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A hybrid system is a dynamic 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 difference equation). Often, the term "hybrid dynamic 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, a hybrid system can be described by a few pieces of information. The state of the system consists of vector (spatial) signals, which can change according to dynamic laws in the system data. The data includes a flow equation, f(x), which describes the continuous dynamics, a flow set, C, in which flow is permitted, a jump equation, g(x), which describes the discrete dynamics, and a jump set, D, in which discrete state evolution is permitted.

Examples Hybrid systems have been used to model several systems, including physical systems with impact, logic-dynamic controllers, and even Internet congestion.

Bouncing ball A canonical example of a hybrid system is the bouncing ball, a physical system with impact. Here, the ball (thought of as a point-mass) is dropped from an initial height and bounces off the ground, dissipating its energy with each bounce. The ball exhibits continuous dynamics between each bounce; however, as the ball impacts the gound, its velocity undergoes a discrete change modeled after an inelastic collision. A mathematical description of the bouncing ball follows. Let x_1 be the height of the ball and x_2 be the velocity of the ball. A hybrid system describing the ball is as follows:

When x \in C = \{x_1 > 0\}, flow is governed by\dot{x_1} = x_2,\dot{x_2} = -g,where g is the force due to gravity. These equations state that when the ball is above ground, it is being drawn to the ground by gravity.

When x \in D = \{x_1 = 0\}, jumps are governed byx_1^+ = x_1,x_2^+ = -\gamma x_2,where 0 < \gamma < 1 is a dissipation factor. This is saying that when the height of the ball is zero (it has impacted the ground), its velocity is reversed and decreased by a factor of \gamma. Effectively, this describes the nature of the inelastic collision.

The bouncing ball is an especially interesting hybrid system, as it exhibits Zeno behavior. Zeno behavior has a strict mathematical definition, but can be described informally as the system making an infinite number of jumps in a finite amount of time. In this example, each time the ball bounces it loses energy, making the subsequent jumps (impacts with the ground) closer and closer together in time.

Other modeling approaches Two basic hybrid system modeling approaches can be classified, an implicit and an explicit one. The explicit approach is often represented by a hybrid automaton or a hybrid Petri net. The implicit approach is often represented by guarded equations to result in systems of differential algebraic equations (DAEs) where the active equations may change, for example by means of a hybrid bond graph.



External links



HybridSoundSystem.com - Official site of Artist/DJ/Production group ...
Hybrid: Mike Truman, Chris Healings and Lee Mullin are Swansea based Hybrid. Their type of music has been described as a mixture of breakbeat and progressive house.

Hybrid vehicle - Wikipedia, the free encyclopedia
A hybrid vehicle is a vehicle that uses two or more distinct power sources to propel the vehicle. [1] Common power sources include: On-board rechargeable energy storage system ...

Digital Displacement® Hybrid Transmissions
System design. A Digital Displacement® Hybrid Transmission consists of connecting a Digital Displacement® Pump mounted to a standard internal combustion engine.

Hybrid Electric Marine Propulsion - Home
HEMP is the result of a five year research program funded by the DTI. An integrated Hybrid system has been developed to provide a complete power and propulsion solution for small ...

Hybrid Electric Marine Propulsion - Production System
HEMP is the result of a five year research program funded by the DTI. An integrated Hybrid system has been developed to provide a complete power and propulsion solution for small ...

HIS Series of International Conferences
A fundamental stimulus to the investigations of Hybrid Intelligent Systems (HIS) is the awareness that combined approaches will be necessary if the remaining tough problems ...

Chevrolet | Fuel Economy - Chevy Hybrid Vehicles
An 'equalizer' has been needed...and the two-mode hybrid system in the Tahoe Hybrid is clearly that equalizer.” — Ron Cogan, &lt;em>Green Car Journal, Editor and Publisher

Hybrid Renewable Energy System
A hybrid renewable energy system project that we developed was the integration of three major sources of renewable energy - wind turbine, anaerobic digester and a gasifier.

Hybrid electric vehicle - Wikipedia, the free encyclopedia
A hybrid electric vehicle (HEV) is a hybrid vehicle which combines a conventional propulsion system with a rechargeable energy storage system (RESS) to achieve better fuel economy ...

HYBRID SYNERGY DRIVE: Technology: Overview
HYBRID SYNERGY DRIVE uses what is called a "Series Parallel Hybrid System". This is an ideal combination of the "Series Hybrid System" that Toyota has been developing and the ...





 
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