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An adaptive \(H^ \infty\) tracking control for a class of nonlinear multiple-input-multiple-output (MIMO) systems. (English) Zbl 1048.93024

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 \(u\in\mathbb R^p\) is the control input, \(y\in\mathbb R^p\) is the output, \(d \in\mathbb R^p\) is an external disturbance, \(y_i^{(j)}\in\mathbb R^p\) 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.

MSC:

93B36 \(H^\infty\)-control
93B51 Design techniques (robust design, computer-aided design, etc.)
93C10 Nonlinear systems in control theory
93C40 Adaptive control/observation systems
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