This paper presents a new technique for online set membership parameter estimation of linear regression models affected by unknown-but-bounded noise. An orthotopic approximation of the set of feasible parameters is updated at each time step. The proposed technique relies on the solution of a suitable linear program, whenever a new measurement leads to a reduction of the approximating orthotope. The key idea for preventing the size of the linear programs from steadily increasing is to propagate only the binding constraints of these optimization problems. Numerical studies show that the new approach outperforms existing recursive set approximation techniques, while keeping the required computational burden within the same order of magnitude. Copyright © 2016 John Wiley & Sons, Ltd.

Bounding methods for state and parameter estimation

A linear programming approach to online set membership parameter estimation for linear regression models

In this contribution, we present interval methods for mathematical modeling, for parameter identification, and for control design of dynamical systems. The corresponding approaches are applied to the thermal subsystem of a high-temperature solid oxide fuel cell (SOFC) which is available as a test rig at the Chair of Mechatronics at the University of Rostock. In practice, most internal parameters of SOFC stack modules cannot be measured directly. Therefore, system characteristics such as heat capacities or internal thermal resistances cannot be identified exactly, but only bounded. For this reason, intervals represent a good first approach to dealing with parameter uncertainty. In the first part of the paper, we present interval methods for the parameter identification aiming at the computation of globally optimal parameterizations. In comparison with classical local optimization procedures, the approximation quality is improved by the presented identification approach. The corresponding bounds for admissible domains are used to design a robust sliding mode control law for arbitrary operating points compensating the impact of disturbances and parameter uncertainties in a reliable way. In the second part of the paper, we show a simple approach to handling non-smoothness appearing in SOFC models based on ordinary differential equations in a verified way. We use a generalized derivative definition for a certain type of non-smooth functions inside the algorithm of the verified solver ValEncIA-IVP to be able to compute solutions to non-smooth initial value problems. The applicability of our method is demonstrated using the designed sliding mode controller.

methods

Thermal behavior of high-temperature fuel cells: reliable parameter identification and interval-based sliding mode control

background

A new kernel RLS algorithm for systems with bounded noise

https://www.onlinelibrary.wiley.com/doi/pdf/10.1002/acs.1232

Bounding methods for state and parameter estimation

Citations

A linear programming approach to online set membership parameter estimation for linear regression models

Thermal behavior of high-temperature fuel cells: reliable parameter identification and interval-based sliding mode control

A new kernel RLS algorithm for systems with bounded noise

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