Robust and adaptive control using measurements of higher order derivatives

The problem of output stabilization for linear uncertain systems with external perturbations is studied. It is assumed that the output available for measurements is the higher order derivative of the state (acceleration for a second order plant), which is also corrupted by a noise. Applying a series of integration, an estimation algorithm is proposed for identification of values of all parameters and unknown initial conditions for the state vector. Finally, two control algorithms are developed, adaptive and robust ones, providing boundedness of trajectories for the system. Efficiency of the obtained solutions is demonstrated by numerical experiments.