Technical Description of OBD-II Trouble Code
The circuit for controlling the boost of the turbocharger/supercharger is open
What does that mean?
This diagnostic trouble code (DTC) is a generic powertrain code that applies to OBD-II equipped vehicles with a supercharger or turbocharger (Chevrolet / GMC / Duramax, Isuzu, Ford, Toyota, Nissan, VW, Hino, etc.). Although it is a generic code, the specific repair steps may vary depending on the make and model of the vehicle.
Turbochargers and superchargers are devices that force air into the engine to increase power. Superchargers are driven by a belt connected to the engine crankshaft, while turbochargers are driven by the engine’s exhaust.
Many modern turbocharged vehicles use a variable geometry turbocharger (VGT), which has adjustable vanes that can be opened and closed to control the amount of boost pressure. This allows the turbo to be controlled independently of the engine speed. The position of the vanes is controlled by the powertrain control module (PCM) using an electronic control solenoid or motor. The position of the turbo vanes is determined by a dedicated position sensor.
In vehicles that use a traditional fixed displacement turbocharger or supercharger, the boost is controlled by a wastegate or bypass valve. This valve opens to release excess boost pressure. The PCM monitors this system using a boost pressure sensor.
In relation to this trouble code, the “A” indicates a problem with a portion of the system circuit, rather than a specific symptom or component.
Code P0045 is set when the PCM detects an open circuit in the boost control solenoid, regardless of whether the engine uses a VGT turbo or a traditional turbocharger/supercharger.
One type of turbocharger boost control solenoid valve:

Related trouble codes for turbochargers/superchargers:
Code Severity & Symptoms
These codes have a moderate to severe severity. In some cases, problems with the turbocharger/supercharger can cause serious engine damage. It is recommended to address this code as soon as possible.
Symptoms of a P0045 code may include:
Causes
Possible causes for this code to be set are:
Diagnostic and Repair Procedures
Begin by visually inspecting the turbo and turbo control system. Look for loose connections, damaged wiring, vacuum leaks, etc. Next, check for any technical service bulletins (TSBs) related to the issue. If nothing is found, proceed with a step-by-step diagnosis of the system.
The following is a general procedure, as testing for this code can vary between vehicles. To accurately test the system, refer to the manufacturer’s diagnostic flow chart.
Check the system function by commanding the control solenoid to change position using a bidirectional scan tool. Raise the engine RPM to about 1,200 RPM and toggle the solenoid between on and off. While doing this, the engine RPM should change and the sensor position PID on the scan tool should also change. If the RPM fluctuates but the position/pressure PID does not change, suspect a problem with the sensor or its circuit. If the RPM does not change at all, suspect a problem with the control solenoid, turbo/supercharger, or wiring.