Cooperative Output Regulation of Heterogeneous Nonlinear Multi-Agent Systems With Unknown Control Directions

Guo, Meichen; Xu, Dabo; Liu, Lu

doi:10.1109/tac.2016.2609281

Cited by 80 publications

(41 citation statements)

References 29 publications

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“…The dynamical systemẏ ag = g ag (y ag ) with augmented state vector y ag : (6), (29), (31), (32) has a smooth locally Lipschitz map g ag and therefore a maximal solution exists over some interval [0, t f ) [36]. From (34) and Lemma 1 we have that…”

Section: Second-order Agentsmentioning

confidence: 99%

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PI consensus error transformation for adaptive cooperative control of nonlinear multi-agent systems

Psillakis

2019

Journal of the Franklin Institute

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A solution is provided in this note for the adaptive consensus problem of nonlinear multi-agent systems with unknown and non-identical control directions assuming a strongly connected underlying graph topology. This is achieved with the introduction of a novel variable transformation called PI consensus error transformation. The new variables include the position error of each agent from some arbitrary fixed point along with an integral term of the weighted total displacement of the agent's position from all neighbor positions. It is proven that if these new variables are bounded and regulated to zero, then asymptotic consensus among all agents is ensured. The important feature of this transformation is that it provides input decoupling in the dynamics of the new error variables making the consensus control design a simple and direct task. Using classical Nussbaum gain based techniques, distributed controllers are designed to regulate the PI consensus error variables to zero and ultimately solve the agreement problem. The proposed approach also allows for a specific calculation of the final consensus point based on the controller parameter selection and the associated graph topology. Simulation results verify our theoretical derivations.

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Section: Second-order Agentsmentioning

confidence: 99%

“…The unknown identical control directions assumption was relaxed in [24] and [25] for agent networks having a leader. Nussbaum functions were also employed for unknown identical and non-identical control directions in [26,27,28,29] in the framework of cooperative output regulation with the exosystem having the leader role.…”

Section: Introductionmentioning

confidence: 99%

PI consensus error transformation for adaptive cooperative control of nonlinear multi-agent systems

Psillakis

2019

Journal of the Franklin Institute

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“…In practice, there indeed exist some systems whose control directions are unknown, and correspondingly, the control problems of these systems are more complex and difficult . To handle the issue that the control directions are unknown, the Nussbaum function was first developed, then much progress has been made in multiagent systems . For multiagent systems where the unknown control directions of the follower systems are identical, the consensus problem has been studied in the work of Chen et al To allow the control direction of each agent to be nonidentical, a new Nussbaum function was developed in the work of Guo et al Unfortunately, these works can only guarantee the regulation/tracking errors to be asymptotically convergent since the time derivative of the overall Lyapunov function cannot been ensured to be negative definite.…”

Section: Introductionmentioning

confidence: 99%

Distributed fixed‐time consensus for multiagent systems with unknown control directions

Liu

Yang

2019

Intl J Robust & Nonlinear

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This paper investigates the consensus problem for high-order multiagent systems with unknown control directions and directed communication constraints.To handle the problem of unknown control directions, a logic switching rule is established in the framework of fixed-time stability. Then, the consensus is achieved in two steps. A group of distributed fixed-time observers is designed to estimate the reference signals first. Based on these estimates and the designed logic switching rule, a novel control protocol is proposed for each follower system. Different from the existing results, the consensus is achieved with a fixed-time convergence rate, and the unknown control directions are allowed to be nonidentical for each agent. Finally, simulation results are given to exhibit the validity of the proposed method.tracking has been achieved for high-order multiagent systems under an undirected communication graph. Furthermore, for multiagent systems with nonholonomic chained-form dynamics and a directed communication graph, this problem has been considered by Ning and Han. 19 It is worth noting that the above results are obtained based on an assumption that the control directions of follower systems are clearly known.In practice, there indeed exist some systems whose control directions are unknown, and correspondingly, the control problems of these systems are more complex and difficult. 20 To handle the issue that the control directions are unknown, the Nussbaum function was first developed, 21 then much progress has been made in multiagent systems. [22][23][24][25] For multiagent systems where the unknown control directions of the follower systems are identical, the consensus problem has been studied in the work of Chen et al. 22 To allow the control direction of each agent to be nonidentical, a new Nussbaum function was developed in the work of Guo et al. 23 Unfortunately, these works can only guarantee the regulation/tracking errors to be asymptotically convergent since the time derivative of the overall Lyapunov function cannot been ensured to be negative definite. According to the practical demand, recently, for a single system with an unknown control direction, global finite-time stability has been obtained in the works of Chen et al 26 and Wu et al. 27 In the work of Chen et al, 26 a switching function and a logic switching rule are designed to search the right control direction. When there are multiple unknown control directions in the system, this problem has been solved in the work of Wu et al. 27 However, up to now, there is no result that guarantees the consensus to be achieved in finite time for multiagent systems with unknown control directions. Moreover, different from a single system, the reference signals can only be obtained by a part of follower systems, and followers may have different control directions, which leads to the design being much more complex. Last but not the least, the directed communication networks also increase the difficulties in the stability analysis since the interactions are...

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“…It was presented by Nussbaum, which is the first to address unknown constant coefficients problem by proposing a special function based on a control scheme for a class of first‐order linear systems. Sequentially, based on this result, considerable attention has been received in recent years . In the work of Wang et al, an adaptive actuator failure compensation method was presented by introducing Nussbaum functions for a category of nonlinear systems with unknown control directions.…”

Section: Introductionmentioning

confidence: 99%

“…Sequentially, based on this result, considerable attention has been received in recent years. [40][41][42][43][44][45] In the work of Wang et al, 46 an adaptive actuator failure compensation method was presented by introducing Nussbaum functions for a category of nonlinear systems with unknown control directions. A saturated Nussbaum function-based strategy was studied by Chen et al 47 for robotic systems with unknown actuator dynamics.…”

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confidence: 99%

Nussbaum gain adaptive backstepping control of nonlinear strict‐feedback systems with unmodeled dynamics and unknown dead zone

Liang

et al. 2018

Intl J Robust & Nonlinear

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Summary This paper investigates an adaptive state feedback control problem for a class of single‐input and single‐output nonlinear systems with strict‐feedback form. A novel adaptive control strategy is developed for nonlinear systems with unmodeled dynamics, unknown control directions, dynamic disturbances and unknown dead zone. To stabilize this category of systems, a dynamic signal is introduced to dominate the unmodeled dynamics. Nussbaum gain technique is used to overcome the unknown control directions problem. Nonlinear damping terms are framed to counteract the dynamic disturbances, and the assistant signal is constructed to compensate the influence of symmetric dead zone. The adaptive control approach ensures all signals in the closed‐loop system to be bounded. Finally, a numerical example is used to verify the effectiveness of the theoretical results.

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Cooperative Output Regulation of Heterogeneous Nonlinear Multi-Agent Systems With Unknown Control Directions

Cited by 80 publications

References 29 publications

PI consensus error transformation for adaptive cooperative control of nonlinear multi-agent systems

PI consensus error transformation for adaptive cooperative control of nonlinear multi-agent systems

Distributed fixed‐time consensus for multiagent systems with unknown control directions

Nussbaum gain adaptive backstepping control of nonlinear strict‐feedback systems with unmodeled dynamics and unknown dead zone

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