By An-chyau Huang

ISBN-10: 9814307416

ISBN-13: 9789814307413

This ebook 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 keep watch over in addition to compliant movement keep watch over. it truly is acceptable to the inflexible robotic and the versatile joint robotic. regardless of actuator dynamics, the unified procedure continues to be possible. these types of beneficial properties make the ebook stand proud of different latest courses.

**Read or Download Adaptive Control of Robot Manipulators: A Unified Regressor-free Approach PDF**

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

**Example text**

In many applications, however, it may be desirable to use different number of orthonormal functions for different matrix elements. ,m as f i (x) = w Tf i z f i (10) where w fi , z fi ∈ℜ pi ×1 and pi is the number of terms of the basis functions selected to approximate fi. ,pmax, and then (8) can be expressed in the form p max f ( x) = ∑Wz (14) i i i =1 For approximating the matrix M (t ) ∈ℜ p × q , we may rewrite it into a row p vector as M = [m1 ⋯ m q ] where m i ∈ℜ . 8 Lyapunov Stability Theory The Lyapunov stability theory is widely used in the analysis and design of control systems.

The concept of stability of a dynamic system is usually related to the ability to remain in a state regardless of small perturbations. This leads to the definition of the concept of the equilibrium state or equilibrium point. A state x e is said to be an equilibrium point of (1), if f ( x e , t ) = 0 for all t > 0 . For simplicity, we often transform the system equations in such a way that the equilibrium point is the origin of the state space. The equilibrium point x e = 0 of the autonomous system (2) is said to be (i) stable, if ∀R > 0, ∃r > 0 such that x(0) < r ⇒ x(t ) < R , ∀t ≥ 0 ; (ii) asymptotically stable, if it is stable and if ∃r1 > 0 such that x(0) < r1 implies that x(t ) → 0 as t → ∞ ; (iii) exponentially stable, if ∃α , λ > 0 , such that x(t ) ≤ α x(0) e − λ t for all t > 0 in some neighborhood N of the origin; (iv) globally asymptotically (or exponentially) stable, if the property holds for any initial condition.

Once on the surface, the system behaves like a stable linear system ( d + λ ) n −1 e = 0 ; dt therefore, asymptotic convergence of the tracking error can be obtained. Now, the problem is how to drive the system trajectory to the sliding surface. With s(x, t ) = 0 as the boundary, the state space can be decomposed into two parts: the one with s > 0 and the other with s < 0 . Intuitively, to make the sliding surface attractive, we can design a control u so that s will decrease in the s > 0 region, and it will increase in the s < 0 region.