Topics

Linear Regression

In statistics, linear regression is a linear approach to modeling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable... See More

Time Domain

Time domain refers to the analysis of mathematical functions, physical signals or time series of economic or environmental data, with respect to time. In the time domain, the signal or function's value is known for all real numbers, for the case of continuous time, or at various separate instants in the case of discrete time. An oscilloscope is a tool commonly used to visualize real-world signals in the time domain. A time-domain graph shows how a signal changes with time, whereas a frequency... See More

Linearization

In mathematics, linearization is finding the linear approximation to a function at a given point. The linear approximation of a function is the first-order Taylor expansion around the point of interest. In the study of dynamical systems, linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear differential equations or discrete dynamical systems. This method is used in fields such as engineering, physics, economics, and ecology. from... See More

Loop Shaping

Loop shaping is a technique used for designing controllers that operate on linear-time invariant systems. Its name is derived from shaping the magnitude and phase response for the open loop system - that is, shaping the response such that the open loop transfer function has desirable characteristics. See More

Machine Learning

Machine learning (ML) is the study of computer algorithms that improve automatically through experience. It is seen as a subset of artificial intelligence. Machine learning algorithms build a model based on sample data, known as "training data", in order to make predictions or decisions without being explicitly programmed to do so. Machine learning algorithms are used in a wide variety of applications, such as email filtering and computer vision, where it is difficult or unfeasible to develop... See More

Model Predictive Control

Model predictive control (MPC) is an advanced method of process control that is used to control a process while satisfying a set of constraints. It has been in use in the process industries in chemical plants and oil refineries since the 1980s. In recent years it has also been used in power system balancing models and in power electronics. Model predictive controllers rely on dynamic models of the process, most often linear empirical models obtained by system identification. The main advantage... See More

Neural Network

A neural network is a network or circuit of neurons, or in a modern sense, an artificial neural network, composed of artificial neurons or nodes. Thus a neural network is either a biological neural network, made up of real biological neurons, or an artificial neural network, for solving artificial intelligence (AI) problems. The connections of the biological neuron are modeled as weights. A positive weight reflects an excitatory connection, while negative values mean inhibitory connections. All... See More

Minimum Phase Systems

In control theory and signal processing, a linear, time-invariant system is said to be minimum-phase if the system and its inverse are causal and stable. The most general causal LTI transfer function can be uniquely factored into a series of an all-pass and a minimum phase system. The system function is then the product of the two parts, and in the time domain the response of the system is the convolution of the two-part responses. The difference between a minimum phase and a general transfer... See More

Nonlinear Control

Nonlinear Control is a subsection of control that directly targets and compensates for the nonlinear behavior of a system. See More

Categorical Data Fusion

Categorical data fusion is the process of combining categorical sets of data, assuming overlaps of the variables in each set. Most techniques rely on some version of conditional independence assumptions between data sets. See More

Evidence Theory

The theory of belief functions, also referred to as evidence theory or Dempster–Shafer theory ( DST), is a general framework for reasoning with uncertainty, with understood connections to other frameworks such as probability, possibility and imprecise probability theories. First introduced by Arthur P. Dempster in the context of statistical inference, the theory was later developed by Glenn Shafer into a general framework for modeling epistemic uncertainty—a mathematical theory of evidence. The... See More

Band-Stop Filter

In signal processing, a band-stop filter or band-rejection filter is a filter that passes most frequencies unaltered, but attenuates those in a specific range to very low levels. It is the opposite of a band-pass filter. A notch filter is a band-stop filter with a narrow stopband (high Q factor). Narrow notch filters (optical) are used in Raman spectroscopy, live sound reproduction (public address systems, or PA systems) and in instrument amplifiers (especially amplifiers or preamplifiers for... See More

Evidential Reasoning Networks

Evidential Reasoning Networks, more generally known as Valuation Networks, enable Evidence Theory (Dempster-Shafer Theory) to be expanded beyond a single Frame of Discernment --- the set of possibilities over which Dempster-Shafer reasons. They are similar in concept to Bayesian Belief Networks. See More

