State Estimation and Parameter Identification of Continuous-time Nonlinear Systems
Dhaliwal, Samandeep Singh
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The problem of parameter and state estimation of a class of nonlinear systems is addressed. An adaptive identifier and observer are used to estimate the parameters and the state variables simultaneously. The proposed method is derived using a new formulation. Uncertainty sets are defined for the parameters and a set of auxiliary variables for the state variables. An algorithm is developed to update these sets using the available information. The algorithm proposed guarantees the convergence of parameters and the state variables to their true value. In addition to its application in difficult estimation problems, the algorithm has also been adapted to handle fault detection problems. The technique of estimation is applied to two broad classes of systems. The first involves a class of continuous time nonlinear systems subject to bounded unknown exogenous disturbance with constant parameters. Using the proposed set-based adaptive estimation, the parameters are updated only when an improvement in the precision of the parameter estimates can be guaranteed. The formulation provides robustness to parameter estimation error and bounded disturbance. The parameter uncertainty set and the uncertainty associated with an auxiliary variable is updated such that the set is guaranteed to contain the unknown true values. The second class of system considered is a class of nonlinear systems with timevarying parameters. Using a generalization of the set-based adaptive estimation technique proposed, the estimates of the parameters and state are updated to guarantee convergence to a neighborhood of their true value. The algorithm proposed can also be extended to detect the fault in the system, injected by drastic change in the time-varying parameter values. To study the practical applicability of the developed method, the estimation of state variables and time-varying parameters of salt in a stirred tank process has been performed. The results of the experimental application demonstrate the ability of the proposed techniques to estimate the state variables and time-varying parameters of an uncertain practical system.