## Control Theory: History, Mathematical Achievements and Perspectives

Basic overview of control theory

Encountered--

Time: March 10, 2018

Place: In my own little bubble, staring at my phone, on the morning commute

Pointer from: Transactional control paper from PNNL >> curiosity in “control theory" >> google search

Note type: Direct

- Going backwards in time, we will easily conclude that Romans did use some elements of Control Theory in their aqueducts. Indeed, ingenious systems of regulating valves were used in these constructions in order to keep the water level constant.
- On the other hand, in the ancient Egypt the “harpenodaptai" (string stretchers), were specialized in stretching very long strings leading to long straight segments to help in large constructions. The task of the “harpenodaptai" was precisely to build these “optimal curves"
- The work by Ch. Huygens and R. Hooke at the end of the XVII Century on the oscillations of the pendulum is a more modern example of development in Control Theory. Their goal was to achieve a precise measurement of time and location, so precious in navigation. These works were later adapted to regulate the velocity of windmills
- J. Watt adapted these ideas when he invented the steam engine and this constituted a magnificent step in the industrial revolution. In this mechanism, when the velocity of the balls increases, one or several valves open to let the vapor scape. This makes the pressure diminish. When this happens, i.e. when the pressure inside the boiler becomes weaker, the velocity begins to go down. The goal of introducing and using this mechanism is of course to keep the velocity as close as possible to a constant.
- The British astronomer G. Airy was the first scientist to analyze mathematically the regulating system invented by Watt. But the first definitive mathematical description was given only in the works by J.C. Maxwell, in 1868, where some of the erratic behaviors encountered in the steam engine were described and some control mechanisms were proposed

- So far, we have mentioned three main ingredients arising in Control Theory: the notion of feedback, the need of fluctuations, and optimization.
- Wiener defined Cybernetics as “the science of control and communication in animals and machines"

March 11th, 2018