By Gang Tao
Perceiving a necessity for a scientific and unified realizing of adaptive keep an eye on conception, electric engineer Tao provides and analyzes universal layout methods with the purpose of overlaying the basics and state-of-the-art of the sphere. Chapters conceal platforms thought, adaptive parameter estimation, adaptive kingdom suggestions keep an eye on, continuous-time version reference adaptive regulate, discrete-time version reference adaptive keep watch over, oblique adaptive regulate, multivariable adaptive keep an eye on, and adaptive regulate of platforms with nonlinearities.
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Additional info for Adaptive Control Design and Analysis
On the equality constraint). This section has introduced some popular matrix decompositions used in linear least squares. Choosing which decomposition to use is primarily dependent upon the particular application, numerical concerns, and desired level of accuracy. For example, the singular value decomposition is one of the most robust algorithms to compute the least squares estimates. However, it is also one of the most computationally expensive algorithms. The decompositions presented in this section do not represent an exhaustive treatise of the subject.
Xn ); j = 1, 2, . . 83) where the f j (x1 , x2 , . . , xn ) are m arbitrary independent functions of the unknown parameters xi . These should be interpreted as “functions” in the general sense, as specifying “whatever process one must go through” to compute the y j given the xi (including, for example, numerical solution of differential equations). We do require that f j (x1 , x2 , . . , xn ) and at least its first partial derivatives be single-valued, continuous, and at least once differentiable.
1 creates a singular condition when B is negative. 1. 12) are harmonic series, which can be used to approximate y: y j = a0 + a1 cos(ω t j ) + b1 sin(ω t j ) + . . 102) j = 1, . . , m; m ≥ 2n + 1 where the amplitudes (ai , bi ) are the sought parameters. Suppose we are given y˜ j , t j , W = (Wi j ), and ω = 2π T , where T is the period under consideration. Then, the © 2012 by Taylor & Francis Group, LLC Least Squares Approximation 37 desired least squares estimate (aˆi , bˆ i ) is computable as ⎡ ⎤ aˆ0 ⎢aˆ1 ⎥ ⎢ ⎥ ⎢bˆ 1 ⎥ ⎢ ⎥ xˆ = ⎢ .