator nonlinearities. Firstly, a previously presented model of the hose and drogue systems is extended to describe how the hose and drogue systems restrain the vibration, while the accompanying unknown aerodynamic coefficients are estimated by invoking the parameter projection method. Subsequently, for the actuator nonlinearities of dead-zone and saturation, a smooth dead-zone approximate function is constructed to design the dead-zone compensation method, based upon which the proposed control scheme can handle actuator dead-zone and saturation simultaneously while improving the output efficiency of the actuator. Next, for the actuator nonlinearities of backlash and saturation, a smooth backlash inverse is constructed based upon which the presented control scheme can cope with the both actuator nonlinearities simultaneously. Finally, by utilizing backstepping method and hyperbolic tangent function, the proposed control schemes can also achieve the control objectives of vibration suppression and external disturbance attenuation. Simulation examples are included to demonstrate the validity of the proposed control schemes.

INDEX TERMS Adaptive control, backlash, dead-zone, distributed parameter system, uncertain nonlinear system.

A(t)
Aerodynamic force generated by the elevators Diameter of the hose d drog Diameter of the drogue f t Skin friction drag of the hose C f t Coefficient of f t f n Pressure drag of the hose in the normal direction C f n Coefficient of f n f drog Drag of the drogue C f drog Coefficient of f drog g Acceleration of gravity L Length of the hose m Mass of the drogue and elevators P(z) Tension of the HDS ρ Linear density of the hose ρ air Air density The associate editor coordinating the review of this manuscript and approving it for publication was Chenguang Yang .

θ(t)
Angle of the elevators θ , θ Upper and lower bounds of θ(t) θ 0 Constant angle of the HDS V 0 Constant velocity of the air-tanker w(z, t) Transverse displacement of the HDS N(x) Actuator dead-zone or backlash N (x) Approximation of actuator dead-zone N(x) Estimate error of N (x) ( * ) Partial derivative of ( * ) with respect to t γ Nl , γ Nr Slopes of actuator dead-zone γ l , γ r Approximations of γ Nl , γ Nr γ l (t),γ r (t) Estimates of γ l , γ r γ l (t),γ r (t) Estimate errors of γ l , γ r γ , γ Upper and lower bounds of γ Nl and γ Nr γ ,γ Upper and lower bounds ofγ l (t) andγ r (t) a Nl , a Nr Breakpoints of actuator dead-zone a l , a r Approximations of a Nl , a Nr a l (t),â r (t) Estimates of a l , a r a l (t),ã r (t) Estimate errors of a l , a r a l ,ā r Lower bound of a Nl and upper bound of a Nr a l ,ā r Lower bound ofâ l (t) and upper bound of a r (t) γ l a l (t), γ r a r (t) Estimates of γ l a l and γ r a r γ l a l (t), γ r a r (t) Estimate errors of γ l a l and γ r a r ζ Slope of actuator backlasĥ ζ (t) Estimate of ζ ζ (t) Estimate error of ζ ζ , ζ Upper and lower bounds of ζ ζ,ζ Upper and lower bounds ofζ (t) h l , h r Breakpoints of actuator backlash h Upper bound of −h l and h r ζ h l (t), ζ h r (t) Estimates of ζ h l and ζ h r ζ h l (t), ζ h r (t) Estimate errors of ζ h l and ζ h r ζ h l Upper bound of ζ h l (t) ζ h r Lower bound of ζ h r (t) ( * ) Partial derivative of ( * ) with respect to z

