Output synchronous control of multi‐agent beam equations with boundary and domain structure time‐varying disturbances and general disturbances

Abstract

The design of a synchronous controller for a network beam equation with structural time-varying and general perturbations is studied. An infinite dimensional observer is established to estimate the total disturbance which is composed of structural time-varying disturbance and unknown disturbance. Assuming that all networked partial differential equations (PDEs) are connected by communication graph, a feedback controller based on observer is proposed to solve the synchronization problem, which provides many new methods for the control of distributed systems in network space. The controller designed in this paper has three objectives: (1) asymptotically compensate structural term disturbance and general disturbance; (2) ensure the asymptotic convergence between each network state and the virtual leader state to track the virtual leader; and (3) the converged state errors are converged in the sense of synchronization. By using the analytical semigroup method, the well-posedness of the networked closed-loop system is proved. Three kinds of network beam equations with observer feedback control are simulated, and the simulation results show that this control method is effective for the synchronization of the network PDEs.

Robust Cooperative Output Regulation for Networks of Hyperbolic PIDE–ODE Systems

“…A straightforward calculation which includes taking the derivative of (51) w.r.t. time t, evaluating (51b) at the boundaries and inserting the result in (50) as well as replacing v(t), ε(z, t), w(t) using (51) shows that ( 52) is obtained if Υ v , Υ ε , Υ w are the solution of the so-called extended regulator equations. The following lemma states their solvability.…”

“…Both these aspects were not considered intensively in the previous references for PDE agents. So far, disturbances affecting only the actuated boundary are considered in [8], [9] for networks of wave PDEs and in [50] for agents with beam dynamics. Moreover, in [15] synchronization of more general infinitedimensional agents that are subject to constant disturbances and some structured perturbations which are present at the boundaries or in-domain is achieved.…”

“…Next, the networked controlled MAS ( 50) is examined in order to utilize its stability. Note that the equations (66) hold independent of the boundary condition at z = 1, which allows to use them for the networked controlled MAS (50). Hence, inserting (66) in (50e) with v(t) = ve st and the initial value…”