Abstract

SummaryThis paper addresses the problem of asymptotic tracking for switched linear systems with parametric uncertainties and dwell‐time switching, when input measurements are quantized due to the presence of a communication network closing the control loop. The problem is solved via a dynamic quantizer with dynamic offset that, embedded in a model reference adaptive control framework, allows the design of the adaptive adjustments for the control parameters and for the dynamic range and dynamic offset of the quantizer. The overall design is carried out via a Lyapunov‐based zooming procedure, whose main feature is overcoming the need for zooming out at every switching instant, in order to compensate for the possible increment of the Lyapunov function at the switching instants. It is proven analytically that the resulting adjustments guarantee asymptotic state tracking. The proposed quantized adaptive control is applied to the piecewise linear model of the NASA Generic Transport Model aircraft linearized at multiple operating points.

Highlights

  • Switched systems are used to model many systems, commonly referred to as hybrid systems, exhibiting an interaction between continuous and discrete dynamics

  • Summary This paper addresses the problem of asymptotic tracking for switched linear systems with parametric uncertainties and dwell-time switching, when input measurements are quantized due to the presence of a communication network closing the control loop

  • We have used a time scheduled Lyapunov approach in an adaptive framework to avoid zooming out at every switching instant to compensate the possible increment of the Lyapunov function at the switching instants

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Summary

INTRODUCTION

Switched systems are used to model many systems, commonly referred to as hybrid systems, exhibiting an interaction between continuous and discrete dynamics. An established approach for achieving asymptotic regulation relies on dynamic quantization mechanisms such as the one referred to as “zooming”.25,26 In this mechanism, precision is increased by “zooming in”, ie, by reducing the size of the range so that the quantization resolution becomes finer while the state becomes smaller. The second contribution comes from a novel dynamic quantizer with dynamic offset, which does not require the quantizer to be antisymmetric with respect to the origin and allows high precision even in the tracking case By embedding this quantizer in a model reference quantized adaptive control framework, a Lyapunov-based analysis is used to derive the adjustment laws for the control gains and for the dynamic range and dynamic offset of the quantizer. Xn)T; tr [X ]: the trace of a square matrix X; L∞ class: a vector signal x(·) ∈ [0, ∞) → Rn is said to belong to L∞ class (x ∈ L∞), if maxt≥0||x(t)|| < ∞, ∀t ≥ 0; In: the identity matrix of size n × n

PROBLEM STATEMENT
Switched linear reference model system and controller
Dynamic quantizer design
ADAPTIVE LAW CONTROLLER DESIGN
Preliminaries in stability with slow switching
Preliminaries in hybrid control policy
MAIN RESULT
SIMULATION RESULTS
CONCLUSION
Full Text
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