Model description:
$$\begin{align*} y_{1}(k+1) &=0.9y_{1}(k)-0.3y_{1}(k-1)/[1+y_{2}^{2}(k-1)]+0.7u_{1}(k) \\ &+0.1y_{1}^{2}(k-1)y_{2}^{2}(k)+0.3\sin(u_{1}(k-1))-0.7u_{2}(k)+0.6u_{2}(k-1) \\ y_{2}(k+1) &=-0.1y_{2}(k-1)+0.3y_{1}(k-1)y_{2}(k)+0.8\sin(u_{1}(k)) \\ &+0.1u_{1}(k-1)+0.9u_{2}(k)+0.2u_{2}(k-1)+0.1u_{2}^{2}(k-1) \end{align*}$$
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Publication details:
| Title | Stable adaptive neural network control of MIMO nonaffine nonlinear discrete-time systems |
| Publication Type | Conference Paper |
| Year of Publication | 2008 |
| Authors | Zhai, Lianfei, Chai Tianyou, Yang Chenguang, Ge S.S, and Lee Tong Heng |
| Conference Name | 47th IEEE Conference on Decision and Control, 2008. |
| Date Published | 12/2008 |
| Publisher | IEEE |
| Conference Location | Cancun |
| ISBN Number | 978-1-4244-3123-6 |
| Accession Number | 10442029 |
| Keywords | adaptive control, closed loop systems, control system synthesis, discrete time systems, MIMO systems, neurocontrollers, nonlinear control systems, stability |
| Abstract | In this paper, stable adaptive neural network (NN) control, a combination of weighted one-step-ahead control and adaptive NN is developed for a class of multi-input-multi-output (MIMO) nonaffine nonlinear discrete-time systems. The weighted one-step-ahead control is designed to stabilize the nominal linear system, while the adaptive NN compensator is introduced to deal with the nonlinearities. Under the assumption that the inverse control gain matrix has an either positive definite or negative definite symmetric part, the obstacle in NN weights tuning for the MIMO systems is transformed to unknown control direction problem for single-input-single-output (SISO) system. Discrete Nussbaum gain is introduced into the NN weights adaptation law to overcome the unknown control direction problem. It is proved that all signals of the closed-loop system are bounded, while the tracking error converges to a compact set. Simulation result illustrates the effectiveness of the proposed control. |
| DOI | 10.1109/CDC.2008.4738830 |