# Design of robust adaptive controller based on the control Lyapunov function

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### Cites background from "Design of robust adaptive controlle..."

...For convenience of the following analysis, an assumption is proposed: Assumption 1: The sign of function g(z) is known, and without loss of generality, assume 0)( >zg and that there are given functions )(1 zM g and )(2 zM g that make f(z) and g(z) satisfy the following inequalities: )()( zMzf f≤ )()()(0 21 zMzgzM gg ≤≤ Definition 1: The operator Proj[8] has the following form: others 0 0, 0 0, 0 )(Pr maxi mini...

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...In the end, choose the parameter vector θ ’s self adaptive law: 1 2 1 1 3 1 2 2 3 2 Proj ( ( )) Proj ( ( ) )ce r s h x r s h x u θ θ θ θ = = & & (24) Where r1 and r2 are the learning rates....

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...The properties of operator Proj is shown as follows: (1) }ˆ|ˆ{ˆ maxminˆ θθθθθ θ ≤≤=Ω∈ (2) yyyoj ∀≤−− ,0))()(Prˆ( θ̂ θθ In order to deal with the unknown nonlinear system, a control law based on fuzzy logic control with input singleton fuzzification, product inference and center average defuzzification, is established....

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...For convenience of the following analysis, an assumption is proposed: Assumption 1: The sign of function g(z) is known, and without loss of generality, assume 0 ) ( > z g and that there are given functions ) ( 1 z M g and ) ( 2 z M g that make f(z) and g(z) satisfy the following inequalities: ) ( ) ( z M z f f ≤ ) ( ) ( ) ( 0 2 1 z M z g z M g g ≤ ≤ < Definition 1: The operator Proj[8] has the following form:...

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