1,354 research outputs found
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
On a class of generating vector fields for the extremum seeking problem: Lie bracket approximation and stability properties
In this paper, we describe a broad class of control functions for extremum
seeking problems. We show that it unifies and generalizes existing extremum
seeking strategies which are based on Lie bracket approximations, and allows to
design new controls with favorable properties in extremum seeking and
vibrational stabilization tasks. The second result of this paper is a novel
approach for studying the asymptotic behavior of extremum seeking systems. It
provides a constructive procedure for defining frequencies of control functions
to ensure the practical asymptotic and exponential stability. In contrast to
many known results, we also prove asymptotic and exponential stability in the
sense of Lyapunov for the proposed class of extremum seeking systems under
appropriate assumptions on the vector fields
Partial Stability Concept in Extremum Seeking Problems
The paper deals with the extremum seeking problem for a class of cost
functions depending only on a part of state variables of a control system. This
problem is related to the concept of partial asymptotic stability and analyzed
by Lyapunov's direct method and averaging schemes. Sufficient conditions for
the practical partial stability of a system with oscillating inputs are derived
with the use of Lie bracket approximation techniques. These conditions are
exploited to describe a broad class of extremum-seeking controllers ensuring
the partial stability of the set of minima of a cost function. The obtained
theoretical results are illustrated by the Brockett integrator and rotating
rigid body.Comment: This is the author's version of the manuscript accepted for
publication in the Proceedings of the Joint 8th IFAC Symposium on Mechatronic
Systems and 11th IFAC Symposium on Nonlinear Control Systems (MECHATRONICS &
NOLCOS 2019
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