The purpose of this note is to demonstrate that a unified study of quantization and delay effects in nonlinear control systems is possible by merging the quantized feedback control methodology ...recently developed by the author and the small-gain approach to the analysis of functional differential equations with disturbances proposed earlier by Teel. We prove that under the action of a robustly stabilizing feedback controller in the presence of quantization and time delays satisfying suitable conditions, solutions of the closed-loop system starting in a given region remain bounded and eventually enter a smaller region. We present several versions of this result and show how it enables global asymptotic stabilization via a dynamic quantization strategy.
We consider the problem of stabilizing a linear time-invariant system using sampled encoded measurements of its state or output. We derive a relationship between the number of values taken by the ...encoder and the norm of the transition matrix of the open-loop system over one sampling period, which guarantees that global asymptotic stabilization can be achieved. A coding scheme and a stabilizing control strategy are described explicitly.
We generalize and unify a range of recent results in quantized control systems (QCS) and networked control systems (NCS) literature and provide a unified framework for controller design for control ...systems with quantization and time scheduling via an emulation-like approach. A crucial step in our proofs is finding an appropriate Lyapunov function for the quantization/time-scheduling protocol which verifies its uniform global exponential stability (UGES). We construct Lyapunov functions for several representative protocols that are commonly found in the literature, as well as some new protocols not considered previously. Our approach is flexible and amenable to further extensions which are briefly discussed.
We consider the problem of achieving input-to-state stability (ISS) with respect to external disturbances for control systems with linear dynamics and quantized state measurements. Quantizers ...considered in this paper take finitely many values and have an adjustable "zoom" parameter. Building on an approach applied previously to systems with no disturbances, we develop a control methodology that counteracts an unknown disturbance by switching repeatedly between "zooming out" and "zooming in." Two specific control strategies that yield ISS are presented. The first one is implemented in continuous time and analyzed with the help of a Lyapunov function, similarly to earlier work. The second strategy incorporates time sampling, and its analysis is novel in that it is completely trajectory-based and utilizes a cascade structure of the closed-loop hybrid system. We discover that in the presence of disturbances, time-sampling implementation requires an additional modification which has not been considered in previous work
In this paper we prove that a switched nonlinear system has several useful input-to-state stable (ISS)-type properties under average dwell-time switching signals if each constituent dynamical system ...is ISS. This extends available results for switched linear systems. We apply our result to stabilization of uncertain nonlinear systems via switching supervisory control, and show that the plant states can be kept bounded in the presence of bounded disturbances when the candidate controllers provide ISS properties with respect to the estimation errors. Detailed illustrative examples are included.
Turbulence in the atmospheric boundary layer (ABL) is usually measured using sonic anemometers (sonics), but coarse spatial (
${\sim}10$
cm) and temporal (
${\sim}32$
Hz) resolutions of sonics ...preclude direct measurement of fine-scale parameters such as the turbulent kinetic energy (TKE) dissipation rate
$\unicodeSTIX{x1D700}$
. Instead,
$\unicodeSTIX{x1D700}$
is estimated using techniques based on Kolmogorov theory. Fine-scale measurements of ABL turbulence down to Kolmogorov scale were made with a sonic and hot-film anemometer dyad (a ‘combo’ probe) during the field campaigns of the Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) programme. The hot-film probe was located on a gimbal within the sonic probe volume, and was automated to rotate in the horizontal plane to align with the mean flow measured by sonic. This procedure not only helped satisfy the requirement of hot-film alignment with the mean flow, but also allowed in situ calibration of hot-film probes. This paper analyses a period of nocturnal flow that was similar to a stratified parallel shear flow. The combo-probe measurements showed an interesting phenomenon – the occurrence of strong bursts, characterized by short-term increase of velocity fluctuations and simultaneous increase of TKE dissipation rate by orders of magnitude. These bursts were indicative of unusual turbulence activity at finer (
${\sim}0.1$
–0.4 m) scales that are not captured by sonics since the smallest scales resolved by the latter are greater than 0.6 m. With bursting present, the spectra exhibited bumps at scales intermediate to inertial and dissipation subranges, resembling a bottleneck phenomenon. Its manifestation, although unequivocally related to bursts, may not convincingly fit into the framework of previous bottleneck-effect theories that allude to either viscous effects or buoyancy effects modifying the local energy cascade via non-local effects. The origins of burst are yet to be identified. Stratified ABL with bursts exhibits non-Kolmogorov behaviour, and hence should be modelled with caution.
