On the structural analysis and optimal input design for joint state and parameter estimation

Abstract

This paper addresses the problem of joint state and parameter estimation for nonlinear affine-input systems with positive parameters including the design of a closed-loop optimal input adaptation to increase an identifiability measure for the system. The identifiability itself is considered in the context of structural observability of the system dynamics based on structural analysis of the system including the unknown parameters as additional states. In particular, the network graph-based interpretation of structural observability is employed at this point. This analysis motivates to include time derivatives of the measurements as additional system outputs to enhance the structural observability properties. For this purpose robust exact differentiation is considered, relying on the super-twisting algorithm to obtain finite time convergent estimates of these signals. Using the extended measurement signal, a continuous-discrete Extended Kalman filter is proposed that ensures strictly positive estimates for the parameters. Based on the estimates of states and parameters the input signal is determined using a moving horizon optimal predictive control that evaluates the condition number of the Fisher information matrix, thus maximizing the information content of the measurements with respect to the parameters. The proposed scheme extends and combines different previously discussed approaches from the literature and is evaluated by means of a thermal process example in simulation and experiment, showing high potential for similar system identification problems.