Improve a System’s Behavior

Control Theory, quantum or classical, addresses a fundamental problem: systems do not always behave the way one wants them to behave. Engines run too fast or too slowly; rooms are too hot or too cold; atoms can decay or nuclear spins dephase more rapidly than one desires.

To improve a system’s behavior, control theory adjoins to the system a second system, called a ‘‘Controller,’’ which interacts with the original system in a way that improves its behavior.

A Governor can be added to an engine to regulate its speed; a Thermostat can be added to a room to maintain a desired temperature; pulses of electromagnetic radiation can be applied to an atom or spin to decouple it from its surroundings and slow its decay or dephasing.

Together, the system and controller form a joint dynamical system. If the controller is well designed, this joint ‘‘system-controller’’ system behaves better (according to some appropriate Metric) than the original system on its own.

Controllers are categorized according to the form of their interaction with the system to be controlled. If the interaction is one way, so that the controller acts on the system without obtaining any information about its state, then the controller is called ‘‘open loop.’’ In ‘‘closed-loop’’ control, by contrast, the controller acts on the basis of information that it obtains about the state of the system. A particularly important form of closed-loop control is feedback control, in which the controller obtains information about the system (i.e., the system acts on the controller via sensors), processes it, and feeds it back by acting on the system via actuators. Though more complicated than open-loop control, closed-loop control is typically more accurate as well: the acquisition of information about the system allows greater flexibility in control strategy.