Symbolic control design of incrementally stable nonlinear systems with dynamic regular language specifications

In this paper we consider a control problem where the plant is a continuous-time incrementally stable nonlinear system, the controller is modeled as a finite state machine and the specification is modeled as a regular language. In some applications of interest it can be the case that the system does not know the whole specification to be enforced, but only a first part of it; then, at some time the system will obtain a second specification for which the controller needs to reconfigure. We propose results for the efficient synthesis of controllers in this setting. An analysis of computational complexity of the proposed approach is included which is also compared to traditional ones. An illustrative example is also presented.