A novel method of nonlinear system-simulation with uncertain parameters providing guaranteed bounds

Uncertain or unknown parameters are often an essential part in several biological or technical applications represented by nonlinear systems. These uncertainties cause numerical and analytical problems in finding guaranteed bounds for the solution of the state space representation for such systems. Unfortunately several industrial applications are demanding exactly these guaranteed bounds in order to fulfil regulations by the state authorities. A common and well known method to perform simulations with uncertain parameters is the Monte-Carlo method. This method with its stochastic approach cannot deliver guaranteed bounds. Methods using interval arithmetic provide a lot of overestimation. Thus we have to develop a novel method to find guaranteed bounds as an initial interval for further methods based on interval arithmetic. In this scope a new method is presented which is using a linear Lyapunov like functions to solve this problem. We achieve guaranteed and finite simulation bounds as a result of our approach. The idea is to find an auxiliary function, which helps to bind the state variables. An example from an industrial application completes the paper.