Closed-Form Solutions of Stochastic and Deterministic Nonlinear Control Problems

Abstract

We review our recent results on stabilization and optimal disturbance attenuation for nonlinear systems with uncertainties. The systems are affine in the control and the disturbance but otherwise general. We treat both deterministic and stochastic disturbances. In both cases the disturbance attenuation problem is posed as a differential game (in the stochastic case the player opposed to control is not the noise itself but its covariance). The results are based on control Lyapunov function techniques. The full account of the results is given in our new monograph(Stabilization of Nonlinear Uncertain Systems, Springer, 1998).