Simulation of discrete linear time-invariant fuzzy dynamic systems

In this paper, a new approach to simulation of discrete linear time-invariant dynamic systems with parameters and initial conditions described by fuzzy numbers is proposed. This approach solves the problem of fuzzy simulation by determining at each iteration a nested family of intervals, corresponding to different levels of certainty (α-cuts), that enclose the possible system states using optimisation. The originality of this approach consists in considering uncertain parameters as time-invariant during the simulation process. The optimisation problems associated with the approach proposed must be solved globally in order to guarantee that the minimum volume box enclosing the region of system states for each level of certainty has been derived. Then, a global optimisation algorithm, based on the theory of moments and linear matrix inequality relaxations suitable for the type of problems (polynomial programs) that appear in the fuzzy simulation algorithm, is used. Finally, two real engineering application examples allow assessing the performance of the approach proposed.