Optimal controlOptimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the moon with minimum fuel expenditure.
Control theoryControl 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. To do this, a controller with the requisite corrective behavior is required.
DiscretizationIn applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers. Dichotomization is the special case of discretization in which the number of discrete classes is 2, which can approximate a continuous variable as a binary variable (creating a dichotomy for modeling purposes, as in binary classification).
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. 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.
Perceptual control theoryPerceptual control theory (PCT) is a model of behavior based on the properties of negative feedback control loops. A control loop maintains a sensed variable at or near a reference value by means of the effects of its outputs upon that variable, as mediated by physical properties of the environment. In engineering control theory, reference values are set by a user outside the system. An example is a thermostat. In a living organism, reference values for controlled perceptual variables are endogenously maintained.
Finite element methodThe finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).
Discrete mathematicsDiscrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions). Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry.
Lagrangian mechanicsIn physics, Lagrangian mechanics is a formulation of classical mechanics founded on the stationary-action principle (also known as the principle of least action). It was introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in his 1788 work, Mécanique analytique. Lagrangian mechanics describes a mechanical system as a pair consisting of a configuration space and a smooth function within that space called a Lagrangian. For many systems, where and are the kinetic and potential energy of the system, respectively.
Lagrangian (field theory)Lagrangian field theory is a formalism in classical field theory. It is the field-theoretic analogue of Lagrangian mechanics. Lagrangian mechanics is used to analyze the motion of a system of discrete particles each with a finite number of degrees of freedom. Lagrangian field theory applies to continua and fields, which have an infinite number of degrees of freedom.
Inertial navigation systemAn inertial navigation system (INS) is a navigation device that uses motion sensors (accelerometers), rotation sensors (gyroscopes) and a computer to continuously calculate by dead reckoning the position, the orientation, and the velocity (direction and speed of movement) of a moving object without the need for external references. Often the inertial sensors are supplemented by a barometric altimeter and sometimes by magnetic sensors (magnetometers) and/or speed measuring devices.
Inertial frame of referenceIn classical physics and special relativity, an inertial frame of reference (also called inertial space, or Galilean reference frame) is a frame of reference not undergoing any acceleration. It is a frame in which an isolated physical object—an object with zero net force acting on it—is perceived to move with a constant velocity or, equivalently, it is a frame of reference in which Newton's first law of motion holds.
Inertial measurement unitAn inertial measurement unit (IMU) is an electronic device that measures and reports a body's specific force, angular rate, and sometimes the orientation of the body, using a combination of accelerometers, gyroscopes, and sometimes magnetometers. When the magnetometer is included, IMUs are referred to as IMMUs. IMUs are typically used to maneuver modern vehicles including motorcycles, missiles, aircraft (an attitude and heading reference system), including unmanned aerial vehicles (UAVs), among many others, and spacecraft, including satellites and landers.
Lagrangian systemIn mathematics, a Lagrangian system is a pair (Y, L), consisting of a smooth fiber bundle Y → X and a Lagrangian density L, which yields the Euler–Lagrange differential operator acting on sections of Y → X. In classical mechanics, many dynamical systems are Lagrangian systems. The configuration space of such a Lagrangian system is a fiber bundle Q → R over the time axis R. In particular, Q = R × M if a reference frame is fixed. In classical field theory, all field systems are the Lagrangian ones.
Euler methodIn mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).
Explicit and implicit methodsExplicit and implicit methods are approaches used in numerical analysis for obtaining numerical approximations to the solutions of time-dependent ordinary and partial differential equations, as is required in computer simulations of physical processes. Explicit methods calculate the state of a system at a later time from the state of the system at the current time, while implicit methods find a solution by solving an equation involving both the current state of the system and the later one.
Marcos ChamúdezMarcos Chamúdez Reitich, also known as Marcos Chamudes (16 January 1907 – 25 June 1989) was a Chilean politician, photographer and journalist. Marcos Chamúdez Reitich was born in Santiago on January 16, 1907, into a family of Sephardic Jews, son of Oscar Chamúdez and María Reitich, who arrived in Moisesville (the first Argentine colony of Russian Jewish immigrants) before settling in Chile. He studied at the National Institute and at the Barros Arana National Board (INBA).
Marco EvaristtiMarco Evaristti (born 1963) is a Chilean artist who has lived in Denmark since the 1980s. While a trained and practicing architect, he is best known for hosting a dinner party where the main course was agnolotti pasta that was topped with a meatball made with his own fat, removed earlier in the year in a liposuction operation. Though raised a Catholic, in his teenage years Evaristti found out he was born to a Jewish mother, which some account for the philosophical and religious themes in his work.
Measure for Measure (1943 film)Measure for Measure (Dente per dente, literally "A tooth for a tooth") is a 1943 Italian historical drama film directed by Marco Elter and starring Carlo Tamberlani, Caterina Boratto and Nelly Corradi. It is based on the William Shakespeare's play of the same name. Carlo Tamberlani as Angelo Caterina Boratto as Isabella Nelly Corradi as Marianna Loredana as Giulietta Memo Benassi as Lucio Osvaldo Genazzani as Claudio Alfredo Varelli as Vincenzo Cesco Baseggio as Schiumetta Lamberto Picasso as La Scala Ameli
Jeju languageJeju (Jeju: 제줏말; Jeju RR: , or , or ), often called Jejueo or Jejuan in English-language scholarship, is a Koreanic language originally from Jeju Island, South Korea. It is not mutually intelligible with mainland Korean dialects. While it was historically considered a divergent Jeju dialect of the Korean language, it is increasingly referred to as a language. It is declining in usage, and was classified by UNESCO in 2010 as critically endangered, the highest level of language endangerment possible.
Korean languageKorean (South Korean: , hangugeo; North Korean: , chosŏnmal) is the native language for about 80 million people, mostly of Korean descent. It is the official and national language of both North Korea and South Korea (geographically Korea). The two countries have established standardized norms for Korean, and the differences between them are similar to those between Standard Chinese in mainland China and Taiwan, but political conflicts between the two countries have highlighted the differences between them.
