Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
Level Set Methods for Computation in Hybrid Systems
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Comparison of interval methods for plotting algebraic curves
Computer Aided Geometric Design
Hybridization methods for the analysis of nonlinear systems
Acta Informatica - Hybrid Systems
Image Computation for Polynomial Dynamical Systems Using the Bernstein Expansion
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Reachability Analysis of Hybrid Systems Using Support Functions
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Computing Reachable States for Nonlinear Biological Models
CMSB '09 Proceedings of the 7th International Conference on Computational Methods in Systems Biology
Accurate hybridization of nonlinear systems
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
The image computation problem in hybrid systems model checking
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Symbolic model checking of hybrid systems using template polyhedra
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
SpaceEx: scalable verification of hybrid systems
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Approximate reachability computation for polynomial systems
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Efficient computation of reachable sets of linear time-invariant systems with inputs
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Reachability analysis of large-scale affine systems using low-dimensional polytopes
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Reachability analysis of multi-affine systems
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
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In this paper we propose a new method for reachability analysis of the class of discrete-time polynomial dynamical systems. Our work is based on the approach combining the use of template polyhedra and optimization [25, 7]. These problems are non-convex and are therefore generally difficult to solve exactly. Using the Bernstein form of polynomials, we define a set of equivalent problems which can be relaxed to linear programs. Unlike using affine lower-bound functions in [7], in this work we use piecewise affine lower-bound functions, which allows us to obtain more accurate approximations. In addition, we show that these bounds can be improved by increasing artificially the degree of the polynomials. This new method allows us to compute more accurately guaranteed over-approximations of the reachable sets of discrete-time polynomial dynamical systems. We also show different ways to choose suitable polyhedral templates. Finally, we show the merits of our approach on several examples.