Decentralized Adaptive Control of Mismatched Large Scale Interconnected Nonlinear Systems

We consider decentralized adaptive control design for a class of large-scale interconnected nonlinear systems with unknown interconnections, which do not satisfy the matching condition requirement. Large-scale nonlinear systems transformable to the decentralized strict feedback form are considered. Coordinate free geometric conditions under which any general interconnected nonlinear system can be transformed to this form are derived. The interconnections are assumed to be bounded by unknown polynomials in states. Global stability and asymptotic regulation are established using classical Lyapunov techniques. The controller is robust to a wide class of systems obtained by perturbations in the dynamics of the original system. Furthermore, appending additional subsystems does not require controller redesign for the original subsystems.

我们考虑一类具有未知关联且不满足匹配条件要求的大规模互联非线性系统的分散自适应控制设计。考虑可变换为分散严格反馈形式的大规模非线性系统。推导了任何一般互联非线性系统可变换为此形式的无坐标几何条件。假设关联项由状态的未知多项式界定。利用经典的李雅普诺夫技术建立了全局稳定性和渐近调节。该控制器对由原始系统动力学扰动所得到的一大类系统具有鲁棒性。此外，添加额外的子系统时不需要对原始子系统重新设计控制器。