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Hybrid System
A hybrid system is a dynamical system that exhibits both continuous and discrete dynamic behavior – a system that can both ''flow'' (described by a differential equation) and ''jump'' (described by a state machine or automaton). 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 general, the ''state'' of a hybrid system is defined by the values of the ''continuous variables'' and a discrete ''mode''. The state changes either continuously, according to a flow condition, or discretely according to a ''control graph''. Continuous flow is permitted as long as so-called ''invariants'' hold, while discrete transitions can occur as soon as given ''jump conditions'' are satisfied. Discrete transi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamical System
In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, fluid dynamics, the flow of water in a pipe, the Brownian motion, random motion of particles in the air, and population dynamics, 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 number, 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 (mathematics), set, without the need of a Differentiability, smooth space-time structure defined on it. At any given time, a dynamical system has a State ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hybrid Automaton
In automata theory, a hybrid automaton (plural: ''hybrid automata'' or ''hybrid automatons'') is a mathematical model for precisely describing hybrid systems, for instance systems in which digital computational processes interact with analog physical processes. A hybrid automaton is a finite state machine with a finite set of continuous variables whose values are described by a set of ordinary differential equations. This combined specification of discrete and continuous behaviors enables dynamic systems that comprise both digital and analog components to be modeled and analyzed. Examples A simple example is a room-thermostat-heater system where the temperature of the room evolves according to laws of thermodynamics and the state of the heater (on/off); the thermostat senses the temperature, performs certain computations and turns the heater on and off. In general, hybrid automata have been used to model and analyze a variety of embedded systems including vehicle control systems, air ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variable Structure Control
Variable structure control (VSC) is a form of discontinuous nonlinear control. The method alters the dynamics of a nonlinear system by application of a high-frequency ''switching control''. The state- feedback control law is ''not'' a continuous function of time; it ''switches'' from one smooth condition to another. So the ''structure'' of the control law ''varies'' based on the position of the state trajectory; the method switches from one smooth control law to another and possibly very fast speeds (e.g., for a countably infinite number of times in a finite time interval). VSC and associated sliding mode behaviour was first investigated in early 1950s in the Soviet Union by Emelyanov and several coresearchers. The main mode of VSC operation is sliding mode control (SMC). The strengths of SMC include: * Low sensitivity to plant parameter uncertainty * Greatly reduced-order modeling of plant dynamics * Finite-time convergence (due to discontinuous control law) The weaknesses of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variable Structure System
A variable structure system, or VSS, is a discontinuous nonlinear system of the form :\dot = \varphi( \mathbf, t ) where \mathbf \triangleq _1, x_2, \ldots, x_n \in \mathbb^n is the state vector, t \in \mathbb is the time variable, and \varphi(\mathbf,t) \triangleq \varphi_1(\mathbf,t), \varphi_2(\mathbf,t), \ldots, \varphi_n(\mathbf,t) : \mathbb^ \mapsto \mathbb^n is a ''piecewise continuous'' function. Due to the ''piecewise'' continuity of these systems, they behave like different continuous nonlinear systems in different regions of their state space. At the boundaries of these regions, their dynamics switch abruptly. Hence, their ''structure'' ''varies'' over different parts of their state space. The development of variable structure control depends upon methods of analyzing variable structure systems, which are special cases of hybrid dynamical systems. See also *Variable structure control *Sliding mode control *Hybrid system *Nonlinear control *Robust control *Optimal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sliding Mode Control
In control systems, sliding mode control (SMC) is a nonlinear control method that alters the dynamics of a nonlinear system by applying a discontinuous control signal (or more rigorously, a set-valued control signal) that forces the system to "slide" along a cross-section of the system's normal behavior. The state-feedback control law is not a continuous function of time. Instead, it can switch from one continuous structure to another based on the current position in the state space. Hence, sliding mode control is a variable structure control method. The multiple control structures are designed so that trajectories always move toward an adjacent region with a different control structure, and so the ultimate trajectory will not exist entirely within one control structure. Instead, it will ''slide'' along the boundaries of the control structures. The motion of the system as it slides along these boundaries is called a ''sliding mode'' and the geometrical locus consisting of the boun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hybrid Automaton
