(226e) Rigorous Safety Analysis For Nonlinear Continuous-Time Systems

Safety is a critical issue in the design and operation of modern technological systems. Generally, a system may be considered unsafe when, under the influence of external disturbances or equipment failure, it can reach certain undesirable states [1-3]. In other words, from a given set of possible initial conditions and inputs and a finite time horizon, the problem is to determine the parts of this set for which safe operation can be guaranteed. Certain safety analysis problems of this type can be formulated as optimization problems [1]. In this case, use of a rigorous deterministic global optimization approach is essential. An alternative approach is to use a simulation-based method [2]. In this case, it is essential that the state trajectories be rigorously bounded over all possible initial conditions and inputs. In either case, a additional challenge is dealing with model uncertainty. Furthermore, only problems involving some simple discrete-time models have been solved [1,2] to date, though extension to the more general nonlinear, continuous-time case has been recognized as a future research direction [3].

In this presentation, we describe a simulation- based method in which nonlinear, continuous-time models with uncertain parameters will be used to represent the processes being studied. Uncertain parameters are treated as intervals instead of probability distributions since we seek inherently safe operation that eliminates hazards, not just reduces their probability. A dynamic model is thus obtained with interval-valued parameters, inputs and/or and initial states. A technique is needed that will rigorously enclose the trajectories in this interval- valued dynamic model. This is provided by the new parametric ODE solver (VSPODE) described recently by Lin and Stadtherr [4]. A method, incorporating the use of VSPODE, is described for easily and rigorously identifying operating regions that are guaranteed to be safe. Examples are used to demonstrate the potential of this approach for rigorous safety analysis with nonlinear, continuous-time models.

References

[1] Dimitriadis, V.D.; Shah, N. & Pantelides, C.C., AIChE J, 1997, 43, 1041-1059.

[2] Huang, H.; Adjiman, C.S. & Shah, N., AIChE J, 2002, 48, 78-96.

[3] Barton, P.I.; Lee, C.K. & Yunt, M., Comput Chem Eng, 2006, 30, 1576-1589.

[4] Lin, Y. & Stadtherr, M.A., Appl Num Math, in press, 2007.