Differential Inequality Algorithms for DynamicBounds.jl

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This package implements a continuous-time differential inequality approach to computing state bounds and relaxations using the DynamicBounds.jl framework. These methods solve auxiliary ODE/DAEs to generate relaxations of parametric pODES/pDAEs at specific points in time. Full documentation of this functionality may be found here in the DynamicBounds.jl website.


  • JK Scott, PI Barton, Bounds on the reachable sets of nonlinear control systems, Automatica 49 (1), 93-100
  • JK Scott, PI Barton, Improved relaxations for the parametric solutions of ODEs using differential inequalities, Journal of Global Optimization, 1-34
  • JK Scott, Reachability Analysis and Deterministic Global Optimization of Differential-Algebraic Systems, Massachusetts Institute of Technology
  • K Shen, JK Scott, Rapid and accurate reachability analysis for nonlinear dynamic systems by exploiting model redundancy, Computers & Chemical Engineering 106, 596-608