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Control theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any delay, overshoot, or steady-state error and ensuring a level of control stability; often with the aim to achieve a degree of optimality.
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing signals, such as sound, images, potential fields, seismic signals, altimetry processing, and scientific measurements. Signal processing techniques are used to optimize transmissions, digital storage efficiency, correcting distorted signals, subjective video quality, and to also detect or pinpoint components of interest in a measured signal.
Hendrik Wade Bode was an American engineer, researcher, inventor, author and scientist, of Dutch ancestry. As a pioneer of modern control theory and electronic telecommunications he revolutionized both the content and methodology of his chosen fields of research. His synergy with Claude Shannon, the father of information theory, laid the foundations for the technological convergence of the information age.
Stochastic control or stochastic optimal control is a sub field of control theory that deals with the existence of uncertainty either in observations or in the noise that drives the evolution of the system. The system designer assumes, in a Bayesian probability-driven fashion, that random noise with known probability distribution affects the evolution and observation of the state variables. Stochastic control aims to design the time path of the controlled variables that performs the desired control task with minimum cost, somehow defined, despite the presence of this noise. The context may be either discrete time or continuous time.
Yu-Chi "Larry" Ho is a Chinese-American mathematician, control theorist, and a professor at the School of Engineering and Applied Sciences, Harvard University.
Mustafa Tamer Başar is a control and game theorist who is the Swanlund Endowed Chair and Center for Advanced Study Professor of Electrical and Computer Engineering at the University of Illinois at Urbana-Champaign, USA. He is also the Director of the Center for Advanced Study.
Michael Athans was a Greek-American control theorist and a Professor Emeritus in the Department of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology. He was a Fellow of the IEEE (1973) and a Fellow of the AAAS (1977). He was the recipient of numerous awards for his contributions in the field of control theory. A pioneer in the field of control theory, he helped shape modern control theory and spearheaded the field of multivariable control system design and the field of robust control. Athans was a member of the technical staff at Lincoln Laboratory from 1961 to 1964, and a Department of Electrical Engineering and Computer Science faculty member from 1964 to 1998. Upon retirement, Athans moved to Lisbon, Portugal, where he was an Invited Research Professor in the Institute for Systems and Robotics, Instituto Superior Técnico where he received a honoris causa doctorate from the Universidade Técnica de Lisboa in 2011.
In game theory, differential games are a group of problems related to the modeling and analysis of conflict in the context of a dynamical system. More specifically, a state variable or variables evolve over time according to a differential equation. Early analyses reflected military interests, considering two actors—the pursuer and the evader—with diametrically opposed goals. More recent analyses have reflected engineering or economic considerations.
Miroslav Krstić is an American control theorist and Distinguished Professor of Mechanical and Aerospace Engineering at the University of California, San Diego (UCSD). Krstić is also the director of the Center for Control Systems and Dynamics at UCSD and a Senior Associate Vice Chancellor for Research. In the list of eminent researchers in systems and control, he is the youngest.
Jan Hendrik van Schuppen is a Dutch mathematician and Professor at the Department of Mathematics of the Vrije Universiteit, known for his contributions in the field of systems theory, particularly on control theory and system identification, on probability, and on a number of related practical applications.
Dimitri Panteli Bertsekas is an applied mathematician, electrical engineer, and computer scientist, a McAfee Professor at the Department of Electrical Engineering and Computer Science in School of Engineering at the Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts, and also a Fulton Professor of Computational Decision Making at Arizona State University, Tempe.
Dragoslav D. Šiljak is professor emeritus of Electrical Engineering at Santa Clara University, where he held the title of Benjamin and Mae Swig University Professor. He is best known for developing the mathematical theory and methods for control of complex dynamic systems characterized by large-scale, information structure constraints and uncertainty.
Mean-field game theory is the study of strategic decision making by small interacting agents in very large populations. It lies at the intersection of game theory with stochastic analysis and control theory. The use of the term "mean field" is inspired by mean-field theory in physics, which considers the behavior of systems of large numbers of particles where individual particles have negligible impacts upon the system. In other words, each agent acts according to his minimization or maximization problem taking into account other agents’ decisions and because their population is large we can assume the number of agents goes to infinity and a representative agent exists.
In probability theory, a McKean–Vlasov process is a stochastic process described by a stochastic differential equation where the coefficients of the diffusion depend on the distribution of the solution itself. The equations are a model for Vlasov equation and were first studied by Henry McKean in 1966. It is an example of propagation of chaos, in that it can be obtained as a limit of a mean-field system of interacting particles: as the number of particles tends to infinity, the interactions between any single particle and the rest of the pool will only depend on the particle itself.
Mean-field particle methods are a broad class of interacting type Monte Carlo algorithms for simulating from a sequence of probability distributions satisfying a nonlinear evolution equation. These flows of probability measures can always be interpreted as the distributions of the random states of a Markov process whose transition probabilities depends on the distributions of the current random states. A natural way to simulate these sophisticated nonlinear Markov processes is to sample a large number of copies of the process, replacing in the evolution equation the unknown distributions of the random states by the sampled empirical measures. In contrast with traditional Monte Carlo and Markov chain Monte Carlo methods these mean-field particle techniques rely on sequential interacting samples. The terminology mean-field reflects the fact that each of the samples interacts with the empirical measures of the process. When the size of the system tends to infinity, these random empirical measures converge to the deterministic distribution of the random states of the nonlinear Markov chain, so that the statistical interaction between particles vanishes. In other words, starting with a chaotic configuration based on independent copies of initial state of the nonlinear Markov chain model, the chaos propagates at any time horizon as the size the system tends to infinity; that is, finite blocks of particles reduces to independent copies of the nonlinear Markov process. This result is called the propagation of chaos property. The terminology "propagation of chaos" originated with the work of Mark Kac in 1976 on a colliding mean-field kinetic gas model.
Arthur James Krener is an American mathematician. He is a distinguished visiting professor in the department of applied mathematics at the Naval Postgraduate School. He has made contributions in the areas of control theory, nonlinear control, and stochastic processes.
Bruce Edward Hajek is a Professor in the Coordinated Science Laboratory, the head of the Department of Electrical and Computer Engineering, and the Leonard C. and Mary Lou Hoeft Chair in Engineering at the University of Illinois Urbana–Champaign. He does research in communication networking, auction theory, stochastic analysis, combinatorial optimization, machine learning, information theory, and bioinformatics.
Ji-Feng Zhang was born in Shandong, China. He is currently the vice-chair of the technical board of the International Federation of Automatic Control (IFAC), the vice-president of the Systems Engineering Society of China (SESC), the vice-president of the Chinese Association of Automation (CAA), the chair of the technical committee on Control Theory (CAA), and the editor-in-chief for both All About Systems and Control and the Journal of Systems Science and Mathematical Sciences.
Jürgen Gärtner is a German mathematician, specializing in probability theory and analysis.
Walter Murray Wonham was a Canadian control theorist and professor at the University of Toronto. He focused on multi-variable geometric control theory, stochastic control and stochastic filters, and the control of discrete event systems from the standpoint of mathematical logic and formal languages.
References
- ↑ "Bode Lecture Prize". IEEE.
- ↑ M.Y. Huang, R.P. Malhame and P.E. Caines, "Large Population Stochastic Dynamic Games: Closed-Loop McKean–Vlasov Systems and the Nash Certainty Equivalence Principle," Special issue in honor of the 65th birthday of Tyrone Duncan, Communications in Information and Systems. Vol 6, Number 3, 2006, pp 221–252.
