Joint estimation of state, parameter, and unknown input for nonlinear systems: A composite estimation scheme

This study is concerned with the joint estimation problem for a class of nonlinear systems with the simultaneous unknown of the system state, the parameter, as well as the input signal. A composite estimation scheme is proposed where the estimator consists of both linear and nonlinear components, under which the estimation performance is improved. The analysis and synthesis issues of the developed estimation algorithm are addressed for both the continuous-time case and the discrete-time case. By utilizing the Lyapunov stability theory combined with the singular value decomposition technique, sufficient conditions are established for both continuous-time and discrete-time cases to guarantee the convergence of the estimation error, rather than the boundedness in most of the existing literature. To facilitate the algorithm implementation in practical engineering, the Newton-Raphson method is adopted to deal with the feasibility issue for the discrete-time case. Numerical simulations are provided for both the continuous- and discrete-time cases to demonstrate the effectiveness of the proposed joint estimation strategies.