By An-chyau Huang

This e-book introduces an unified functionality approximation method of the keep watch over of doubtful robotic manipulators containing normal uncertainties. it really works at no cost area monitoring regulate in addition to compliant movement keep watch over. it really is appropriate to the inflexible robotic and the versatile joint robotic. despite actuator dynamics, the unified technique continues to be possible. a majority of these beneficial properties make the ebook stand proud of different current guides.

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**Extra resources for Adaptive Control of Robot Manipulators: A Unified Regressor-free Approach **

**Sample text**

The persistent excitation condition is investigated for the convergence of estimated parameters. Two modifications to the update law are introduced to robustify the adaptive loop when the system contains unmodeled dynamics or external disturbances. 1 MRAC of LTI scalar systems Consider a linear time-invariant system described by the differential equation xɺ p = a p x p + b p u (1) where x p ∈ℜ is the state of the plant and u ∈ℜ the control input. The parameters ap and bp are unknown constants, but sgn(bp) is available.

A nn ) . An identity matrix is a diagonal matrix with a11 = ⋯ = a nn = 1. A matrix A ∈ℜ n × n is nonsingular if ∃B ∈ℜ n × n such that AB = BA = I where I is an n × n identity matrix. If B exists, then it is known as the inverse of A and is denoted by A −1 . The inverse operation has the following properties: ( A −1 ) −1 = A (2a) ( A T ) −1 = ( A −1 )T (2b) (α A) −1 = 1 α A −1 ∀α ∈ℜ, α ≠ 0 ( AB) −1 = B −1A −1 ∀B ∈ℜ n × n with valid inverse (2c) (2d) A matrix A ∈ℜ n × n is said to be positive semi-definite (denoted by A ≥ 0 ) if x Ax ≥ 0 ∀x ∈ℜ n .

A matrix A ∈ℜ n × n is diagonal if aij = 0 , ∀i ≠ j . , a nn ) . An identity matrix is a diagonal matrix with a11 = ⋯ = a nn = 1. A matrix A ∈ℜ n × n is nonsingular if ∃B ∈ℜ n × n such that AB = BA = I where I is an n × n identity matrix. If B exists, then it is known as the inverse of A and is denoted by A −1 . The inverse operation has the following properties: ( A −1 ) −1 = A (2a) ( A T ) −1 = ( A −1 )T (2b) (α A) −1 = 1 α A −1 ∀α ∈ℜ, α ≠ 0 ( AB) −1 = B −1A −1 ∀B ∈ℜ n × n with valid inverse (2c) (2d) A matrix A ∈ℜ n × n is said to be positive semi-definite (denoted by A ≥ 0 ) if x Ax ≥ 0 ∀x ∈ℜ n .