Transfer Learning

Transfer learning (TL) is a research problem in machine learning (ML) that focuses on storing knowledge gained while solving one problem and applying it to a different but related problem. For example, knowledge gained while learning to recognize cars could apply when trying to recognize trucks. (source: wikipedia) See More

Fuzzy Logic

In logic, fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. By contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1. The term fuzzy logic was introduced with the 1965 proposal of fuzzy set theory by Iranian scientist Lotfi Zadeh. Fuzzy logic had... See More

Nyquist Stability Criterion

In control theory and stability theory, the Nyquist stability criterion or Strecker–Nyquist stability criterion, independently discovered by the German electrical engineer Felix Strecker at Siemens in 1930 and the Swedish-American electrical engineer Harry Nyquist at Bell Telephone Laboratories in 1932, is a graphical technique for determining the stability of a dynamical system. Because it only looks at the Nyquist plot of the open loop systems, it can be applied without explicitly computing... See More

Extremum Seeking Control (ESC)

Extremum seeking control (ESC) is an adaptive control method that seeks the control signal that finds a local maximum for an objective function. The basic idea behind this method is that a system is perturbed with a slowly varying periodic signal and then by observing the output of the system and comparing it to the perturbation signal the gradient of the objective function can be estimated. The gradient is ascended pushing the control signal further in the direction of the local maximum. See More

Constraint Enforcement

Constrain enforcement is the process of ensuring that a system doesn't violate any constraints or limitations that it is subjected to. This is especially important in learning-based control systems where safety metrics like margin can be difficult to quantize and prove. See More

Observability

In control theory, observability is a measure of how well internal states of a system can be inferred from knowledge of its external outputs. The observability and controllability of a linear system are mathematical duals. The concept of observability was introduced by Hungarian-American engineer Rudolf E. Kálmán for linear dynamic systems. A dynamical system designed to estimate the state of a system from measurements of the outputs is called a state observer or simply an observer for that... See More

Process Control

An industrial process control in continuous production processes is a discipline that uses industrial control systems to achieve a production level of consistency, economy and safety which could not be achieved purely by human manual control. It is implemented widely in industries such as automotive, mining, dredging, oil refining, pulp and paper manufacturing, chemical processing and power generating plants. There is a wide range of size, type and complexity, but it enables a small number of... See More

Pole Placement

Full state feedback (FSF), or pole placement, is a method employed in feedback control system theory to place the closed-loop poles of a plant in pre-determined locations in the s-plane. Placing poles is desirable because the location of the poles corresponds directly to the eigenvalues of the system, which control the characteristics of the response of the system. The system must be considered controllable in order to implement this method. from Full State Feedback - Wikipedia See More

Programmable Logic Controller (PLC)

A programmable logic controller (PLC) or programmable controller is an industrial computer that has been ruggedized and adapted for the control of manufacturing processes, such as assembly lines, machines, robotic devices, or any activity that requires high reliability, ease of programming, and process fault diagnosis. Dick Morley is considered as the father of PLC as he had invented the first PLC, the Modicon 084, for General Motors in 1968. PLCs can range from small modular devices with tens... See More

Principal Component Analysis (PCA)

The principal components of a collection of points in a real p-space are a sequence of p direction vectors, where the ith vector is the direction of a line that best fits the data while being orthogonal to the first i-1 vectors. Here, a best-fitting line is defined as one that minimizes the average squared distance from the points to the line. These directions constitute an orthonormal basis in which different individual dimensions of the data are linearly uncorrelated. Principal component... See More

Bayesian Statistics

Bayesian statistics is a theory in the field of statistics based on the Bayesian interpretation of probability where probability expresses a degree of belief in an event. The degree of belief may be based on prior knowledge about the event, such as the results of previous experiments, or on personal beliefs about the event. This differs from a number of other interpretations of probability, such as the frequentist interpretation that views probability as the limit of the relative frequency of an... See More

Reinforcement Learning

Reinforcement learning (RL) is an area of machine learning concerned with how software agents ought to take actions in an environment in order to maximize the notion of cumulative reward. Reinforcement learning is one of three basic machine learning paradigms, alongside supervised learning and unsupervised learning. Reinforcement learning differs from supervised learning in not needing labeled input/output pairs be presented, and in not needing sub-optimal actions to be explicitly corrected... See More