Global asymptotic regulation control for MIMO mechanical systems with unknown model parameters and disturbances

Abstract

A global asymptotic regulation control scheme based on the adaptive disturbance estimation is proposed for the MIMO mechanical systems with unknown model parameters and disturbances. By transforming the motion model of the mechanical system and the disturbances into the parametric forms, respectively, the disturbance rejection control for the MIMO mechanical systems is converted into the adaptive control problem. The robust adaptive control law is then designed using the adaptive backstepping method. Stability analysis shows that the designed control law achieves the global asymptotic regulation of the output vector. Simulations on regulation control of two marine vessels verify the effectiveness of the proposed control scheme.

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Correspondence to Xinjiang Wei.

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This study was funded by National Natural Science Foundation of China (Grant No. 61374108).

Appendix

Appendix

Proposition 1

[45] Consider the Sylvester matrix equation

$$\begin{aligned} X\varPi - EX = \varPsi \varXi \end{aligned}$$
(69)

with \(X \in R^{r_1 \times r_1 } \), \(\varPi \in R^{r_1 \times r_1 } \), \(E \in R^{r_1 \times r_1 } \), \(\varPsi \in R^{r_1 \times r_2 } \) and \(\varXi \in R^{r_2 \times r_1 } \). Assume \(\varPi \) and E have no common eigenvalues, \((E,\varPsi )\) is a controllable pair, and \((\varPi ,{} {} \varXi )\) is an observable pair. Then the Sylvester matrix equation (69) has a unique nonsingular solution .

Barbalat’s lemma: [46] For a vector signal \(\hbar (t) \in R^m \), if \(\int _0^\infty {||\hbar (t)||^2 } dt \leqslant c_1\) and \(\sup _{t \geqslant 0} ||{\dot{\hbar }} (t)||^2 \leqslant c_2 \) for positive constants \(c_1\) and \(c_2\), then \(\mathop {\lim }\limits _{t \rightarrow \infty } ||\hbar (t)|| = 0\).

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Hu, X., Wei, X., Zhang, H. et al. Global asymptotic regulation control for MIMO mechanical systems with unknown model parameters and disturbances. Nonlinear Dyn 95, 2293–2305 (2019). https://doi.org/10.1007/s11071-018-4692-1

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Keywords

  • Mechanical systems
  • Unknown model parameters
  • Unknown disturbances
  • Disturbance observer
  • Adaptive backstepping method