Nonlinear convex and concave relaxations for the solutions of parametric ODEs
By Joseph K. Scott, Benoît Chachuat, Paul I. Barton. 2013
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Convex and concave relaxations for the parametric solutions of ordinary differential equations (ODEs) are central to deterministic global optimization methods for nonconvex dynamic optimization and open‐loop optimal control problems with control parametrization. Given a general system of ODEs with parameter dependence in the initial conditions and right‐hand sides, this work derives sufficient conditions under which an auxiliary system of ODEs describes convex and concave relaxations of the parametric solutions, pointwise in the independent variable. Convergence results for these relaxations are also established. A fully automatable procedure for constructing an appropriate auxiliary system has been developed previously by the authors. Thus, the developments here lead to an efficient, automatic method for computing convex and concave relaxations for the parametric solutions of a very general class of nonlinear ODEs. The proposed method is presented in detail for a simple example problem. Copyright © 2012 John Wiley & Sons, Ltd.
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/8f1e626a7531b1efe39fd0cfc4f92f6af0709214
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In Computational Theory and Mathematics
In Control and Systems Engineering
In Numerical Analysis
Citations in the corpus
- Set-Theoretic Approaches in Analysis, Estimation and Control of Nonlinear Systems (2015, methodology): “These methods are inspired from the theory of differential inequalities (Walter, 1970; Scott et al., 2012), viability theory (Aubin, 1991), or other set-theoretic methods such as ellipsoidal calculus (Kurzhanski and Valyi, 1997; Houska et al., 2012).”