摘要：AbstractThis paper proposes the adaptive state observer for linear time-invariant systems. The problem statement is classical except that there is no assumption about the sufficiently rich input signal. The solution is based on the generalized parameter estimation based observer (GPEBO). Firstly, the linear regression for the unknown parameters and initial conditions are constructed. With the proposed novel parameterization, a sufficient number of independent linear regressions are generated in contrast to the original GPEBO. Then the mixing stage of the dynamic regressor extension and mixing method is applied to obtain independent scalar regression models. Next, the parameters and initial conditions are estimated by the gradient descent method with finite-time modification. Finally, with obtained estimates, the value of the state vector is reconstructed. Under weak assumptions about interval excitation, the proposed observer provides convergence of the parameter and state estimation errors to zero at the predefined finite time in the noise-free case. The numerical simulations demonstrate the efficiency of the proposed observer in comparison with the original GPEBO.
