# Hybrid Control

Hybrid systems are those that transition discreetly between continuous dynamic modes when particular times or conditions are reached. A straightforward example is a dynamic system with impacts. Hybrid systems are typically challenging in the context of path planning, system identification, and optimization because of the nonsmooth behavior the systems exhibit.

Our research focuses on developing algorithms for data association, parameter estimation, and switching time optimization for hybrid systems that are robust, computationally efficient, and real time feasible. Our approach has been to focus on computational aspects of hybrid optimization, ensuring that the optimization has guaranteed convergence rates so that the optimization performs well and so that one can tell when the numerical routine should be terminated. We also focus on how to optimize over the number and order of the "modes" of a system.

Applications include skid-steering vehicles, estimation of flight modes in air vehicles, and power grid fault determination.

**Projects**

**Optimal Control of Switched Systems **

Switching time optimization involves optimizing over the times which discreet changes in the mode of a system (switching times) occur and/or the mode order, in order to minimize a given cost function (i.e. energy, deviation from a desired trajectory).

**Data Association Using Impulse Optimization**

Data association addresses the following question: If one has multiple tracks of data, but is only sampling from one of them at any given time, how should each individual piece of data be assigned to the tracks? For instance, in the movie below, two planes are circling a sensor (that is roughly like a radar). Whenever one objects gets in front of the other object, "bad" measurements are taken, thus affecting the quality of the state estimate. The goal of this research is to automatically throw out the bad data in real time or with a fixed delay.

A plane is being tracked by a radar system, but another, unknown, plane occasionally gets in the way. Data Association attempts to algorithmically throw away the data points that come from this second plane.

Credits: Matthew Travers, Todd D. Murphey