State-Bound Estimation for Nonlinear Systems Using Randomized Mu- Analysis

摘要

Developing state bound estimation algorithms for nonlinear systems has been of high importance in robustness analysis of dynamic systems. For many cases, Monte-Carlo simulation might be the only tool to estimate these bounds for a general type of nonlinear systems. The required number of simulations for a tight bound, however, would be very large and it might be impossible to complete within a given computation time. mu-formulation for state bounds transforms the bound estimation problem to a singularity problem and the singular problem is solved using a randomized optimization approach. The performance of the algorithms is demonstrated by multi-dimensional Rosenbrock function; simple discrete system; large-scale biological system; hybrid system; and navigation error propagation for underwater vehicle. For a given error tolerance of the bounds, a formula to calculate the required number of sampling in the algorithms is provided. Because of the inherent complexity of general nonlinear optimization problems, the required sampling number increases very fast as the problem dimension increases. The suggested algorithms would produce, however, tighter estimation faster than random blind search. In addition, for exploiting parallel computation architecture, the suggested algorithms could be the solution for real-time robustness analysis in the future.