By An-chyau Huang

ISBN-10: 9814307416

ISBN-13: 9789814307413

This publication introduces an unified functionality approximation method of the regulate of doubtful robotic manipulators containing common uncertainties. it really works at no cost house monitoring keep an eye on in addition to compliant movement keep watch over. it really is acceptable to the inflexible robotic and the versatile joint robotic. regardless of actuator dynamics, the unified method remains to be possible. some of these gains make the publication stand proud of different latest courses.

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

**Example text**

For any matrix A ∈ℜ n × n , A + A T is symmetric and A − A T is skew-symmetric. If A is a m × n matrix, then A T A is symmetric. 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 .

For nonlinear systems, the sliding control is perhaps the most popular approach to achieve the robust performance requirement. In the sliding control, a sliding surface is designed so that the system trajectory is force to converge to the surface by some worst-case control efforts. Once on the surface, the system dynamics is reduced to a stable linear time invariant system which is irrelevant to the perturbations no matter from internal or external sources. Convergence of the output error is then easily achieved.

To investigate the problem of parameter convergence, we need the concept of persistent excitation. , parameter convergence when t → ∞ . 3. 2 MRAC of LTI systems: vector case Consider a linear time-invariant system xɺ p = A p x p + B p u (18) where x p ∈ℜ n is the state vector, u ∈ℜ m is the control vector, and A p ∈ℜ n × n and B p ∈ℜ n × m are unknown constant matrices. The pair (Ap, Bp) is controllable. 10 Model Reference Adaptive Control (MRAC) 49 n×n n×m where A m ∈ℜ and B m ∈ℜ are known and r ∈ℜ m is a bounded reference input vector.

### Adaptive Control of Robot Manipulators: A Unified Regressor-free Approach by An-chyau Huang

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