Activity: Talk or presentation › Talk at workshop, seminar or course › Science to science
This talk shows the construction of a first-order robust exact differentiator with optimal accuracy. First, the problem of differentiating a function with bounded second derivative from noisy measurements and its performance limitations are discussed. A differentiator is then constructed via the adaptation of a single parameter of a linear differentiator. It is demonstrated that the resulting differentiator is robust with respect to noise, that it instantaneously converges to the exact derivative in the absence of noise, and that it attains the smallest possible---hence optimal---upper bound for its differentiation error under noisy measurements. For practical realization in the presence of sampled measurements, a discrete-time realization is shown that achieves optimal asymptotic accuracy with respect to the noise and the sampling time.