I. INTRODUCTION
The hose and drogue system (HDS) is vital equipment in aerial refueling, which can transfer fuel from the air-tanker to the receiver [1]. As depicted in Fig. 1, the HDS is composed of a hose, a drogue at the end of the hose, and a set of active control surfaces (elevators) mounted on the drogue. The active control surfaces were developed in the last decade [2], to restrain the vibration of the HDS by generating additional aerodynamic force. It is noteworthy that the vibration of the HDS is ineluctable due to the intrinsic flexible nature of the HDS [3], and this phenomenon lengthens the docking process as well as increasing the risk of docking failure [4]- [6]. Therefore, vibration suppression is mandatory for the HDS to work effectively.
In the last few decades, vibration suppression of flexible systems has been vastly investigated, and a plethora of research advances have been documented [7]- [12], [16]. For instance, an overhead crane with flexible cable was studied based upon a backstepping-approach-based controller [7]. Two control schemes respectively based on active disturbance rejection control and sliding mode control were proposed for a one-dimensional Euler-Bernoulli beam equation, to cope with the external disturbance flowing to the control end [8].
In three-dimensional space, an effective control strategy was developed for nonlinear slender beams with large translational and rotational motions [9]. A boundary controller for an axially moving string was proposed to suppress the vibration of the system [10]. And the boundary control of a robotic aircraft with articulated flexible wings was investigated in [11]. With respect to the HDS investigated in this paper, Liu et al. established a novel dynamic model by utilizing the partial differential equation (PDE), and developed several control strategies to suppress the vibration of the HDS as well as achieving additional objectives [12]- [15]. However, it is noteworthy that the model developed by Liu et al. does not consider how the active control surfaces (elevators) generate the control force. Furthermore, the uncertainties of the HDS are also neglected in the above model which will influence the control performance of the closed-loop system [16]- [18], [34]- [36]. Accordingly, challenges still remain regarding vibration suppression of the HDS.
The dead-zone or backlash usually appears in the actuator of mechanical equipment, the HDS is no exception [13], [23]. These nonlinearities degrade the control performance of mechanical equipment, and there have been amounts of control schemes developed to handle them [19]- [25]. For dead-zone nonlinearity, the control problem of uncertain systems with actuator dead-zone was investigated [19], and the effect of dead-zone nonlinearity was eliminated by designing a novel smooth dead-zone inverse. Further, two control schemes were developed by utilizing the fuzzy control method, in which both schemes compensate the dead-zone in the actuator successfully [20], [21]. A neural-networkbased control strategy was presented to cope with actuator dead-zone for a vibrating string system [22]. For backlash nonlinearity, an adaptive backlash inverse scheme was developed for a known linear plant with unknown backlash in the actuator [23]. Furthermore, two smooth backlash inverses were employed to cope with unknown backlash for nonlinear systems [24], [25]. However, it is noteworthy that the above works do not involve actuator saturation, which is also a common actuator nonlinearity that degrades the control performance of mechanical equipment [26], [27], [36]- [39]. Accordingly, it is meaningful to study the control scheme which can cope with actuator dead-zone and saturation or actuator backlash and saturation simultaneously.
In this paper, two novel control schemes are presented for the uncertain HDS with actuator nonlinearities. The contributions of this paper are summarized as follows.
1) Compared with the traditional model presented in [12], [13], our extended model considers how the active control surfaces (elevators) generate the aerodynamic force to suppress the vibration of the HDS, which increases the design difficulty of the controller. The unknown aerodynamic coefficients of the extended model are estimated by the parameter projection method, which will improve the control performance of the closed-loop system.
2) Compared with the traditional control schemes, our first control scheme will handle the actuator nonlinearities of dead-zone and saturation simultaneously. Furthermore, it is noted that the output efficiency of the actuator will decline if we handle the two aforementioned actuator nonlinearities. To address it, a novel dead-zone approximate function is constructed, such that our first control scheme will improve the output efficiency of the actuator while handling the two aforementioned actuator nonlinearities simultaneously.
3) Compared with the traditional control schemes, our second control scheme will handle the actuator nonlinearities of backlash and saturation simultaneously. It is noteworthy that the two aforementioned actuator nonlinearities affect each other, thus the control difficulty here is how to cope with them simultaneously. To overcome it, a novel smooth backlash inverse is constructed, based upon which our second control scheme will resolve this problem properly.
The remainder of this paper is organized as follows: the extended model of the HDS is established in Section II, Section III designs the novel dead-zone approximate function which is the basis of our first control scheme. And then our two control schemes are developed in Section IV, followed by illustrative examples in Section V. Conclusions are drawn in Section VI.

II. PROBLEM FORMULATION
In this paper, we only investigate the vibration of the HDS in the vertical plane, and its axial motion is ignored, as advocated in [2], [12].
The HDS is illustrated in Fig. 1. The Earth-fixed coordinate system is (O 0 XY ). The air-tanker keeps a level flight with a constant velocity V 0 . The HDS is released from the wings of the air-tanker [1], and (O 1 ZW ) is the body-fixed coordinate system attached to the HDS. θ 0 is the constant angle between X axis and Z axis, w(z, t) is the transverse displacement of the HDS. The elevators mounted on the drogue are the actuator of the HDS, θ(t) is the elevators' angle, A(t) is the aerodynamic force generated by the elevators. Let T be the position vector of the HDS relative to (O 0 XY ), and can be expressed as: (1)

