  In this work we present a nonlinear adaptive suboptimal control strategy for
uncertain nonlinear systems. Stochastic parametric uncertainty is dealt with by
employing spectral decomposition of the random variables by means of the
generalized polynomial chaos expansion. The projection of uncertainty onto the
orthogonal polynomial basis, prescribed by the Wiener-Askey scheme, provides a
deterministic model from which the control laws are designed. We apply the
nonlinear feedback control law to an automatic pilot system for recovering an
aircraft with uncertain aerodynamic data from stall while providing acceptable
dynamic response. The control law is obtained by approximating the
Hamilton-Jacobi-Bellman equation by a pertubational procedure and asymptotic
weak stability in probability of the controlled nonlinear system is verified in
a deterministic way.
