References
Continuous-Time Methods
- Scott JK, Barton PI (2013), Bounds on the reachable sets of nonlinear control systems, Automatica 49 (1), 93-100.
- Scott JK, Barton PI (2013), Improved relaxations for the parametric solutions of ODEs using differential inequalities, Journal of Global Optimization, 1-34.
- Scott JK (2012), Reachability Analysis and Deterministic Global Optimization of Differential-Algebraic Systems, Massachusetts Institute of Technology.
- Shen K, Scott JK (2017), Rapid and accurate reachability analysis for nonlinear dynamic systems by exploiting model redundancy, Computers & Chemical Engineering 106, 596-608.
Discrete-Time Methods
- Corliss GF, and Rihm R (1996). Validating an a priori enclosure using high-order Taylor series. MATHEMATICAL RESEARCH, 90, 228-238.
- Lohner RJ (1992). Computation of guaranteed enclosures for the solutions of ordinary initial and boundary value problems. In Institute of mathematics and its applications conference series. Oxford University Press. Vol. 39: 425-425.
- Nedialkov NS, and Jackson KR (1999). An interval Hermite-Obreschkoff method for computing rigorous bounds on the solution of an initial value problem for an ordinary differential equation. Reliable Computing 5.3: 289-310.
- Nedialkov NS (2000). Computing rigorous bounds on the solution of an initial value problem for an ordinary differential equation. University of Toronto.
- Nedialkov NS, & Jackson KR (2000). ODE software that computes guaranteed bounds on the solution. In Advances in Software Tools for Scientific Computing (pp. 197-224). Springer, Berlin, Heidelberg.
- Sahlodin AM, & Chachuat B. (2011). Discretize-then-relax approach for convex/concave relaxations of the solutions of parametric ODEs. Applied Numerical Mathematics, 61(7), 803-820.
- Wilhelm, ME, Le AV, & Stuber, MD (2019). Global optimization of stiff dynamical systems. AIChE Journal, 65(12), e16836.