This note addresses the problem of designing robust tracking controls for a class of nonlinear MIMO systems involving parametric uncertainties, unmodelled dynamics and external disturbances, represented by the following set of differential equations $$y_i^{(n_i)}=f_i(x)+\sum_{j=1}^pg_{ij}(x)u_j+d_j,\quad i=1,\dots,p,$$ where $u\in\Bbb R^p$ is the control input, $y\in\Bbb R^p$ is the output, $d \in\Bbb R^p$ is an external disturbance, $y_i^{(j)}\in\Bbb R^p$ is the $j$th derivative of $y_i$ and $n_1,\dots,n_p$ are positive integers. The functions $f_i(x)$ and $g_{ij}(x)$ for $i,j=1,\dots,p$ are unknown smooth nonlinearities which could depend on $y_i$, $y_1^{(1)},\dots,y_i^{(n_i-1)}$. Hybrid adaptive-robust $H^\infty$ tracking control schemes are developed to guarantee a transient and asymptotical output tracking performance in the sense that all the signals and states of the closed-loop system are bounded, the tracking error is uniformly ultimately bounded and an $H^\infty$ tracking performance is achieved. The $H^\infty$ tracking control relies only on the solution to a modified algebraic Riccati-like matrix equation and so the developed control law can easily be implemented. Consequently, compared with the existing $H^\infty$ tracking control scheme and the robust/adaptive control scheme, the developed adaptive-robust $H^\infty$ tracking control design can be extended to handle a broader class of uncertain nonlinear MIMO systems.
Reviewer: Alexandr B. Vasil’ev (Odessa)