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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.
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a set, without the need of a smooth space-time structure defined on it.
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.
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists since most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems.
Armand Borel was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993. He worked in algebraic topology, in the theory of Lie groups, and was one of the creators of the contemporary theory of linear algebraic groups.
A hybrid system is a dynamical system that exhibits both continuous and discrete dynamic behavior – a system that can both flow and jump. Often, the term "hybrid dynamical system" is used, to distinguish over hybrid systems such as those that combine neural nets and fuzzy logic, or electrical and mechanical drivelines. A hybrid system has the benefit of encompassing a larger class of systems within its structure, allowing for more flexibility in modeling dynamic phenomena.
In mathematics, a Bézout matrix is a special square matrix associated with two polynomials, introduced by James Joseph Sylvester (1853) and Arthur Cayley (1857) and named after Étienne Bézout. Bézoutian may also refer to the determinant of this matrix, which is equal to the resultant of the two polynomials. Bézout matrices are sometimes used to test the stability of a given polynomial.
Jacob Theodore "Jack" Schwartz was an American mathematician, computer scientist, and professor of computer science at the New York University Courant Institute of Mathematical Sciences. He was the designer of the SETL programming language and started the NYU Ultracomputer project. He founded the New York University Department of Computer Science, chairing it from 1964 to 1980.
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 mathematics, the concept of graph dynamical systems can be used to capture a wide range of processes taking place on graphs or networks. A major theme in the mathematical and computational analysis of GDSs is to relate their structural properties and the global dynamics that result.
Sergio Albeverio is a Swiss mathematician and mathematical physicist working in numerous fields of mathematics and its applications. In particular he is known for his work in probability theory, analysis, mathematical physics, and in the areas algebra, geometry, number theory, as well as in applications, from natural to social-economic sciences.
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.
Institute of Mathematics of the National Academy of Sciences of Ukraine is a government-owned research institute in Ukraine that carries out basic research and trains highly qualified professionals in the field of mathematics. It was founded on 13 February 1934.
The following outline is provided as an overview of and topical guide to control engineering:
Jürgen Jost is a German mathematician specializing in geometry. He has been a director of the Max Planck Institute for Mathematics in the Sciences in Leipzig since 1996.
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.
Igor Dmitrievich Chueshov was a Ukrainian mathematician. He was both a correspondent member of the Mathematics section of the National Academy of Sciences of Ukraine and a professor in the Department of Mathematical Physics and Computational Mathematics at the National University of Kharkiv.
Tetsuji Miwa is a Japanese mathematician, specializing in mathematical physics.
Hans-Wilhelm Knobloch was a German mathematician, specializing in dynamical systems and control theory. Although the field of mathematical systems and control theory was already well-established in several other countries, Hans-Wilhelm Knobloch and Diederich Hinrichsen were the two mathematicians of most importance in establishing this field in Germany.
References
- ↑ Zum Tod von Prof. Dr. Heinz Bauer
- ↑ Institut für Dynamische Systeme Archived 2007-02-08 at the Wayback Machine
- ↑ "Professors in Madrid". Archived from the original on 2007-04-06. Retrieved 2007-03-23.
