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Containment consensus with multiple leaders
The main objective of containment control is to design appropriate protocol such that all followers can converge to the convex hull spanned by the leaders.
In Liu & Xu (2012); Liu et al. (2012), over fixed directed topology, distributed containment control of single integrator FOMASs with input delay was investi-gated by using the algebraic graph theory, matrix theory, Nyquist stability crite-rion and frequency domain method. In Chen et al. (2016), over fixed undirected communication topology, containment control of general linear FOMASs with pa-rameter uncertainty was studied based on the stability theory of fractional-order systems and matrix theory. In Gong (2017), over fixed undirected communica-tion topology, by using the fractional Lyapunov direct method, the distributed robust containment control problem for a class of FOMASs with heterogeneous unknown nonlinearities and external disturbances was studied based on the neu-ral networks-based adaptive control. In Zou & Xiang (2017), over fixed directed communication topology, the containment control problem of nonlinear FOMASs was addressed by using the fractional-order Lyapunov function method. In Yang et al. (2018), containment control of single integrator FOMASs without/with time delays was analyzed in a directed/undirected communication topology by using Laplace transform and frequency domain theorem. In Liu et al. (2019b), over fixed directed communication topology, periodic sampling-data control was applied to the containment control of FOMASs, where single integrator FOMAS with-out/with time delays and double integrator FOMASs were considered. In Yang et al. (2019a), containment control of FOMAS without/with input delays under fixed directed weighted communication topology was studied by applying fre-quency domain analysis theory, where the FOMASs were formulated with diverse dynamical equations. In Yuan et al. (2019), observer-based quasi-containment of general linear FOMASs was investigated via event-triggered control strategy based on fixed directed communication topology.
Consensus-based formation control
Consensus algorithms normally guarantee the agreement of a team of agents on some common states without taking group formation into consideration. To reflect many practical applications where a group of agents are normally required to form some preferred geometric structures, it is desirable to consider a task-oriented formation control problem for a group of mobile agents, which motivates the study of formation control presented in this subsection. Compared with the consensus problem where the final states of all agents typi-cally reach a singleton, the final states of all agents can be more diversified under the formation control scenario. Indeed, formation control is more desirable in many practical applications such as formation flying, cooperative transportation, sensor networks, as well as combat intelligence, surveillance, and reconnaissance. In addition, the performance of a team of agents working cooperatively often exceeds the simple integration of the performance of all individual agents. For its broad applications and advantages, formation control has been a very active research subject in the control systems community, where a certain geometric pattern is aimed to form with or without a group reference. More precisely, the main objective of formation control is to coordinate a group of agents such that they can achieve some desired formation so that some tasks can be finished by the collaboration of the agents.
Contributions and outline of dissertation
This dissertation presents parameter identification based on artificial intelligent optimization and distributed tracking control of fractional-order multi-agent sys-tems (FOMASs) under fixed communication topology. The main contributions are summarized as follows.
Chapter 2: In many physical systems, the time delays universally exist because the signal propagation speed is limited, the sensor needs extra time to obtain the measurement information, the controller needs additional computation
and execution time to produce and implement the control inputs. The undesir-able instability and poor performance can easily happen due to the existence of time delays. Secondly, note that for most existing results about the leader-following consensus of fractional-order multi-agent systems (FOMASs), the frac-tional orders between the leader and followers are all homogeneous, while in some complex environment, the fractional orders for the leader and followers may be heterogeneous, which can be more accurate and flexible in describing the dynamics of the leader-following FOMASs. Therefore, it is interesting and significant to learn the leader-following consensus of FOMASs with heterogenous fractional orders between leader and followers, which can be viewed as HFOMASs.
Therefore, in this Chapter, over fixed directed communication graph, the leader-following consensus of heterogenous HFOMASs is investigated with re-spect to input delays, where the fractional orders between leader and followers are heterogenous, which is more general. Firstly, a control algorithm with a fractional-order estimator is proposed to guarantee the leader-following consen-sus of the HFOMASs. Then, the identical input delays are taken into account in the above control algorithm, and the leader-following consensus of the HFOMASs can be achieved under the derived sufficient and necessary condition. Thirdly, the diverse input delays are further considered in the HFOMASs, and a sufficient con-dition is put forward under the designed control algorithm. Finally, simulations are conducted to make the results be convinced.
The main contributions are as follows: firstly, different from the leaderless con-sensus of FOMASs and leader-following consensus of FOMASs with homogeneous orders between leader and followers, the leader-following consensus of FOMASs with heterogenous orders between leader and followers is investigated and a novel control algorithm with a fractional-order estimator is designed. Secondly, in con-trast with leaderless consensus of delayed FOMASs and leader-following consen-sus of FOMASs without time delays, the leader-following consensus of HFOMASs under input delays is considered based on the proposed control algorithm.
