A generalized framework for perturbation-based derivative estimation in multivariable extremum-seeking

In the context of model-free optimization of dynamic nonlinear multiple-input-single-output (MISO) systems using extremum-seeking (ES), accurate and fast derivative estimation of the systems steady-state performance map is essential. This paper presents a generalized derivative estimator (DE) framework for unknown MISO static maps. To this extent, the map input is perturbed with sinusoidal dither signals with different frequencies. Using the proposed framework, the derivatives can be estimated up to an arbitrary order, for maps with an arbitrary number of inputs. Conditions on the dither frequencies are provided, which optimize the DE time-scale, such that derivative estimation is as fast as possible. Simulation examples are provided to demonstrate the effectiveness of the proposed framework.