A computationally efficient approach for stochastic reachability set analysis

The reachability set is defined as the collection of all states which can be traversed from arbitrary initial conditions due to the application of admissible control. Three different probabilistic approaches to compute the reachability sets for a class of discrete time nonlinear systems is discussed. The main idea of the probabilistic approach is to consider the bounded control variables as random variables and represent the reachability sets as the level sets of the state probability density function. In the first approach, the computation of the state density function due to variation in control input at each time is made tractable by computing the Mfold convolution of state density function at each time. To overcome the significant challenge of taking multi-dimension convolution of state density function, the second approach computes the probability density function using the Principle of Maximum Entropy (PME). The third approach utilizes the Conjugate Unscented Transform (CUT) method to curtail the combinatorial growth of samples. Finally, three numerical example problems are considered to show the efficacy and utility of the proposed ideas.