Stabilisation for cascade of nonlinear ODEs and counter-convecting transport dynamics

ABSTRACT

We consider stabilisation for a nonlinear ordinary differential equation (ODE) and counter-convecting transport partial differential equations (PDEs) cascaded system in which the transport coefficients depend on the ODE state. Stability analysis of the closed-loop system is based on the infinite-dimensional backstepping transformations and a Lyapunov functional. A predictor control is proposed such that the closed-loop system is globally asymptotically stable. The proposed design method is illustrated by a single-link manipulator.

KEYWORDS:

• Cascaded system
• counter-convecting transport dynamics
• predictor control
• backstepping transformations

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (61773350, 61471163, 61673178) and the Natural Science Foundation of Zhejiang Province of China (LY17F030001). Science Fund for Distinguished Young Scholars of Hubei Province of China, Grant/Award Number: 2017CFA034.