Incremental single shooting—A robust method for the estimation of parameters in dynamical systems

Estimating the parameters of a dynamical system based on measurement data is an important but complex task in industrial and scientific practice [Schittkowski, K. (2002). Numerical data fitting in dynamical systems: A practical introduction with applications and software. Kluwer Academic Publishers]. Due to its importance, different approaches to solve this kind of problem have been developed. The most established ones are single shooting [Bard, Y. (1974). Nonlinear parameter estimation. New York: Academic Press], multiple shooting [Bock, H. G. (1983). Recent advances in parameter identification techniques for ODE. In P. Deuflhard, & E. Hairer (Eds.), Numerical treatment of inverse problems in differential and integral equations (pp. 95–121). Boston: Birkhäuser] and full discretization techniques [Biegler, L. T. (1984). Solution of dynamic optimization problems by successive quadratic programming and orthogonal collocation. Computers & Chemical Engineering, 8, 243–248]. Single shooting is the most natural and simple approach to the problem, directly combining numerical integration and optimization techniques. However, for unstable or singular systems the numerical integration of the dynamic model may fail. This problem is especially severe in the framework of parameter estimation, since the dynamic model has to be integrated many times with different parameter estimates. Multiple shooting and full discretization aim at overcoming these deficiencies but suffer from other drawbacks. Therefore single shooting is still widely applied in industry and academia. In this work we present a novel method called Incremental Single Shooting or ISS for short, which aims at overcoming the deficiencies of the classical single shooting approach while keeping its advantages.