System identificationThe field of system identification uses statistical methods to build mathematical models of dynamical systems from measured data. System identification also includes the optimaldesign of experiments for efficiently generating informative data for fitting such models as well as model reduction.
Stochastic controlStochastic 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.
Design methodsDesign methods are procedures, techniques, aids, or tools for designing. They offer a number of different kinds of activities that a designer might use within an overall design process. Conventional procedures of design, such as drawing, can be regarded as design methods, but since the 1950s new procedures have been developed that are more usually grouped under the name of "design methods".
Robust controlA central theme of control theory is feedback regulation — the design of a feedback controller to achieve stability and a level of performance for a given dynamical system. Tolerance to modeling uncertainty is an essential part of any feedback control scheme, that is, the ability to maintain a satisfactory level of performance when the system dynamics deviate from the nominal value used in the design.
Control theoryControl theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems. The aim 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.Optimization problemIn mathematics, engineering, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete: An optimization problem with discrete variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must be found from a countable set.
Frequency domainIn mathematics, physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency (and possibly phase), rather than time, as in time series. While a time-domain graph shows how a signal changes over time, a frequency-domain graph shows how the signal is distributed within different frequency bands over a range of frequencies.
Physical systemA physical system is a collection of physical objects under study. The collection differs from a set; the objects must coexist and have some physical relationship. In other words, it is a portion of the physical universe chosen for analysis. Everything outside the system is known as the environment, which is ignored except for its effects on the system. The split between system and environment is the analyst's choice, generally made to simplify the analysis.
Discrete Fourier transformFunction in discrete mathematicsDiscrete Fourier Transform of the sum of a sine and a cosine with different frequencies. This plot illustrates how the DFT of a real signal is symmetric around the middle point, and so only half of the transform points are needed to reconstruct the original signal.
Large eddy simulationMathematical model for turbulenceLarge eddy simulation of a turbulent gas velocity field.Large eddy simulation (LES) is a mathematical model for turbulence used in computational fluid dynamics. It was initially proposed in 1963 by Joseph Smagorinsky to simulate atmospheric air currents, and first explored by James Deardorff (1970).Tractor bundleIn conformal geometry, the tractor bundle is a particular vector bundle constructed on a conformal manifold whose fibres form an effective representation of the conformal group (see associated bundle).Newman–Penrose formalismThe Newman–Penrose (NP) formalism is a set of notation developed by Ezra T. Newman and Roger Penrose for general relativity (GR). Their notation is an effort to treat general relativity in terms of spinor notation, which introduces complex forms of the usual variables used in GR. The NP formalism is itself a special case of the tetrad formalism, where the tensors of the theory are projected onto a complete vector basis at each point in spacetime.*As an Amazon Associate I earn from qualifying purchases.