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Hybrid Dynamical 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, automaton, or a difference equation). Often, the term "hybrid dynamical system" is used instead of "hybrid system", to distinguish from other usages of "hybrid system", such as the combination neural nets and fuzzy logic, or of 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 o ... [...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, such as in a parametric curve. 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, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use Conditional (computer programming), conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). In contrast, a Heuristic (computer science), heuristic is an approach to solving problems without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variable Structure System
A variable structure system, or VSS, is a Classification of discontinuities, discontinuous nonlinear system of the form :\dot = \varphi( \mathbf, t ) where \mathbf \triangleq [x_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 (controls), state space. At the boundaries of these regions, their dynamic system, 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 system, hybrid dynamical systems. See also *Variable struc ... [...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 dynamic system, 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 space (controls), 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 g ... [...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 use ... [...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 motivating factor for the development of computer science. Logical foundations While the roots of formalized Logicism, logic go back to Aristotelian logic, Aristotle, the end of the 19th and early 20th centuries saw the development of modern logic and formalized mathematics. Gottlob Frege, Frege's ''Begriffsschrift'' (1879) introduced both a complete propositional logic, propositional calculus and what is essentially modern predicate logic. His ''The Foundations of Arithmetic, Foundations of Arithmetic'', published in 1884, expressed (parts of) mathematics in formal logic. This approach was continued by Bertrand Russell, Russell and Alfred North Whitehead, Whitehead in their influential ''Principia Mathematica'', first published 1910� ... [...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. 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 being a tool for ... [...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. , MATLAB has more than four million users worldwide. They come from various backgrounds of engineering, science, and economics. , more than 5000 global colleges and universities use MATLAB to support instruction and research. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was base ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PowerDEVS
PowerDEVS is a general purpose software tool for DEVS modeling and simulation oriented to the simulation of hybrid systems. The environment allows defining atomic DEVS models in C++ language that can be then graphically coupled in hierarchical block diagrams to create more complex systems. It is developed at Universidad Nacional de Rosario (Argentina Argentina, officially the Argentine Republic, is a country in the southern half of South America. It covers an area of , making it the List of South American countries by area, second-largest country in South America after Brazil, the fourt ...) by Ernesto Kofman, Federico Bergero, Gustavo Migoni, Enrique Hansen, Joaquín Fernandez, Marcelo Lapadula and Esteban Pagliero. The distribution is totally free. References * K06 * eigler76 * K11{{cite news, author1=Bergero, Federico , author2=Kofman, Ernesto , name-list-style=amp , year = 2011, title = PowerDEVS: a tool for hybrid system modeling and real-time simulation, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
DEVS
DEVS, abbreviating Discrete Event System Specification, is a modular and hierarchical formalism for modeling and analyzing general systems that can be discrete event systems which might be described by state transition tables, and continuous state systems which might be described by differential equations, and hybrid continuous state and discrete event systems. DEVS is a timed event system. History DEVS is a formalism for modeling and analysis of discrete event systems (DESs). The DEVS formalism was invented by Bernard P. Zeigler, who is emeritus professor at the University of Arizona. DEVS was introduced to the public in Zeigler's first book, ''Theory of Modeling and Simulation'' in 1976, while Zeigler was an associate professor at University of Michigan. DEVS can be seen as an extension of the Moore machine formalism,automata were the mathematical models of Dr. Zeigler's Ph.D. thesis which is a finite state automaton where the outputs are determined by the current state alone (a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hybrid Bond Graph
A hybrid bond graph is a graphical description of a physical dynamic system 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 ... with discontinuities (i.e., a hybrid dynamical system). Similar to a regular bond graph, it is an energy-based technique. However, it allows instantaneous switching of the junction structure, which may violate the principle of continuity of power (Mosterman and Biswas, 1998). References * Pieter Mosterman and Gautam Biswas, 1998: "A Theory of Discontinuities in Physical System Models" in ''Journal of the Franklin Institute'', Volume 335B, Number 3, pp. 401-439, January, 1998. Further reading * Pieter Mosterman, 2001: "HyBrSim - A Modeling and Simulation Environment for Hybrid Bond Graphs" in ''Journal of Systems and Control Engineering'', vol. 21 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
