EECE 396-1Hybrid and Embedded Systems: Computation

T. John Koo, Ph.D.

Institute for Software Integrated Systems

Department of Electrical Engineering and Computer Science

Vanderbilt University

300 Featheringill HallFebruary 3, 2004

john.koo@vanderbilt.edu

http://www.vuse.vanderbilt.edu/~kootj

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Hybrid System

A system built from atomic discrete components and continuous components by parallel and serial composition, arbitrarily nested.

The behaviors and interactions of components are governed by models of computation (MOCs).

Discrete Components Finite State Machine (FSM) Discrete Event (DE) Synchronous Data Flow (SDF)

Continuous Components Ordinary Differential Equation (ODE) Partial Differential Equation (PDE)

q1q2

q3

u

xç= f (x) + g(x)u

x

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Modeling:Ordinary Differential Equations

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Topics

Ordinary Differential Equations Definitions Examples Existence and Uniqueness of Solutions Properties of Solutions

Ref: [1] S. S. Sastry, Nonlinear Systems: Analysis, Stability, and Control,

Springer, 1999. [2] J. J. Slotine and W. Li, Applied Nonlinear Control, Prentice Hall, 1991. [3] H. K. Khalil, Nonlinear Systems, Macmillan, 1992.

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Ordinary Differential Equations

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Ordinary Differential Equations

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Ordinary Differential Equations

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Ordinary Differential Equations

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Ordinary Differential Equations

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Ordinary Differential Equations

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Ordinary Differential Equations

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Ordinary Differential Equations

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Ordinary Differential Equations

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Ordinary Differential Equations

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Ordinary Differential Equations

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Ordinary Differential Equations

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Ordinary Differential Equations

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