Deterministic Global Optimization for Dynamic Systems Using Interval Analysis

A new approach is described for the deterministic global optimization of dynamic systems, including problems in parameter estimation and optimal control. The method is based on interval analysis and Taylor models, and employs a sequential approach using a type of branch-and-reduce strategy. A key feature of the method is the use of a new validated solver for parametric ODEs, which is used to produce guaranteed bounds on the solutions of dynamic systems with interval-valued parameters. This is combined with a new technique for domain reduction based on using Taylor models in an efficient constraint propagation scheme. The result is that problems can be solved to global optimality with both mathematical and computational certainty. Examples are presented to demonstrate the computational efficiency of the method.