嵌入式控制与网络限制下的混合系统简介

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"《混合动力系统入门》这篇文章由Michael S. Branicky撰写，发表在Case Western Reserve University的电气工程与计算机科学系，探讨了混合动力系统这一独特领域的基本概念。混合动力系统是连续和离散元素的融合，它在现实世界的多个领域中广泛存在。例如，在嵌入式控制系统中，数字控制器、计算机以及用有限状态机模型的子系统与由偏微分方程或差分方程描述的控制器和被控对象相结合。这种系统的特征在于它们能够处理连续物理过程，并受到逻辑控制的指导，如在嵌入式控制中的应用。首先，作者从完全连续的角度出发，阐述了混合系统的起源，强调了如何通过连续输入、输出、状态和动力学来构建这类系统。这些系统的特点在于它们的动态行为既可以是连续的（如连续时间的控制行为），也可以是间断的（如数字逻辑决策）。混合动力系统不仅适用于控制理论家，也对计算机科学家具有吸引力，因为它们融合了两个学科的知识。接着，文章深入探讨了混合系统在实际应用中的实例，特别是在网络控制系统中，网络结构和拓扑限制与连续控制的交互起着关键作用。这种系统设计时需要考虑如何在连续性和离散性之间进行无缝切换，以确保整体性能的稳定和高效。混合动力系统的研究涉及到了动态系统的统一表达，包括状态转换、事件触发条件、以及如何通过离散事件系统的理论来分析和设计这类复杂系统。作者可能会介绍各种建模方法，如离散事件系统（DES）、混合自动机（HMA）或者混合逻辑动态（HLD），这些都是理解混合动力系统行为的核心工具。此外，文章还可能涵盖了混合系统的稳定性分析、控制策略设计、仿真与验证，以及一些实际案例研究，以展示混合动力系统在工业自动化、航空航天、机器人技术等领域的具体应用。《混合动力系统入门》为读者提供了一个从基础到实践的全面视角，使读者能够理解和掌握这一领域的重要理论和技术。"

Introduction to Hybrid Systems 95

Flight Compression

Thrust Decompression

![ (h =0)∧ (

h<0) ]

![ ˙x =0]/T := 0

![ (h =0)∧ (

h>0) ]

![ T =

thrust

]

Fig. 5. Raibert’s hopping robot: (left) dynamic phases (reproduced from [4], p. 260,

Fig. 3,

 Springer-Verlag), (right) ﬁnite-state controller with transitions speciﬁed

Inputs

i ∈ I

u ∈ U



Hybrid System:

ODEs & Logic

Outputs

o ∈ O

y ∈ Y



Fig. 6. Block diagram of prototypical hybrid control system

96 M. S. Branicky

having a state determined by continuous variables (such as velocity, engine

RPM, and distance to car ahead) and the ﬁnite states of its protocol-enacting

state machines.

Flight control: Flight controllers are organized around the idea of modes.For

example, one might easily imagine diﬀerent control schemes for Take-Oﬀ, As-

cend, Cruise, Descend,andLand. More complex is a whole ﬂight vehicle man-

agement system, which coordinates ﬂight in these diﬀerent regimes, while also

planning ﬂight paths considering air traﬃc, weather, fuel economy, and pas-

senger comfort [27].

Preview

Now that we have given a taste of the hybrid nature of real applications,

we turn to developing mathematical models that can capture their behavior.

Instead of proceeding directly to such hybrid models, we build them up, step

by step, from well-known models of completely continuous (viz., ODEs in

Section 2) and completely discrete (viz., ﬁnite automata in Section 3) systems.

Then, in Section 4, we present an overarching model of hybrid systems that

combines ODEs and automata. Throughout, we ﬁx ideas using examples.

2 From Continuous Toward Hybrid

In this section, we review ordinary diﬀerential equations (ODEs) as a base

continuous model,

then show how to add various discrete phenomena to

them, as seen in the applications above.

2.1 Base continuous model: ODEs

In this chapter, the base continuous dynamical systems dealt with are deﬁned

by the solutions of ODEs:

˙x(t)=f(x(t)), (2)

where x(t) ∈ X ⊂ R

. The function f : X −→ R

is called a vector ﬁeld on

. We assume existence and uniqueness of solutions.

Actually, the system of ODEs in (2) is called autonomous or time invariant

because its vector ﬁeld does not depend explicitly on time. If it did depend

One can easily use diﬀerence equations instead. See [7].

See [22] for conditions. A well-known suﬃcient condition is that f is Lipschitz

continuous. That is, there exists L>0 (called the Lipschitz constant ) such that

f(x) −f(y)≤Lx − y, for all x, y ∈ X.

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