Data-driven control of nonlinear systems: An on-line direct approach

Abstract

A data-driven method to design reference tracking controllers for nonlinear systems is presented. The technique does not derive explicitly a model of the system, rather it delivers directly a time-varying state-feedback controller by combining an on-line and an off-line scheme. Like in other on-line algorithms, the measurements collected in closed-loop operation are exploited to modify the controller in order to improve the tracking performance over time. At the same time, a predictable closed-loop behavior is guaranteed by making use of a batch of available data, which is a feature of off-line algorithms. The feedback controller is parameterized with kernel functions and the design approach exploits results in set membership identification and learning by projections. Under the assumptions of Lipschitz continuity and stabilizability of the system's dynamics, it is shown that if the initial batch of data is informative enough, then the resulting closed-loop system is guaranteed to be finite gain stable. In addition to the main theoretical properties of the approach, the design algorithm is demonstrated experimentally on a water tank system

Safe Approximate Dynamic Programming via Kernelized Lipschitz Estimation

“…We invoke the assumption in [20], [21] regarding the availability of legacy/archival/historical data generated by the system during prior experiments. That is, at design time, we have a dataset D consisting of unique triples: stateinput pairs along with corresponding state update information.…”

Model‐based vs data‐driven adaptive control: An overview

“…We can also mention other approaches that have been used in data‐driven adaptive control, like, for instance, the evolutionary methods, eg, genetic algorithms, NN deep learning algorithms and deep RL algorithms,) kernel function–based parameterization, particle filters, and iterative learning control (ILC) …”

“…Another important improvement direction in data‐driven adaptive methods is the fact that these algorithms rely on some tuning parameters, eg, amplitudes and frequencies of the dither signals in some extremum seekers, or the choice of the kernel parameters in kernel function–based approaches; these tuning parameters can strongly influence the performances of these data‐driven approaches. An open research area is to design algorithms that are robust with respect to these tuning parameters, with performance guarantees.…”

Combing Instrumental Variable and Variance Matching for Aircraft Flutter Model Parameters Identification

“…It usually needs to establish a parameterized frequency-domain transfer function (frequency response function) model and obtain the model parameters of each order by fitting the estimated frequency response function from the experiment. e rational fractional method proposed by Tanaskovic [16] is used in flutter model parameter identification. e rational fractional method is to represent the frequency response function as a rational fractional form, and then apply the linear least squares method to fit the estimated flutter frequency and damping.…”