Decomposition algorithms for on-line estimation with nonlinear models

Dynamic state and parameter estimation for nonlinear systems usually leads to large nonlinear problems when the governing differential constraints are discretized under a simultaneous solution strategy. In this paper we discretize the set of ordinary differential equations using an implicit Runge-Kutta integration method, and use the successive quadratic programming (SQP) method to solve the resulting nonlinear programming problem (NLP). The optimality conditions for each data set at the QP subproblem level are decoupled using an affine transform, so that the first order conditions in the state and input variables can be solved recursively and expressed as functions of the optimality conditions in the parameters, thus reducing the size of the problem and turning the effort of solving it linear with the number of data sets. As seen in our example, this approach is over two orders of magnitude faster than general purpose NLP solvers.