Abstracting Partially Feedback Linearizable Systems Compositionally

Omar Hussien, Aaron D. Ames, Paulo Tabuada

Abstract: Symbolic controller synthesis offers the ability to design controllers enforcing a rich class of specifications such as those expressible in temporal logic. Despite the promise of symbolic controller synthesis and correct-by-design control software, this design methodology is not yet widely applicable due to the complexity of constructing finite-state abstractions for large continuous systems. In this letter, we investigate a compositional approach to the construction of abstractions by exploiting the cascading structure of partially feedback linearizable systems. We show how the linearized part and the zero dynamics can be independently abstracted and subsequently composed to obtain an abstraction of the original continuous system. We also illustrate through examples how this compositional approach significantly reduces the time required for construction of abstractions.