Rigorous simulation of hybrid dynamic systems with symbolic and interval methods

Dynamic systems with a mix of continuous and discrete components, often called hybrid dynamic systems, frequently arise in engineering applications. Since many of these applications are safety critical, it is important to use reliable methods to simulate hybrid systems. The paper illustrates two approaches to rigorous simulation of hybrid dynamic systems. In the first approach, we use symbolic methods to compute closed-form solutions, thus avoiding round off and truncation errors. In the second approach, we use interval methods to compute rigorous bounds on the solution of a hybrid system.