A. TRADITIONAL MODEL
The traditional model of the HDS presented in [12], [13] is expressed as [30]: and the boundary conditions of (2) are obtained as: where ρ is the linear density of the hose, g is the acceleration of gravity, m is the mass of the drogue and elevators, L is the length of the hose, d L 1 (t) is the disturbance, P(z) is the tension of the HDS expressed as [12], [28], [29]: f t is the skin friction drag of the hose, f drog is the drag of the drogue, f n is the pressure drag of the hose in the normal direction, C f t , C f drog , and C f n are the corresponding coefficients, ρ air is the air density, d h and d drog are the diameters of the hose and drogue, respectively. Furthermore, P(z) in (6) satisfies the following property. Lemma 1: For any z ∈ [0, L], there exist constants P min , P max , and P min such that the following inequalities hold: (10) Proof: Notice that V 0 is a constant parameter, thus from (6)-(8), we derive that (10) holds. This completes the proof.

B. EXTENDED MODEL
We found that the traditional model (2)-(5) regards the aerodynamic force A(t) as the input, and neglects how A(t) is generated. From Fig. 1, it is seen that A(t) is generated by the elevators, thus we can utilize the linearization approach [31] to obtain the following equations: where F θ > 0 and A 0 are the unknown coefficients of the aerodynamic force A(t), d L 2 (t) is the disturbance induced by linearization, θ(t) is the actuator output (i.e., elevators' angle), u(t) is the actuator input (i.e., controller to be designed), Sat( * ) is the actuator saturation defined as: −θ,θ are positive constants, N is the actuator nonlinearity which can be dead-zone or backlash, the expression of N can be found in the following subsection.
Then substitute (11) into (4), we can derive the extended model of the HDS as: where and satisfies the following assumption. Assumption 1: The disturbance d L (t) in (13) satisfies 0 ≤ |d L (t)| ≤d L , whered L is a positive constant.
Remark 1: Compared with the traditional model (2)-(5), the extended model (13) considers how the aerodynamic force A(t) is generated, as described by (11). The accompanying unknown parameters F θ , A 0 and disturbance d L 2 (t) increase the controller design difficulty, which will be handled in Section IV.

C. ACTUATOR NONLINEARITIES
In this paper, we consider the following two nonlinearities in the actuator:

1) DEAD-ZONE
The dead-zone nonlinearity N(x) is described as [13]: where x is the actuator input, γ Nr , γ Nl , a Nr , and a Nl are the unknown constant slopes and breakpoints of N(x), respectively. Besides, x(t) is a function of t, here we write only x for brevity of notation. In the following equation, x(t) is written as x for the same reason.

2) BACKLASH
The backlash nonlinearity N(x) is described as [24]: where x is the actuator input, ζ is the unknown constant slope of N(x), h r , h l are the unknown constant parameters, N(t − ) denotes that there is no change in N.
The parameters in the above two actuator nonlinearities satisfy the following assumption.
Assumption 2: There exist known positive constants γ ,γ , a r , ζ ,ζ , andh as well as known negative constant a l such that γ Nr , γ Nl , a Nr , a Nl , ζ , h r , and h l satisfy The control objective of this paper is that design controller u(t) such that the closed-loop system of (13) is stable subject to the actuator dead-zone (14) and saturation (12) or actuator backlash (15) and saturation (12). Furthermore, w(z, t) is uniformly ultimately bounded.

