<p>This paper addresses the problem of achieving practical consensus in large-scale agent clusters governed by nonlinear reaction-diffusion equations, while considering actuator saturation and external disturbances. Different with the traditional consensus methods, the proposed observer-based boundary control relies on non-collocated and incomplete local measurements rather than idealistic global spatiotemporal dynamics. First, the discrete agents with a chain topology are regarded as a continuum, resulting in the derivation of a reaction-diffusion equation to replace the cumbersome ordinary differential equations (ODEs). Subsequently, an observer is constructed based on the non-collocated measurements to estimate the errors between the leader-following agent clusters. Then, a sufficient condition for the consensus controller is derived by improving the Lyapunov direct method, mean value theorem of integrals and a variation of Wirtinger’s inequality. Furthermore, an optimization problem is proposed to effectively enhance the <i>H</i>∞ disturbance attenuation performance in the presence of actuator saturation. Finally, the comparison simulation is given to illustrate the superiority of proposed methodology.</p>

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Practical Consensus Boundary Control for Nonlinear Reaction-Diffusion Agents with Non-Collocated Measurements

  • Jiaqi Zhong,
  • Yan Feng,
  • Kezhi Wang,
  • Yong Chen

摘要

This paper addresses the problem of achieving practical consensus in large-scale agent clusters governed by nonlinear reaction-diffusion equations, while considering actuator saturation and external disturbances. Different with the traditional consensus methods, the proposed observer-based boundary control relies on non-collocated and incomplete local measurements rather than idealistic global spatiotemporal dynamics. First, the discrete agents with a chain topology are regarded as a continuum, resulting in the derivation of a reaction-diffusion equation to replace the cumbersome ordinary differential equations (ODEs). Subsequently, an observer is constructed based on the non-collocated measurements to estimate the errors between the leader-following agent clusters. Then, a sufficient condition for the consensus controller is derived by improving the Lyapunov direct method, mean value theorem of integrals and a variation of Wirtinger’s inequality. Furthermore, an optimization problem is proposed to effectively enhance the H∞ disturbance attenuation performance in the presence of actuator saturation. Finally, the comparison simulation is given to illustrate the superiority of proposed methodology.