Robust observer-based  tracking control for polynomial uncertain systems via a homogeneous Lyapunov approach

Abstract

In this paper, an observer-based tracking control problem is considered for a polynomial system with parameter uncertainties and external disturbances. Noting that some states are difficult to measure in practice, a polynomial state observer is employed to obtain the unknown states. Then a robust observer-based tracking controller is designed to force the states of the polynomial uncertain system to follow the ones of the reference model and satisfy $H_{\mathrm{\infty }}$ performance. By using a full-state-dependent homogeneous polynomial function, the solvability condition is derived for the observer-based tracking control strategy, which reduces conservatism. Sum of squares technique is utilised to calculate the corresponding observer and controller, effectively dealing with the calculation problem in polynomial systems. Simulation examples are given to illustrate the effectiveness of the presented control strategy.

Keywords:

• Polynomial system
• homogeneous polynomial Lyapunov function
• tracking control
• $H_{\mathrm{\infty }}$ performance
• sum of squares

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Grant Number U1713223), the Natural Science Foundation of Fujian Province, China (Grant Number 2020J01284) and the Research Project (Grant Number PZ2020016).