Deterministic global optimization of nonlinear dynamic systems

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Validated solutions of initial value problems for parametric ODEs (2007, methodology): “The method presented, as implemented in VSPODE, is now being used in a number of practical applications, including simulation of bioreactors with parametric uncertainties [13], model-based fault diagnosis [14], deterministic global optimization for fitting time series data [10] and for optimal contr”
Nonlinear convex and concave relaxations for the solutions of parametric ODEs (2013, methodology): “On the whole, global dynamic optimization solvers can presently only solve relatively small problems in reasonable computational time because of the lack of an efficient method for computing tight convex and concave relaxations [2, 3, 13, 18].”
A review of recent advances in global optimization (2009, methodology): “…2007) created a new interval solver for parametric ODEs, which is used to produce guaranteed bounds on the solution of dynamic systems with intervalvalued parameters, and incorporated it within the framework of a global optimization solver for dynamic systems, including optimal control problems.”
Set-Theoretic Approaches in Analysis, Estimation and Control of Nonlinear Systems (2015, methodology): “Both phases typically rely on a high-order Taylor expansion of the ODE solutions in time, and the enclosures are propagated by a variety of affine set-parameterization extensions (Berz and Makino, 2006; Lin and Stadtherr, 2007b; Neher et al., 2007).”