This note is concerned with the problem of stabilizing a nonlinear continuous-time system by using sampled encoded measurements of the state. We demonstrate that global asymptotic stabilization is ...possible if a suitable relationship holds between the number of values taken by the encoder, the sampling period, and a system parameter, provided that a feedback law achieving input-to-state stability with respect to measurement errors can be found. The issue of relaxing the latter condition is also discussed.
Quantized control via locational optimization Bullo, F.; Liberzon, D.
IEEE transactions on automatic control,
2006-Jan., 2006, 2006-01-00, 20060101, Letnik:
51, Številka:
1
Journal Article
Recenzirano
This paper studies state quantization schemes for feedback stabilization of control systems with limited information. The focus is on designing the least destabilizing quantizer subject to a given ...information constraint. We explore several ways of measuring the destabilizing effect of a quantizer on the closed-loop system, including (but not limited to) the worst-case quantization error. In each case, we show how quantizer design can be naturally reduced to a version of the so-called multicenter problem from locational optimization. Algorithms for obtaining solutions to such problems, all in terms of suitable Voronoi quantizers, are discussed. In particular, an iterative solver is developed for a novel weighted multicenter problem which most accurately represents the least destabilizing quantizer design. A simulation study is also presented.
Summary
Effects of wind speed and wind gustiness on horizontal and vertical subsurface gas transport and subsurface–atmosphere gas exchange were investigated experimentally using a 40 cm × 40 cm, ...35‐cm‐deep stainless steel container, filled with a dry granular porous medium (crushed basalt) of 2–4‐mm grain size. Experiments used CO2 and O2 as tracer gases and were conducted under both steady and gusty wind at speeds ranging from 0 to 5.6 m s−1. Tracer gas breakthrough curves were measured at 20 locations within the porous medium to assess both horizontal and vertical gas movement. Results indicated that horizontal gas movement in wind‐exposed porous materials is important, especially near the wind‐exposed surface, and suggested considerable effects of both wind speed and wind gustiness on both horizontal and vertical gas transport inside the porous medium as well as subsurface–atmospheric gas exchange. Although wind‐induced subsurface gas transport is likely to be multidimensional, one‐dimensional model simulations indicated that vertical transport is an adequate approximation of the resulting average gas transport and exchange with the atmosphere over a larger area.
Highlights
Experimental assessment of near‐surface gas movement in wind‐exposed porous medium
Near‐surface gas movement in wind‐exposed porous media occurs both horizontally and vertically.
Wind speed and wind gustiness affect gas movement near the soil–atmosphere interface.
Wind‐induced bulk subsurface‐to‐atmosphere gas mass transport may be approximated as vertical.
This note is concerned with stability analysis and stabilization of randomly switched systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are ...triggered by a stochastic process which is independent of the state of the system, and between two consecutive switching instants the dynamics are deterministic. Our results provide sufficient conditions for almost sure stability and stability in the mean using Lyapunov-based methods when individual subsystems are stable and a certain ldquoslow switchingrdquo condition holds. This slow switching condition takes the form of an asymptotic upper bound on the probability mass function of the number of switches that occur between the initial and current time instants. This condition is shown to hold for switching signals coming from the states of finite-dimensional continuous-time Markov chains; our results, therefore, hold for Markovian jump systems in particular. For systems with control inputs, we provide explicit control schemes for feedback stabilization using the universal formula for stabilization of nonlinear systems.
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