In automata theory, a hybrid automaton (plural: ''hybrid automata'' or ''hybrid automatons'') is a mathematical model for precisely describing hybrid systems, for instance systems in which digital computational processes interact with analog physical processes. A hybrid automaton is a finite state machine with a finite set of continuous variables whose values are described by a set of ordinary differential equations. This combined specification of discrete and continuous behaviors enables dynamic systems that comprise both digital and analog components to be modeled and analyzed. Examples A simple example is a room-thermostat-heater system where the temperature of the room evolves according to laws of thermodynamics and the state of the heater (on/off); the thermostat senses the temperature, performs certain computations and turns the heater on and off. In general, hybrid automata have been used to model and analyze a variety of embedded systems including vehicle control systems, air ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Controller Synthesis
Controller may refer to: Occupations * Controller or financial controller, or in government accounting comptroller, a senior accounting position * Controller, someone who performs agent handling in espionage * Air traffic controller, a person who directs aircraft Computing and electronics * Model–view–controller, an architectural pattern used in software engineering * Controller (computing) (other) * Microcontroller, a small computer on a single integrated circuit * Game controller, an input device used for playing video games Control engineering * Control theory, control of continuously operating dynamical systems in engineered processes and machines ** Irrigation controller, a device to automate irrigation systems ** PID controller, a control loop feedback mechanism * Control loop, contains all the control elements for controlling a process variable ** Anti-lock brake controller, in an anti-lock braking system * Industrial control system, a general term used ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automated Theorem Proving
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major impetus for the development of computer science. Logical foundations While the roots of formalised logic go back to Aristotle, the end of the 19th and early 20th centuries saw the development of modern logic and formalised mathematics. Frege's ''Begriffsschrift'' (1879) introduced both a complete propositional calculus and what is essentially modern predicate logic. His ''Foundations of Arithmetic'', published 1884, expressed (parts of) mathematics in formal logic. This approach was continued by Russell and Whitehead in their influential ''Principia Mathematica'', first published 1910–1913, and with a revised second edition in 1927. Russell and Whitehead thought they could derive all mathematical truth using axioms and inference ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simulink
Simulink is a MATLAB-based graphical programming environment for modeling, simulating and analyzing multidomain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block libraries. It offers tight integration with the rest of the MATLAB environment and can either drive MATLAB or be scripted from it. Simulink is widely used in automatic control and digital signal processing for multidomain simulation and model-based design. Add-on products MathWorks and other third-party hardware and software products can be used with Simulink. For example, Stateflow extends Simulink with a design environment for developing state machines and flow charts. MathWorks claims that, coupled with another of their products, Simulink can automatically generate C source code for real-time implementation of systems. As the efficiency and flexibility of the code improves, this is becoming more widely adopted for production systems, in addition to bein ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities. An additional package, Simulink, adds graphical multi-domain simulation and model-based design for dynamic and embedded systems. As of 2020, MATLAB has more than 4 million users worldwide. They come from various backgrounds of engineering, science, and economics. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was based on his 1960s PhD thesis. Moler became a math professor at the University of New Mexico and starte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
DEVS
''Devs'' is an American science fiction thriller television miniseries created, written, and directed by Alex Garland. It premiered on March 5, 2020, on FX on Hulu. Lily Chan (Sonoya Mizuno) is a software engineer for Amaya, a quantum computing company run by Forest (Nick Offerman). Lily soon becomes embroiled in the mysterious death of her boyfriend, who died on the first day of his new job at Devs. The series explores themes related to free will and determinism, as well as Silicon Valley. It received generally positive reviews, with critics praising its imagination, cinematography, acting, and soundtrack. Cast and characters Main * Sonoya Mizuno as Lily Chan, a software engineer at Amaya * Nick Offerman as Forest, CEO of Amaya * Jin Ha as Jamie, a cybersecurity specialist and Lily's ex-boyfriend * Zach Grenier as Kenton, head of security at Amaya * Stephen McKinley Henderson as Stewart, a member of the Devs team at Amaya * Cailee Spaeny as Lyndon, a member of the Devs team spe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