III. DEAD-ZONE APPROXIMATE FUNCTION
To develop the control scheme handling actuator dead-zone and saturation, a novel dead-zone approximate function and its properties are presented in this section.
Our control scheme for actuator dead-zone and saturation requires differentiability of actuator dead-zone (14), which obviously cannot be satisfied. Thus we need to design a differentiable function N (x) to approximate actuator deadzone (14). The differentiable function N (x) is designed as: where η γ , η a1 , η a2 are positive constants,ā r andâ l are constants satisfyingā r >ā r ,â l < a l ; γ r , γ l , a r , a l are unknown parameters denoted as: a r ,ā l are small known constants. Remark 2: It is noteworthy that the actuator deadzone (14) equals a linear function minus a saturation function, and can be approximated by a linear function minus a hyperbolic tangent function. Inspired by this property, the differentiable function (18) is designed to approximate the dead-zone nonlinearity (14).
The following lemma presents the properties of the differentiable function (18).
It is noteworthy that (18) is an unknown function, we cannot utilize it to design our control scheme directly. To address this problem, letγ r (t),γ l (t),â r (t),â l (t), γ r a r (t), and γ l a l (t) be the estimates of the unknown parameters γ r , γ l , a r , a l , VOLUME 8, 2020 γ r a r , and γ l a l , respectively. Then we can present the following piecewise function to estimate N (x): It is seen thatN is a function of seven arguments: x,γ r ,γ l , a r ,â l , γ r a r , and γ l a l , but we denote it asN (x) for brevity of notation. Similarly, we omit the independent variable t ofγ r , γ l ,â r ,â l , γ r a r , and γ l a l .
To proceed, we define whereγ ,γ are positive constants satisfying [γ ,γ ] ⊃ [γ ,γ ], a r ,â l are defined below (18). Then the properties of the novel dead-zone approximate function (22) can be presented in the following lemma.
For any (x,γ r ,γ l ,â r ,â l , γ r a r , γ l a l ) ∈ R × , if positive constantsγ ,γ , η γ , η a1 , η a2 satisfy: then we can have (iii) DefineÑ (x,γ r ,γ l ,ã r ,ã l , γ r a r , γ l a l ) as (for brevity of notation, we write onlyÑ (x) in the remainder of this paper): then the following equation always holds: (ii) Owing to the proofs of x ≥ 0 and x < 0 are similar, we only discuss the case of x ≥ 0.
. Then from (23), (31) can be ensured if the following inequality holds: In view of (36), one derives Next, consider the following two cases.
, it is apparent that 1 is monotonous increase respect toγ r , and monotonous decrease respect tô a r and γ r a r . Then recalling (γ r ,γ l ,â r ,â l , γ r a r , γ l a l ) ∈ and (24), we can have that (36) holds if the following inequality holds: Next, consider the following two subcases.
In this subcase, 2 is monotonous increase respect to x. Then notice 0 ≤ x < −ā r ln(0.5), we can have that (40) can be ensured by (27).
Remark 3: It is seen that (25)- (27) are always feasible if η a1 > 0.5 and η a2 is sufficiently large. Nevertheless, a excessively large η a2 may deteriorate the performance of the closed-loop system. Thus η a2 should be chosen properly.
Remark 4: Constructing a dead-zone approximate function which can satisfy the property of ∂N (x) ∂x > 0 is the design difficulty in this section. Due to the unknown parameters of the dead-zone nonlinearity, the designed dead-zone approximate function must have time-varying estimate parameters, which will increase the difficulty proving the aforementioned property.

IV. CONTROL SCHEMES DESIGN
In Subsection IV.A, the control scheme coping with actuator dead-zone and saturation is developed based upon the dead-zone approximate function (22). Then the control scheme handling actuator backlash and saturation is designed in Subsection IV.B. Besides, the following two lemmas are useful for our proof.

A. CONTROL SCHEME FOR ACTUATOR DEAD-ZONE AND SATURATION
The control scheme is developed by utilizing the backstepping method. Thus we introduce the change of coordinate as: where β 1 , β 2 , k 1 , and δ d L are positive constants,F θ inv (t) andÂ 0 (t) are estimates of 1/F θ and A 0 , respectively.

Remark 5: The control scheme presented in this subsection can be summarized as follows: 1) For actuator deadzone: N(u) is firstly approximated and estimated byN (u), thenN (u) is transformed to dN (u)
dt by the change of variables, in the end, dN (u) dt is compensated by controllers (64)

B. CONTROL SCHEME FOR ACTUATOR BACKLASH AND SATURATION
In this subsection, N(u) indicates the actuator backlash expressed in (15), and u(t) is the corresponding controller that will be designed later. Besides, we denoteζ , ζ h r , ζ h l as the estimates of the unknown backlash parameters ζ , ζ h r , ζ h l , respectively, and define a set re as: where ζ h r < 0,¯ ζ h l > 0 are constants with sufficiently small magnitudes,ζ ,ζ are positive constants which satisfy [ζ ,ζ ] ⊃ [ζ ,ζ ] and the following assumption. Assumption 3: The following inequality always holds: Now we can develop the control scheme for actuator backlash and saturation. It is also developed by using the backstepping method. Thus we introduce the change of coordinate as: where u 1 will be designed later, α is defined in (49).

