Computational Methods for Analyzing and Controlling Hybrid Systems

Prof. Claire Tomlin, Department of Aeronautics and Astronautics, Stanford University

Hybrid systems exhibit dynamics which evolve both continuously and in discrete jumps. Such behavior arises in many contexts, both in man-made systems and in nature. Continuous systems which have a phased operation, such as insect motion and biological cell growth and division, are well-suited to be modeled as hybrid systems, as are continuous systems which are controlled by a discrete logic, such as a chemical plant controlled with valves and pumps, or the autopilot modes for controlling an aircraft. Hybrid systems are also natural models for systems comprised of many interacting subsystems or processes, such as air or ground transportation systems. In these examples, the continuous dynamics model system motion, biochemical or chemical reactions, while the discrete dynamics model the sequence of contacts or collisions in the gait cycle, cell divisions, valves and pumps switching, and coordination protocols. In all of these examples, the system dynamics are complex enough that traditional analysis and control methods are not computationally feasible. To understand the behavior of hybrid systems, to simulate, and to control these systems, theoretical advances and analytical tools are needed.

In this talk, I will present a method that we have designed for analyzing and controlling hybrid systems, and will focus on the numerical methods that we are now developing to achieve efficient computation of the control law. These methods will be presented in the context of three applications: the assurance of aircraft separation in automated air traffic control, verified mode switching algorithms for autopilots, and the development of computationally feasible models of cell regulatory networks.