Consensus of uncertain parabolic PDE agents via adaptive unit-vector control scheme

• Published in: IET control theory & applications Vol. 12; no. 18; pp. 2488 - 2494
• Main Author: He, Ping
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 18.12.2018
• Subjects: adaptive control; adaptive distributed unit‐vector control scheme; adaptive gain; adaptive unit‐vector control scheme; asymptotical consensus; coupled uncertain parabolic partial differential equation agents; Dirichlet boundary condition; distributed control; distributed disturbance; distributed unit‐vector controller; gradient‐based mono‐directional gain adaptation; Lyapunov functional scheme; Lyapunov methods; Neumann boundary condition; parabolic equations; partial differential equations; Research Article; uncertain parabolic PDE agents; uncertain systems; adaptive unit-vector control scheme; coupled uncertain parabolic partial differential equation agents; uncertain parabolic PDE agents; distributed control; uncertain systems; Lyapunov functional scheme; gradient-based mono-directional gain adaptation; Neumann boundary condition; adaptive control; adaptive distributed unit-vector control scheme; Dirichlet boundary condition; asymptotical consensus; distributed unit-vector controller; adaptive gain; distributed disturbance; partial differential equations; Lyapunov methods; parabolic equations
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2018.5202

This study focuses on the asymptotical consensus and synchronisation for coupled uncertain parabolic partial differential equation (PDE) agents with Neumann boundary condition (or Dirichlet boundary condition) and subject to a distributed disturbance whose $\mathcal {L}_2$L2 norm is bounded by a constant which is not known a priori. Based on adaptive distributed unit-vector control scheme and Lyapunov functional scheme, the distributed unit-vector controller with adaptive gain is suggested to provide for the leader–following tracking of uncertain parabolic PDE agents. The suggested gradient-based and mono-directional gain adaptation provides convergence without requiring the knowledge of an upper bound to the norm of the external disturbance. The simulation is proposed to account for the effectiveness and robustness of the provided method.