1) STEP 1
Consider the Lyapunov function defined in (51), then from (52), we havė To proceed, we design controller u (i.e., actuator input) as: where v re (t) will be designed later, k u is a positive constant. Then we can have the following lemma. Lemma 9: Consider controller (79). Then ifζ , ζ h r , and ζ h l satisfy the following condition: the following properties always hold: whereδ Nre is a positive constant. Proof: See APPENDIX C. Now we suppose that (83) holds (this will be proved in Lemma (10)). Then substituting (79) into (78), and in view of Lemma (9) and (77), we havė To proceed, using the similar procedures presented in Subsection IV.A.1, we deducė Consider the following Lyapunov function candidate: then differentiating V 2re , and in view of (77) and (80), we deducė To proceed, we design v re as: and design update laws ofζ , ζ h r , ζ h l ,F θ ,Â 0 , andF θ inv as: where τ F θ , τ A 0 , and τ F θ inv can be found below (65), k ζ > 0, k ζ h r > 0, k ζ h l > 0, ζ 0 , ζ h r0 , and ζ h l0 are constants. Then we can have the following lemma.
Proof: The proof is omitted because it is similar to one of Theorem 1. This completes the proof.
Remark 7: It is noteworthy that actuator backlash and saturation affect each other, for instance, the anti-windup control cannot be adopted here because actuator backlash is unknown. Thus the control difficulty in this subsection is how to handle actuator backlash and saturation simultaneously. In our control scheme, actuator backlash N(u) is firstly compensated by constructing the smooth backlash inverse (79), and then actuator saturation Sat(N(u)) is also handled by adopting controllers (80) and (91)-(93), the unknown parameters and disturbance d L (t) are finally resolved by parameter update laws (94) and controller (50), respectively. Remark 8: In the end of Introduction, we claim that the control scheme presented in Subsection IV.A can handle the actuator nonlinearities of dead-zone and saturation simultaneously while improving the output efficiency of the actuator, here is the explanation. Without the dead-zone approximate function (22), we can utilize the similar idea in Subsection IV.B to develop the proposed control scheme (for narrative convenience, here we assume γ Nr = γ Nl = ζ , a Nr = h r , a Nl = h l ). In this way, we can use controller (79) to handle the actuator nonlinearities (here (79) needs to be revised slightly, the independent variable of u 2 and u 3 needs to be turned into u 1 ). Then, when | ζ h r | and | ζ h l | are small, the maximum magnitude of controller (79) is close to (−θ − ζζh/ζ )/ζ or (θ −ζζh/ζ )/ζ . As a contrast, the maximum magnitude of controller (53) is close to −θ/ζ orθ/ζ , which is larger than the one of (79). Therefore, it is seen that the output efficiency of the actuator is improved by the control scheme presented in Subsection IV.A.
Remark 9: Based upon the computing approach presented in [40], all the variables utilized in our control schemes can be obtained by measuring or computing. It is noteworthy that the measuring or computing errors of these variables are ineluctable, which influences the performance of the closed-loop system.

V. SIMULATION
In this section, two illustrative examples are presented to demonstrate the effectiveness of our control schemes developed in Section IV. The two examples are defined as: Case I : uncertain HDS (13) subject to actuator dead-zone (14) and saturation (12), Case II : uncertain HDS (13) subject to actuator backlash (15) and saturation (12).
And they are simulated by utilizing the finite difference method [42].
The simulation results are shown in Figs. 2-7. Fig. 2 displays the transverse displacement of the HDS without controller. It is seen that owing to the disturbance, the vibration   of the HDS is large, which may lead to docking failure in the aerial refueling process.
The control performance of the HDS with our proposed control scheme is shown in Figs. 3 and 6-7. We can see that the vibration of the HDS is suppressed to a small neighborhood of the desired position in the presence of unknown aerodynamic coefficients as well as non-symmetrical actuator dead-zone and saturation.
Compared with the proposed control scheme, most previous works only consider one of the two actuator nonlinearities: dead-zone or saturation (for instance, [12], [13], [19], [20]), and that may degrade the control performance of the closed-loop system, as shown in Figs. 4-6.           Compared to the proposed control scheme, most traditional control schemes usually neglect one of the two actuator nonlinearities: backlash or saturation (for instance, [12], [23]- [25]). The corresponding results can be found in Figs. 9-11. Evidently, when we overlook backlash or saturation, the vibration of the HDS becomes larger, which means that the control performance of the HDS is degraded. Therefore, the above simulation results demonstrate that our proposed control schemes are valid for our control problem.

