As the operation of large systems becomes ever more dependent on extensive automation , the need for an effective solution to the problem of design and validation of the underlying software becomes more critical . Large systems possesses much detailed structure , typically hierarchical , and they are hybrid . Information processing at the top of the hierarchy is by means of formal logic and sentences ; on the bottom it is by means of simple scalar differential equations and functions of time ; and in the middle it is by an interacting mix of nonlinear multi - axis differential equations and automata , and functions of time and discrete events . The lecture will address the overall problem as it relates to flight vehicle management , describe the middle level , and offer a design approach that is based on Differential Geometry and Discrete Event Dynamic Systems Theory .