Feedback Control Theory for Dynamic Traffic Assignment by Pushkin Kachroo & Kaan M.A. Özbay

Author:Pushkin Kachroo & Kaan M.A. Özbay
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(5.23)

Here, is the state vector, u is the control input and x is the output state. The superscript n on x(t) signifies the order of differentiation.

For example, is used for is used for and so on. In the equation, and are generally nonlinear functions of time and the states.

A time-varying surface S(t) is defined by equating the variable s(t), defined below, to zero.

(5.24)

Here, is a constant, taken to be the bandwidth of the system, and is the error in the output state where is the desired output state. When is a constant, the surface S(t) is in fact time invariant. Condition

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