VI. CONCLUSION
This paper investigated vibration control of the uncertain HDS in the presence of actuator nonlinearities. Based upon the linearization approach, a traditional model of the HDS has been extended, to depict how the HDS generate the control force to restrain the vibration of the HDS, while the unknown aerodynamic coefficients of the model have been estimated by invoking the parameter projection method. Subsequently, for actuator dead-zone and saturation, a smooth dead-zone approximate function has been constructed to design the dead-zone compensation method, based upon which the proposed control scheme can handle actuator dead-zone and saturation simultaneously while improving the output efficiency of the actuator. Next, for actuator backlash and saturation, a smooth backlash inverse has been constructed, based upon which the presented control scheme can cope with the both actuator nonlinearities at the same time. Finally, the proposed control schemes have also achieved the control objectives of vibration suppression and external disturbance attenuation. Additionally, since the excessive slack of the HDS may cause the damage of the equipment, our future work will focus on the tension control of the HDS.

APPENDIX B
Proof: Consider the following Lyapunov function candidate: where β 1 and β 2 satisfy the following inequality: It is proven in [12] that V 3 − V 2 is positive definite if (104) holds, thus V 3 is a proper Lyapunov function candidate. Utilizing (13) and integration by parts, we can derive the derivative of V 3 as: To proceed, we employ Young's inequality to obtain the following inequalities: where 1 , 2 , 3 are positive constants, and note that (108) still holds if we replace F θ with F θ inv , A 0 , γ r , γ l , a r , a l , γ r a r , or γ l a l . Then in view of (10), (74), and (105)-(108), we derivė where + k a l (a l − a l0 ) 2 + k γ r a r (γ r a r − γ r a r0 ) 2 + k γ l a l (γ l a l − γ l a l0 ) 2 ] + k p δ d L > 0. Now choose appropriate constants β 1 , β 2 , k 1 , 1 , 2 , 3 to ensure that (104) is feasible and c 2 , c 3 , c 4 , c 5 are positive. Evidently, the appropriate constants always exist. Then from (110) and the following inequality based upon (109): we can derive thaṫ where c min = min{ c 6 c 1 +1 , 2c 4 m , 2k 2 , k F θ , k A 0 , k F θ inv , k γ r , k γ l ,k a r , k a l , k γ r a r , k γ l a l } > 0, c 1 is defined in (104), c 6 = min{ c 2 β 1 ρ , c 3 β 1 P max }. In view of (111), we derive where c U = c c min + 1 k χ t 0 ( du dv U (χ) − 1)χe −c min (t−s) ds. Then from (112) and the Theorem 1 presented in [34], we deduce that V 3 (t) is bounded.

VOLUME 8, 2020
Therefore, we can obtain that w(z, t) is uniformly ultimately bounded. This completes the proof.

APPENDIX C
Proof: (i) In view of (75), (81)-(83), and noticing that the magnitudes of ζ h r and¯ ζ h l are sufficiently small, we can have | ζ h r u 2 − ζ h l u 3 | ≤ζh.
then in light of (81)-(82), (118)-(120), and (126), we deduce |δ Nre (u)| = |ζ h r u 2 (t) − ζ h l u 3 (t) Therefore, we conclude that (86) is feasible. This completes the proof. He has published numerous papers in refereed journals and conference proceedings, particularly in the areas of management science and computer science. He has published more than eight academic books, including a book on network organizations and information (Japanese edition). His current research interests include automata theory, artificial intelligence, systems control, the quantitative analysis of inter-firm relationships using graph theory, and the engineering approach of organizational structures using complex systems theory. He was one of the winner of the Best Paper Award from the International Symposium on Artificial Life and Robotics (ISAROB), in 2006, and the International Conference on Artificial Life and Robotics (ICAROB), in 2015. In addition, he is one of the co-general-chair of the International Conference on Artificial Life and Robotics. He is one of the Associate Editor of the International Journal of Advances in Information Sciences and Service Sciences and the international Journal of Robotics, Networking, and Artificial Life, and a member of the editorial review board of the International Journal of Data Mining, Modeling, and Management, and Information and Communication Technologies for the Advanced Enterprise. VOLUME 8, 2020