Block-triangular MIMO system 1

Model description: 

$$\Sigma _{S_{1}}: \cases{ \begin{align*} \dot{x}_{1,1} &=f_{1,1}(\bar {x}_{1,1},\bar {x}_{2,1})+g_{1,1}(\bar {x}_{1,1},\bar{x}_{2,1})x_{1,2} \\ \dot{x}_{1,2} &=f_{1,2}(X)+g_{1,2}(\bar{x}_{1,1},\bar{x}_{2,1})u_{1} \\ \dot{x}_{2,1} &=f_{2,1}(\bar {x}_{1,1},\bar {x}_{2,1})+g_{2,1}(\bar{x}_{1,1},\bar{x}_{2,1})x_{2,2} \\ \dot{x}_{2,2} &=f_{2,2}(X,u_{1})+g_{2,2}(\bar{x}_{1,1},\bar {x} _{2,1})u_{2} \\ y_{j} &=x_{j,1}, \quad j=1,2, \end{align*}}$$

where $X = [\bar{x}_{1,2}^{\mathrm T}, \bar{x}_{2,2}^{\mathrm T}]^{\mathrm T}$ with $\bar{x}_{j,2}=[x_{j,1},x_{j,2}]^{\mathrm T},j=1,2$.



Time domain: 


Publication details: 

TitleAdaptive neural control of uncertain MIMO nonlinear systems
Publication TypeJournal Article
Year of Publication2004
AuthorsGe, Shuzhi Sam, and Wang Cong
JournalIEEE Transactions on Neural Networks
Start Page674
Date Published05/2004
Accession Number8012935
Keywordsadaptive control, closed loop systems, control system synthesis, MIMO systems, neurocontrollers, nonlinear control systems
AbstractIn this paper, adaptive neural control schemes are proposed for two classes of uncertain multi-input/multi-output (MIMO) nonlinear systems in block-triangular forms. The MIMO systems consist of interconnected subsystems, with couplings in the forms of unknown nonlinearities and/or parametric uncertainties in the input matrices, as well as in the system interconnections without any bounding restrictions. Using the block-triangular structure properties, the stability analyses of the closed-loop MIMO systems are shown in a nested iterative manner for all the states. By exploiting the special properties of the affine terms of the two classes of MIMO systems, the developed neural control schemes avoid the controller singularity problem completely without using projection algorithms. Semiglobal uniform ultimate boundedness (SGUUB) of all the signals in the closed-loop of MIMO nonlinear systems is achieved. The outputs of the systems are proven to converge to a small neighborhood of the desired trajectories. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters. The proposed schemes offer systematic design procedures for the control of the two classes of uncertain MIMO nonlinear systems. Simulation results are presented to show the effectiveness of the approach.