On the Approximation of Complicated Dynamical Behavior
SIAM Journal on Numerical Analysis
Uncertainty propagation in dynamical systems
Automatica (Journal of IFAC)
Survey paper: Research on probabilistic methods for control system design
Automatica (Journal of IFAC)
Survey A survey of computational complexity results in systems and control
Automatica (Journal of IFAC)
| Hi-index | 22.14 |
In this paper we consider the problem of optimal design of an uncertain discrete time nonlinear dynamical system. The problem is formulated using an a-posterori design criterion, which can account for uncertainties generated by the dynamics of the system itself as well as parametric uncertainties. In general, for most uncertain complex dynamical systems, this type of method is difficult to solve analytically. A numerical scheme is developed for the optimal design that involves two steps. First, in order to obtain a numerical algorithm for the optimal solution, we apply randomized algorithms for average performance synthesis to approximate the optimal solution. Second, using the properties of the Perron-Frobenius operator we develop an efficient computation approach to calculate the stationary distribution for the uncertain dynamical systems and the average performance criteria.