Chapter 3: Note that the results studied in Chapter 2 are based on single integrator systems. In practice, more complex intrinsic nonlinear dynamics may exist in mobile agents. However, due to the complexity of the FOMASs, stability of the nonlinear FOMASs is difficult to be verified. Besides, in real applications, unknown external disturbances arising from environment and
Contributions and outline of dissertation
communication are usually unavoidable. External disturbances can easily lead to instability or bad performance. Therefore, in this Chapter, over fixed undirected communication topology and based on the fractional Lyapunov direct method, the distributed consensus tracking of nonlinear FOMASs with external disturbances is addressed. Firstly, a nonlinear discontinuous distributed control protocol is put forward to solve the distributed consensus tracking when some conditions are satisfied. Secondly, a nonlinear continuous distributed control algorithm is further proposed to suppress the chattering behavior of the discontinuous controller, where the upper bound of the tracking error is uniformly ultimately bounded and can be made small enough by choosing the parameters properly. Finally, some simulations are provided to validate the advantages of the obtained results. Compared with the existing results, There are four main differences. Firstly, different from the most results studying the integer-order models, the MASs with fractional dynamics are studied. Secondly, in contrast with most results about the consensus tracking of FOMASs without considering the external disturbances, the external disturbances are considered into the FOMASs in this Chapter. Thirdly, different from most results where the style of the external disturbances are known, in this Chapter we do not known the style of the external disturbances beforehand. Fourthly, different from most results using a linear control protocol, we propose two effective nonlinear control algorithms.
Table of contents :
Acknowledgements
Table of Contents
List of Figures
List of Tables
Abbreviations and notations
1 Introduction
1.1 Background and motivation
1.2 Overview of distributed coordination of FOMASs
1.2.1 Consensus problem
1.2.1.1 Leaderless consensus/consensus producing
1.2.1.2 Leader-following consensus/consensus tracking
1.2.1.3 Containment consensus with multiple leaders
1.2.2 Consensus-based formation control
1.3 Overview of parameter identification problem
1.4 Preliminaries
1.4.1 Graph Theory
1.4.2 Caputo fractional-order derivative
1.4.3 Mathematical knowledge
1.5 Contributions and outline of dissertation
2 Leader-following consensus of heterogenous FOMASs under input delays
2.1 Introduction
2.2 Problem formulation
2.3 Main results
2.3.1 Case without input delays
2.3.2 Case with identical input delays
2.3.3 Case with diverse input delays
2.4 Simulations
2.5 Conclusion
3 Distributed consensus tracking of nonlinear FOMASs with external disturbances based on nonlinear algorithms
3.1 Introduction
3.2 Problem formulation
3.3 Main results
3.3.1 Nonlinear discontinuous tracking control algorithm
3.3.2 Nonlinear continuous tracking control algorithm
3.4 Simulations
3.5 Conclusion
4 Distributed consensus tracking of unknown nonlinear delayed FOMASs with external disturbances based on ABC algorithm
4.1 Introduction
4.2 Problem description for consensus tracking of FOMASs
4.3 ABC algorithm-based parameter identification scheme for FOMASs
4.3.1 Problem formulation for parameter identification
4.3.2 The standard ABC algorithm
4.3.3 The proposed ABC algorithm-based parameter identifica- tion scheme
4.4 Distributed consensus tracking of FOMASs based on ABC algorithm
4.4.1 Discontinuous distributed control algorithm
4.4.2 Continuous distributed control algorithm
4.5 Simulations
4.5.1 ABC algorithm-based parameter identification results
4.5.2 Simulation results on distributed consensus tracking
4.6 Conclusion
5 Distributed cooperative synchronization of heterogenous uncertain nonlinear delayed FOMASs with unknown leader based on DE algorithm
5.1 Introduction
5.2 Problem description for synchronization of FOMASs
5.3 DE-based parameter identification for FOMASs
5.3.1 Differential evolution
5.3.2 The proposed DE-based parameter identification scheme
5.4 Distributed cooperative synchronization of FOMASs based on DE
5.4.1 Discontinuous distributed control algorithm
5.4.2 Continuous distributed control algorithm
5.5 Simulations
5.5.1 DE-based parameter identification results
5.5.1.1 Parameter identification without noise
5.5.1.2 Parameter identification with noise
5.5.2 Simulation results on distributed cooperative synchronization
5.6 Conclusion
6 Parameter identification of unknown nonlinear FOMASs by a modified artificial bee colony algorithm
6.1 Introduction
6.2 The proposed mABC algorithm
6.2.1 Chaos map-based random parameter generator
6.2.2 Opposition-based generation jumping
6.2.3 Two new searching equations
6.2.4 The proposed mABC algorithm
6.3 The proposed mABC algorithm-based parameter identification approach
6.3.1 Problem formulation for the parameter identification
6.3.2 The mABC algorithm-based parameter identification approach
6.4 Experimental setup and results
6.4.1 Experimental setup
6.4.2 Parameter identification results
6.5 Conclusion
Conclusions and Perspectives
References
