Switched autonomous systems are a class of hybrid systems where continuous dynamics are "pieced" together in a discontinuous manner. The switching between these modes may be controlled, where the user designs control inputs to force a system into a desired mode, or uncontrolled, where the system naturally switches between modes. This thesis is concerned with designing a mode estimator for systems with natural switches. For many systems, the timing of the discontinuous switching is not obvious, but a precise knowledge of the switching times is necessary for proper control of the system. Current approaches find the switching times that optimize some performance index of the system. First-order descent methods, such as steepest descent, are commonly employed to numerically descend to the optimal switching times. This technique suffers from the slow convergence rate intrinsic to the poor scaling of steepest descent. We present Newton's method, a second-order descent method, for estimating the optimal switching times.

Newton's method exhibits a q-quadratic convergence rate compared to the slower q-linear convergence rate of steepest descent. This is verified by example using a simple switched LTI system and a more complicated stick/slip system. The stick/slip system of interest is a slip-steered vehicle. By design, the contact state of the vehicle's wheels with the ground must transition between sticking and slipping in order to accomplish even simple maneuvers. The goal is to estimate when the vehicle transitions between these slipping and sticking modes given some noisy reference trajectory interpolated from an inexpensive GPS sensor.