Model description:
Consider a truck-trailer system depicted in the attached image. Its dynamics is described by
$$\begin{align*} x_{1}(t+1) &=\left(1-\frac{vT}{L}\right)x_{1}(t)+\frac{vT}{l}u(t) \\ x_{2}(t+1) &=\frac{vT}{L}x_1(t)+x_{2}(t) \\ x_{3}(t+1) &=x_{3}(t)+vT\sin\left(\frac{vT}{2L}x_{1}(t)+x_{2}(t)\right)x_{1}(t), \end{align*}$$
where $x_1(t)$ : angle difference between truck and trailer. $x_2(t)$ : angle of trailer. $x_3(t)$ : vertical position of rear of trailer, $u(t)$ : steering angle, $T$ : sampling time. In this example, the parameters are $T=2.0s$, $l=2.8m$, $L=5.5m$, $v=-1.0m/s$.
Type:
Form:
Model order:
3
Time domain:
Linearity:
Attachment:
Publication details:
| Title | Stabilization of discrete-time nonlinear control systems - Multiple fuzzy Lyapunov function approach |
| Publication Type | Conference Paper |
| Year of Publication | 2009 |
| Authors | Kau, Shih-Wei, Huang Xin-Yuan, Shiu Sheng-Yu, and Fang Chun-Hsiung |
| Conference Name | International Conference on Information and Automation, 2009. ICIA '09. |
| Date Published | 06/2009 |
| Publisher | IEEE |
| Conference Location | Zhuhai, Macau |
| ISBN Number | 978-1-4244-3607-1 |
| Accession Number | 10837484 |
| Keywords | discrete time systems, fuzzy control, linear matrix inequalities, Lyapunov methods, nonlinear control systems, stability |
| Abstract | This paper deals with the stabilization problem for discrete-time nonlinear systems that are represented by the Takagi - Sugeno fuzzy model. By the multiple fuzzy Lyapunov function and the three-index algebraic combination technique, a new stabilization condition is developed. The condition is expressed in the form of linear matrix inequalities (LMIs) and proved to be less conservative than existing results in the literature. Finally, a truck-trailer system is given to illustrate the novelty of the proposed approach. |
| DOI | 10.1109/ICINFA.2009.5204890 |