Prescribed Performance Control of Multiple Parametric Strict-Feedback Systems in the Presence of Unknown Control Directions
Junmin Peng, Kaining Wang, Chaoyong Li, Shenping Xiao
Abstract
In this article, we study the problem of prescribed performance control (PPC) for multiple parametric strict-feedback (PSF) uncertain systems with unknown and nonidentical control directions. The designed distributed controller guarantees that the synchronization errors between followers and the leader are evolved within a prescribed range, meanwhile, states in the closed-loop system are bounded. Moreover, the results are independent of the initial values. In addition, by applying command-filtered technology, the complex derivation of virtual control in the traditional backstepping procedure is avoided, thus, the computational burden on each agent is greatly reduced. At the same time, the neighborhood information which is necessary for agent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$i$ </tex-math></inline-formula> to construct its controller is minimized, i.e., only <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$x_{j1}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$x_{j2}$ </tex-math></inline-formula> are transmitted throughout the network. As a result, the communication burden of the network is reduced as well. Both theoretical analysis and numerical simulations are performed to verify the effectiveness of the proposed method.