Reachability analysis of multi-affine systems. We present a technique for reachability analysis of continuous multi-affine systems based on rectangular partitions. The method is iterative. At each step, finer partitions and larger discrete quotients are produced. We exploit some interesting convexity properties of multi-affine functions on rectangles to show that the construction of the discrete quotient at each step requires only the evaluation of the vector field at the set of all vertices of all rectangles in the partition and finding the roots of a finite set of scalar affine functions. The methodology promises to be easily extendable to rectangular hybrid automata with multi-affine vector fields and is expected to find important applications in analysis of biological networks and robot control.

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  1. Sloth, Christoffer; Wisniewski, Rafael: Complete abstractions of dynamical systems by timed automata (2013)
  2. Ben Sassi, Mohamed Amin; Testylier, Romain; Dang, Thao; Girard, Antoine: Reachability analysis of polynomial systems using linear programming relaxations (2012)
  3. Sun, Yajuan; Lin, Hai; Chen, Ben M.: An input-output simulation approach to controlling multi-affine systems for linear temporal logic specifications (2012)
  4. Ramdani, Nacim; Nedialkov, Nedialko S.: Computing reachable sets for uncertain nonlinear hybrid systems using interval constraint-propagation techniques (2011)
  5. Ramdani, Nacim; Meslem, Nacim; Candau, Yves: Computing reachable sets for uncertain nonlinear monotone systems (2010)
  6. Asarin, Eugene; Dang, Thao; Girard, Antoine: Hybridization methods for the analysis of nonlinear systems (2007)
  7. Batt, Grégory; Belta, Calin; Weiss, Ron: Model checking genetic regulatory networks with parameter uncertainty (2007)
  8. Berman, Spring; Halász, Ádám; Kumar, Vijay: MARCO: A reachability algorithm for multi-affine systems with applications to biological systems (2007)
  9. Klaedtke, Felix; Ratschan, Stefan; She, Zhikun: Language-based abstraction refinement for hybrid system verification (2007)
  10. Mitchell, Ian M.: Comparing forward and backward reachability as tools for safety analysis (2007)
  11. Tabuada, Paulo: Approximate simulation relations and finite abstractions of quantized control systems (2007)
  12. Kloetzer, Marius; Belta, Calin: Reachability analysis of multi-affine systems (2006)