Identification, Estimation, and Control for Linear Uncertain Systems Using Measurements of Higher-Order Derivatives

In this paper, the problem of output control for linear uncertain systems with external perturbations is studied. First, it is assumed that the output available for measurement is only the higher-order derivative of the state variable, instead of the state variable itself (for example, the acceleration for a second-order plant), and the measurement is also corrupted by noise. Then, via series of integration, an identification algorithm is proposed to identify all unknown parameters of the model and all unknown initial conditions of the state vector. Finally, two control algorithms are developed, adaptive and robust; both provide boundedness of trajectories of the system. The efficiency of the obtained solutions is demonstrated by numerical simulation.