|Title||Bounds on Reachable Sets Using Ordinary Differential Equations with Linear Programs Embedded|
|Publication Type||Conference Paper|
|Year of Publication||2013|
|Authors||Harwood SM, Scott JK, Barton PI|
|Conference Name||9th IFAC Symposium on Nonlinear Control Systems|
|Conference Location||INP-ENSEEIHT, Toulouse, France|
|Keywords||Invariants, reachable states, uncertain dynamic systems|
This work considers the computation of time-varying enclosures of the reachable sets of nonlinear control systems via the solution of an initial value problem in ordinary diﬀerential equations (ODEs) with linear programs (LPs) embedded. To ensure the numerical tractability of such a formulation, the properties of the ODEs with LPs embedded are discussed including existence and uniqueness of the solutions of the initial value problem in ODEs with LPs embedded. This formulation is then applied to the computation of rigorous componentwise time-varying bounds on the states of a nonlinear control system. The bounding theory used in this work exploits physical information to yield tight bounds on the states; this work develops a new implementation of this theory. Finally, the tightness of the bounds are demonstrated for a model of a reacting chemical system with uncertain rate parameters.