Symbolic models for unstable nonlinear control systems

In this paper we take an important step in our quest to synthesize correct-by-design embedded control software for nonlinear systems. We have shown in previous work that by relying on diverse stability and stabilizability assumptions it is possible to construct finite-state models describing the dynamics of nonlinear control systems. Such finite-state models enable the use of algorithmic techniques to automatically synthesize controllers enforcing control and software requirements. In the present paper, we show that similar results can still be obtained by replacing the stability or stabilizability assumptions by the much weaker assumption of incremental forward completeness. We illustrate the new results by synthesizing a controller for an inverted pendulum subject to a schedulability constraint.