A Tutorial on Numerical Methods for State and Parameter Estimation in Nonlinear Dynamic Systems

In this chapter we provide a tutorial on state of the art numerical methods for state and parameter estimation in nonlinear dynamic systems. Here, we concentrate on the case that the underlying models are based on first-principles, giving rise to systems of ordinary differential equations (ODEs). As a general introduction the different dynamic model types, the generic modeling cycle and several approaches for dynamic optimization, i.e., optimization problems with dynamic systems as constraints, are briefly mentioned. Then, the estimation problem is posed as a maximum likelihood dynamic optimization problem. Afterwards, we review Multiple Shooting techniques and generalized Gauss-Newton methods for general least-squares and L1-norm optimization problems and discuss the benefits of the recently developed Lifted Newton Method in the context of state and parameter estimation. Finally, we present an illustrative example involving the estimation of the states and parameters of a pendulum using the freely available software environment ACADO Toolkit in which many of the discussed algorithms are implemented.

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