Structurally stable output regulation of nonlinear systems
The paper revisits the (structurally stable) output regulation problem for nonlinear systems modeled by equations of the form \(\dot x=f(x,u,w)\), \(\dot w=s(w)\), \(e= h(x,w)\), where \(x\) is the state, \(u\) the control, \(e\) the regulated output and \(w\) an exogenous disturbance produced by an arbitrary exosystem. The regulator problem consists of seeking a controller \(\dot z=g(z,e)\), \(u= k(z)\) such that 1) the disturbance-free closed loop system has \((x,u)=(0,0)\) as a locally exponentially stable equilibrium, and 2) for small initial \((x(0),z(0),w(0))\) the regulated output \(e(t)\) goes asymptotically to zero for \(t\) going to infinity. Under suitable hypothesis, a necessary condition in terms of an invariant manifold is rederived (as was already shown in earlier work on the subject by the first and third author). This necessary condition is further extended into a necessary and sufficient condition for the local solvability of the regulator problem. Further results dealing with harmonic exogeneous disturbance \(w\), and variants of the regulator problem under parameter uncertainty (so-called structurally stable regulation) are investigated.
scientific article; zbMATH DE number 1017015
scientific article