Computing fuzzy trajectories for nonlinear dynamic systems

One approach for representing uncertainty is the use of fuzzy sets or fuzzy numbers. A new approach is described for the solution of nonlinear dynamic systems with parameters and/or initial states that are uncertain and represented by fuzzy sets or fuzzy numbers. Unlike current methods, which address this problem through the use of sampling techniques and do not account rigorously for the effect of the uncertain quantities, the new approach is not based on sampling and provides mathematically and computationally rigorous results. This is achieved through the use of explicit analytic representations (Taylor models) of state variable bounds in terms of the uncertain quantities. Examples are given that demonstrate the use of this new approach and its computational performance.

► We consider nonlinear dynamic systems with uncertain parameters and/or initial states. ► Uncertainties are represented by fuzzy sets or fuzzy numbers. ► We present a new method for solving such systems to obtain fuzzy state trajectories. ► Unlike previous methods, this approach provides mathematically rigorous results. ► Computational studies demonstrate the method and its computational performance.