Hybrid system, the Glossary
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).[1]
Table of Contents
37 relations: Abstract model checking, Algorithm, Automata theory, Automated theorem proving, Barrier certificate, Behavior tree (artificial intelligence, robotics and control), Bouncing ball, C++, Control theory, Cyber–physical system, DEVS, Differential equation, Differential-algebraic system of equations, Dynamical system, Finite-state machine, Flow (mathematics), Formal verification, Fuzzy logic, Hybrid automaton, Hybrid bond graph, Inelastic collision, Internet, Joint spectral radius, Jump diffusion, Jump process, MATLAB, Neural network (machine learning), Petri net, Physical system, Piecewise-deterministic Markov process, PowerDEVS, Probability, Simulink, Sliding mode control, Variable structure control, Variable structure system, Zeno of Elea.
Abstract model checking
In computer science and in mathematics, abstraction model checking is a form of model checking for systems where an actual representation is too complex in developing the model alone.
See Hybrid system and Abstract model checking
Algorithm
In mathematics and computer science, an algorithm is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation.
See Hybrid system and Algorithm
Automata theory
Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them.
See Hybrid system and Automata theory
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.
See Hybrid system and Automated theorem proving
Barrier certificate
A barrier certificate or barrier function is used to prove that a given region is forward invariant for a given ordinary differential equation or hybrid dynamical system. Hybrid system and barrier certificate are differential equations.
See Hybrid system and Barrier certificate
Behavior tree (artificial intelligence, robotics and control)
A behavior tree is a mathematical model of plan execution used in computer science, robotics, control systems and video games.
See Hybrid system and Behavior tree (artificial intelligence, robotics and control)
Bouncing ball
The physics of a bouncing ball concerns the physical behaviour of bouncing balls, particularly its motion before, during, and after impact against the surface of another body. Hybrid system and bouncing ball are dynamical systems.
See Hybrid system and Bouncing ball
C++
C++ (pronounced "C plus plus" and sometimes abbreviated as CPP) is a high-level, general-purpose programming language created by Danish computer scientist Bjarne Stroustrup.
Control theory
Control theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems in engineered processes and machines. Hybrid system and control theory are dynamical systems.
See Hybrid system and Control theory
Cyber–physical system
Cyber-Physical Systems (CPS) are integrations of computation with physical processes. Hybrid system and Cyber–physical system are systems theory.
See Hybrid system and Cyber–physical system
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.
Differential equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. Hybrid system and differential equation are differential equations.
See Hybrid system and Differential equation
Differential-algebraic system of equations
In mathematics, a differential-algebraic system of equations (DAE) is a system of equations that either contains differential equations and algebraic equations, or is equivalent to such a system. Hybrid system and differential-algebraic system of equations are differential equations.
See Hybrid system and Differential-algebraic system of equations
Dynamical 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. Hybrid system and dynamical system are dynamical systems and systems theory.
See Hybrid system and Dynamical system
Finite-state machine
A finite-state machine (FSM) or finite-state automaton (FSA, plural: automata), finite automaton, or simply a state machine, is a mathematical model of computation.
See Hybrid system and Finite-state machine
Flow (mathematics)
In mathematics, a flow formalizes the idea of the motion of particles in a fluid. Hybrid system and flow (mathematics) are dynamical systems.
See Hybrid system and Flow (mathematics)
Formal verification
In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of a system with respect to a certain formal specification or property, using formal methods of mathematics.
See Hybrid system and Formal verification
Fuzzy 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.
See Hybrid system and Fuzzy logic
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. Hybrid system and hybrid automaton are differential equations.
See Hybrid system and Hybrid automaton
Hybrid bond graph
A hybrid bond graph is a graphical description of a physical dynamic system with discontinuities (i.e., a hybrid dynamical system). Hybrid system and hybrid bond graph are dynamical systems.
See Hybrid system and Hybrid bond graph
Inelastic collision
An inelastic collision, in contrast to an elastic collision, is a collision in which kinetic energy is not conserved due to the action of internal friction.
See Hybrid system and Inelastic collision
Internet
The Internet (or internet) is the global system of interconnected computer networks that uses the Internet protocol suite (TCP/IP) to communicate between networks and devices.
See Hybrid system and Internet
Joint spectral radius
In mathematics, the joint spectral radius is a generalization of the classical notion of spectral radius of a matrix, to sets of matrices. Hybrid system and joint spectral radius are control theory.
See Hybrid system and Joint spectral radius
Jump diffusion
Jump diffusion is a stochastic process that involves jumps and diffusion.
See Hybrid system and Jump diffusion
Jump process
A jump process is a type of stochastic process that has discrete movements, called jumps, with random arrival times, rather than continuous movement, typically modelled as a simple or compound Poisson process.
See Hybrid system and Jump process
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.
Neural network (machine learning)
In machine learning, a neural network (also artificial neural network or neural net, abbreviated ANN or NN) is a model inspired by the structure and function of biological neural networks in animal brains.
See Hybrid system and Neural network (machine learning)
Petri net
A Petri net, also known as a place/transition net (PT net), is one of several mathematical modeling languages for the description of distributed systems.
See Hybrid system and Petri net
Physical system
A physical system is a collection of physical objects under study.
See Hybrid system and Physical system
Piecewise-deterministic Markov process
In probability theory, a piecewise-deterministic Markov process (PDMP) is a process whose behaviour is governed by random jumps at points in time, but whose evolution is deterministically governed by an ordinary differential equation between those times.
See Hybrid system and Piecewise-deterministic Markov process
PowerDEVS
PowerDEVS BK011 is a general purpose software tool for DEVS modeling and simulation oriented to the simulation of hybrid systems.
See Hybrid system and PowerDEVS
Probability
Probability is the branch of mathematics concerning events and numerical descriptions of how likely they are to occur.
See Hybrid system and Probability
Simulink
Simulink is a MATLAB-based graphical programming environment for modeling, simulating and analyzing multidomain dynamical systems.
See Hybrid system and Simulink
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.
See Hybrid system and Sliding mode control
Variable structure control
Variable structure control (VSC) is a form of discontinuous nonlinear control.
See Hybrid system and Variable structure control
Variable structure system
A variable structure system, or VSS, is a discontinuous nonlinear system of the form where \mathbf \triangleq ^ \in \mathbb^n is the state vector, t \in \mathbb is the time variable, and \varphi(\mathbf,t) \triangleq ^: \mathbb^ \mapsto \mathbb^n is a piecewise continuous function. Hybrid system and variable structure system are dynamical systems.
See Hybrid system and Variable structure system
Zeno of Elea
Zeno of Elea (Ζήνων ὁ Ἐλεᾱ́της) was a pre-Socratic Greek philosopher.
See Hybrid system and Zeno of Elea
References
[1] https://en.wikipedia.org/wiki/Hybrid_system
Also known as Hybrid dynamical system, Hybrid systems.