We present our approach to several control challenges in high-speed autonomous racing for the Indy Autonomous Challenge (IAC). The IAC involves autonomous head-to-head racing at speeds approaching 200 mph. The autonomy system must maintain traction and stability when operating at such high speeds while also maneuvering aggressively around other competitor vehicles. One key challenge arises from limited actuator update frequency. We propose two lateral control methods to follow the desired trajectory: a cross-track error method and a pure pursuit lookahead angle method. Analysis shows that, when linearized, cross-track error and pure pursuit angle are related by a first-order system. To analyze the effect of actuator update frequency on closed-loop performance, we emulate the discrete rate as a time delay. Control parameters and gains for both controllers can be solved by using loop-shaping techniques to guarantee closed-loop bandwidth and phase margin. The bandwidth is limited by the time delay associated with the loop frequency. The results depict that the steering actuator update frequency should be as high as possible to maximize vehicle stability and indicate that increasing the steering actuator update frequency allows for a higher closed-loop control bandwidth and increased tracking performance. (For example, a 50 Hz control bandwidth can be achieved by a 1 kHz actuator update frequency.) Our acceleration and longitudinal control strategy maximizes acceleration performance while respecting traction and engine revolutions per minute (RPM) limits by applying throttle and shifting gears based on the engine torque-speed profile to achieve the desired wheel traction forces. We demonstrate our control strategies in simulation at various control loop frequencies. A higher control loop frequency allows for higher-bandwidth lateral controllers exhibiting a faster response to changes in the desired trajectory. From a rolling start in an initial acceleration test at a constant control loop frequency, our longitudinal control and shifting strategy outperforms the IAC default automatic transmission.