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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 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 tr ... [...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] |
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. In finance, various stochastic models are used to model the price movements of financial instruments; for example the Black–Scholes model for pricing options assumes that the underlying instrument follows a traditional diffusion process, with continuous, random movements at all scales, no matter how small. John Carrington Cox and Stephen Ross proposed that prices actually follow a 'jump process'. Robert C. Merton extended this approach to a hybrid model known as jump diffusion, which states that the prices have large jumps interspersed with small continuous movements. See also *Poisson process, an example of a jump process *Continuous-time Markov chain (CTMC), an example of a jump process and a generalization of the Poisson process *Counting process, an example of a j ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Behavior Trees (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. They describe switchings between a finite set of tasks in a modular fashion. Their strength comes from their ability to create very complex tasks composed of simple tasks, without worrying how the simple tasks are implemented. Behavior trees present some similarities to hierarchical state machines with the key difference that the main building block of a behavior is a task rather than a state. Its ease of human understanding make behavior trees less error prone and very popular in the game developer community. Behavior trees have been shown to generalize several other control architectures. Background Behavior trees originate from the computer game industry as a powerful tool to model the behavior of non-player characters (NPCs). They have been extensively used in high-profile video games such as Halo, Bioshock, and Spore. Recent works propose behav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cyber-physical System
A cyber-physical system (CPS) or intelligent system is a computer system in which a mechanism is controlled or monitored by computer-based algorithms. In cyber-physical systems, physical and software components are deeply intertwined, able to operate on different spatial and temporal scales, exhibit multiple and distinct behavioral modalities, and interact with each other in ways that change with context.Hu, J.; Lennox, B.; Arvin, F.,Robust formation control for networked robotic systems using Negative Imaginary dynamics Automatica, 2022. CPS involves transdisciplinary approaches, merging theory of cybernetics, mechatronics, design and process science.Suh, S.C., Carbone, J.N., Eroglu, A.E.: ''Applied Cyber-Physical Systems.'' Springer, 2014. The process control is often referred to as embedded systems. In embedded systems, the emphasis tends to be more on the computational elements, and less on an intense link between the computational and physical elements. CPS is also similar to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. In recent years this notion has found applications in a large number of engineering fields and is still a topic of active research. General description The joint spectral radius of a set of matrices is the maximal asymptotic growth rate of products of matrices taken in that set. For a finite (or more generally compact) set of matrices \mathcal M=\ \subset \mathbb R^, the joint spectral radius is defined as follows: : \rho (\mathcal M)= \lim_\max. \, It can be proved that the limit exists and that the quantity actually does not depend on the chosen matrix norm (this is true for any norm but particularly easy to see if the norm is sub-multiplicative). The joint spectral radius was introduced in 1960 by Gian-Carlo Rota and Gilbert Strang, two mathematicians from MIT, but started attracting attention with the work of Ingrid Daubechies and J ... [...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] |
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] |
