Extremum Seeking-based Iterative Learning Linear MPC

In this work we study the problem of adaptive MPC for linear time-invariant uncertain models. We assume linear models with parametric uncertainties, and propose an iterative multi-variable extremum seeking (MES)-based learning MPC algorithm to learn on-line the uncertain parameters and update the MPC model. We show the effectiveness of this algorithm on a DC servo motor control example.Comment: To appear at the IEEE MSC 201

Improved Maximum Entropy Analysis with an Extended Search Space

The standard implementation of the Maximum Entropy Method (MEM) follows Bryan and deploys a Singular Value Decomposition (SVD) to limit the dimensionality of the underlying solution space apriori. Here we present arguments based on the shape of the SVD basis functions and numerical evidence from a mock data analysis, which show that the correct Bayesian solution is not in general recovered with this approach. As a remedy we propose to extend the search basis systematically, which will eventually recover the full solution space and the correct solution. In order to adequately approach problems where an exponentially damped kernel is used, we provide an open-source implementation, using the C/C++ language that utilizes high precision arithmetic adjustable at run-time. The LBFGS algorithm is included in the code in order to attack problems without the need to resort to a particular search space restriction.Comment: 18 pages, 6 figures, v3 includes several changes in text and figures, t.b.p. in Journal of Computational Physics, source code at http://www.scicode.org/ExtME

Multi-Parametric Extremum Seeking-based Auto-Tuning for Robust Input-Output Linearization Control

We study in this paper the problem of iterative feedback gains tuning for a class of nonlinear systems. We consider Input-Output linearizable nonlinear systems with additive uncertainties. We first design a nominal Input-Output linearization-based controller that ensures global uniform boundedness of the output tracking error dynamics. Then, we complement the robust controller with a model-free multi-parametric extremum seeking (MES) control to iteratively auto-tune the feedback gains. We analyze the stability of the whole controller, i.e. robust nonlinear controller plus model-free learning algorithm. We use numerical tests to demonstrate the performance of this method on a mechatronics example.Comment: To appear at the IEEE CDC 201