## Global adaptive output-feedback control of nonlinear systems. I: Linear parameterization.(English)Zbl 0783.93032

This paper deals with the design of global adaptive output compensators for regulation or, more generally, output reference tracking problem. The authors consider nonlinear systems which can be transformed, by a global change of coordinates, into $\begin{cases} \dot\zeta= A\zeta+ b(\theta)\sigma(y)u+ \psi(\theta,y)\\ y= C\zeta\end{cases}\tag{1}$ where $$\zeta\in{\mathbf R}^ n$$, $$u,y\in{\mathbf R}$$, $$\theta\in\Omega\subset{\mathbf R}^ m$$, $$b\in{\mathbf R}^ m$$ and $$\sigma\in{\mathbf R}$$. Here, $$\Omega$$ is a preassigned set of parameters. Moreover, the pair $$(A,C)$$ is in canonical observer form and the maps $$b$$, $$\psi$$ depend linearly on $$\theta$$.
In other words, (1) can be viewed as an observable linear system with output dependent nonlinearities.
For such a system there is an asymptotic observer with linear error dynamics. Moreover, under additional assumptions, the system is minimum phase.
The tracking problem for (1) is solved first for the relative degree $$\rho=1$$, and then for $$\rho\geq 2$$ by constructing global adaptive output compensators. The assumptions are coordinate-free and have a geometric nature. Assumptions like feedback linearizability, growth conditions, matching conditions, existence of Lyapunov functions are not required.

### MSC:

 93B51 Design techniques (robust design, computer-aided design, etc.) 93C40 Adaptive control/observation systems 93C10 Nonlinear systems in control theory 93C15 Control/observation systems governed by ordinary differential equations
Full Text: