Abstract
A computational method for the approximation of reachable sets for non-linear dynamic systems is suggested. The method is based on a discretization of the interesting region and a projection onto grid points. The projections require to solve optimal control problems which are solved by a direct discretization approach. These optimal control problems allow a flexible formulation and it is possible to add non-linear state and/or control constraints and boundary conditions to the dynamic system. Numerical results for non-convex reachable sets are presented. Possible applications include robust optimal control problems.
Highlights
The subject of this paper is the description of an algorithm for the approximation of reachable sets of non-linear control problems
The occurring optimal control problems are not solved theoretically by use of the Pontryagin’s maximum principle as in [23] but numerically by suitable discretization methods. This approach turns out to be powerful in practice and allows to include control and/or state constraints and even boundary conditions
We suggest a computational method which allows to approximate the reachable set of a nonlinear dynamic system at a fixed time point T by using optimal control techniques
Summary
The subject of this paper is the description of an algorithm for the approximation of reachable sets of non-linear control problems. The occurring optimal control problems are not solved theoretically by use of the Pontryagin’s maximum principle as in [23] but numerically by suitable discretization methods. This approach turns out to be powerful in practice and allows to include control and/or state constraints and even boundary conditions. Consider a suitable one-step discretization scheme, e.g. an explicit Runge-Kutta method, with increment function Φ on an equidistant time grid with time points ti = t0 + ih, i = 0, 1, .
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.