control theory
In plain wordsThe mathematics of making machines behave as intended by constantly measuring what they are doing and correcting them, as a thermostat, cruise control or self-balancing robot does.
The mathematics and engineering of steering dynamical systems — machines, vehicles, chemical processes, power grids, robots — by choosing their inputs so that their outputs track a desired reference despite disturbances and modeling errors. Its central idea is feedback: a controller compares measurements with the goal and adjusts its inputs continuously (closed-loop control), whereas open-loop control applies a precomputed input without checking the result. Classical control analyzes linear single-input, single-output systems in the frequency domain (transfer functions, Bode and Nyquist plots, gain and phase margins) and yields the PID controllerPID controller, n.: The most common automatic controller in industry. It corrects a machine using three ingredients: how far off it is now, how long it has been off, and how fast the error is changing.. Modern control uses state-space models, controllability and observability, optimal controloptimal control, n.: Finding the best way to steer a system over time, such as the most fuel-efficient path for a rocket or the smoothest motion for a robot arm, by minimizing a cost while obeying the laws of motion. such as the linear-quadratic regulator, the Kalman filterKalman filter, n.: A method that keeps a running best guess of something you cannot measure exactly, such as a vehicle's position, by blending predictions from a motion model with noisy sensor readings. for estimation, and model predictive controlmodel predictive control, n.: A control method that repeatedly plans the best moves a few seconds ahead using a model of the machine, carries out only the first move, then plans again with fresh measurements.; robust and adaptive control handle uncertainty. Stability, meaning that errors die out rather than grow, is the core requirement. Reinforcement learningreinforcement learning, n.: A way of teaching a computer program by trial and error: it tries actions, earns points for good results and penalties for bad ones, and gradually learns which choices pay off over time. tackles the same problem of choosing actions over time, usually without an explicit model, and the two fields share the Bellman equationBellman equation, n.: A rule saying that how good a situation is equals the reward you get now plus how good the next situation is, slightly discounted — so long-term planning can be solved one step at a time..
The learned policy looked great in simulation, but control theory showed it had no stability margin.
Origin
James Clerk Maxwell's 1868 analysis of steam-engine governors, 'On Governors', is usually taken as the founding paper. Edward Routh (1874) and Aleksandr Lyapunov (1892) developed stability theory, Harry Nyquist (1932) and Hendrik Bode feedback-amplifier methods, and Rudolf Kálmán (1960) state-space theory; Norbert Wiener's cyberneticscybernetics, n.: The study of how animals, machines and organizations steer themselves using feedback: sensing the result of an action and correcting course. It was both a parent and an early rival of AI. (1948) linked control with communication and biology.
Usage note
Not to be confused with AI controlAI control, n.: Safety measures meant to stop a powerful AI from causing serious harm even if it is secretly working against us — like bank security, which assumes some insiders may be dishonest. in AI safety, which means safeguards that keep a possibly misaligned AI system from causing harm even if it tries. In robotics a 'controller' is the algorithm, not a handheld device.
Related
- PID controllerPID controller, n.: The most common automatic controller in industry. It corrects a machine using three ingredients: how far off it is now, how long it has been off, and how fast the error is changing.
- model predictive controlmodel predictive control, n.: A control method that repeatedly plans the best moves a few seconds ahead using a model of the machine, carries out only the first move, then plans again with fresh measurements.
- optimal controloptimal control, n.: Finding the best way to steer a system over time, such as the most fuel-efficient path for a rocket or the smoothest motion for a robot arm, by minimizing a cost while obeying the laws of motion.
- Kalman filterKalman filter, n.: A method that keeps a running best guess of something you cannot measure exactly, such as a vehicle's position, by blending predictions from a motion model with noisy sensor readings.
- reinforcement learningreinforcement learning, n.: A way of teaching a computer program by trial and error: it tries actions, earns points for good results and penalties for bad ones, and gradually learns which choices pay off over time.
- cyberneticscybernetics, n.: The study of how animals, machines and organizations steer themselves using feedback: sensing the result of an action and correcting course. It was both a parent and an early rival of AI.
- impedance controlimpedance control, n.: A way of controlling a robot so that it behaves like a spring and shock absorber when it touches things, giving way gently instead of pushing rigidly.
- reinforcement learningreinforcement learning, n.: A way of teaching a computer program by trial and error: it tries actions, earns points for good results and penalties for bad ones, and gradually learns which choices pay off over time.
- AI controlAI control, n.: Safety measures meant to stop a powerful AI from causing serious harm even if it is secretly working against us — like bank security, which assumes some insiders may be dishonest.
Sources
- Maxwell, J. C. (1868). On governors. Proceedings of the Royal Society of London 16, 270–283.
- Åström, K. J. & Murray, R. M. (2008). Feedback Systems: An Introduction for Scientists and Engineers. Princeton University Press.
Mentioned in
robotrobot, n.: A machine that senses its surroundings, decides what to do and physically acts, moving itself or handling objects, with some independence from a human operator. Factory arms, robot vacuums and self-driving cars are all robots., roboticsrobotics, n.: The science and engineering of building robots and making them work: designing their bodies, sensors and motors, and writing the software that lets them see, plan and move safely., feedback loopfeedback loop, n.: A cycle in which what a system produces comes back to shape its own future input, like a microphone howling near its loudspeaker. In AI, a model's predictions can shape the very data it later learns from., Kalman filterKalman filter, n.: A method that keeps a running best guess of something you cannot measure exactly, such as a vehicle's position, by blending predictions from a motion model with noisy sensor readings., model predictive controlmodel predictive control, n.: A control method that repeatedly plans the best moves a few seconds ahead using a model of the machine, carries out only the first move, then plans again with fresh measurements., PID controllerPID controller, n.: The most common automatic controller in industry. It corrects a machine using three ingredients: how far off it is now, how long it has been off, and how fast the error is changing., robot learningrobot learning, n.: Teaching robots skills from data and experience, such as watching demonstrations, practicing by trial and error or training in simulation, instead of programming every movement by hand., impedance controlimpedance control, n.: A way of controlling a robot so that it behaves like a spring and shock absorber when it touches things, giving way gently instead of pushing rigidly., optimal controloptimal control, n.: Finding the best way to steer a system over time, such as the most fuel-efficient path for a rocket or the smoothest motion for a robot arm, by minimizing a cost while obeying the laws of motion., trajectory optimizationtrajectory optimization, n.: Calculating the best way for a robot to move over time, choosing exact positions, speeds and forces moment by moment so the motion is smooth, fast or energy-efficient and avoids obstacles., zero moment pointzero moment point, n.: The spot on the ground beneath a walking robot where the floor's push balances out; keeping it inside the area under the robot's feet stops the robot from tipping over.