Continuous Abstraction of Nonlinear Systems using Sum-of-Squares Programming

Understand

We present a control design procedure for nonlinear control systems in which we represent a potentially high dimensional system with a low dimensional continuous-state abstraction.

• The abstraction generates a reference which the original system follows with a low level controller.
• We propose sum-of-squares programming as a tool to design this controller and to provide an upper bound on the relative error between the system and its abstraction.
• We compute the low level controller simultaneously with a simulation function that gives the boundedness guarantee for the relative error.