Solving Algebraic Riccati Equation Real Time for Integrated VehicleDynamics Control

In this paper we present a comparison study of different computational methods to implement State Dependent Riccati Equation (SDRE) based control in real time for a vehicle dynamics control application. Vehicles are mechatronic systems with nonlinear dynamics. One of the promising nonlinear control methods to control vehicle dynamics is based on SDRE. In this method, an Algebraic Riccati Equation (ARE) is solved at each sample to generate the control signal. However solving ARE is computationally complex. In this work, Extended Kalman Filter (EKF) iterative, Schur, Eigenvector, and Hamiltonian methods to solve ARE real time are implemented and studied for their timing, accuracy, and feasibility. Three methods, Schur, Eigenvector, and Hamiltonian are found to have an average calculation time of 3.9, 2.5, and 1.6 milliseconds on a dSPACE real time processor. This timing is acceptable as the controller sampling time is 10 milliseconds. In addition to the least processing time, the Hamiltonian based approach yields the lowest quadratic cost for SDRE based Integrated Vehicle Dynamics Control (IVDC)

Probing the Jaynes-Cummings Ladder with Spin Circuit Quantum Electrodynamics

We report observations of transitions between excited states in the Jaynes-Cummings ladder of circuit quantum electrodynamics with electron spins (spin circuit QED). We show that unexplained features in recent experimental work correspond to such transitions and present an input-output framework that includes these effects. In new experiments, we first reproduce previous observations and then reveal both excited-state transitions and multiphoton transitions by increasing the probe power and using two-tone spectroscopy. This ability to probe the Jaynes-Cummings ladder is enabled by improvements in the coupling-to-decoherence ratio, and shows an increase in the maturity of spin circuit QED as an interesting platform for studying quantum phenomena. </p