3,445 research outputs found
Quantized output feedback stabilization by Luenberger observers
We study a stabilization problem for systems with quantized output feedback.
The state estimate from a Luenberger observer is used for control inputs and
quantization centers. First we consider the case when only the output is
quantized and provide data-rate conditions for stabilization. We next
generalize the results to the case where both of the plant input and output are
quantized and where controllers send the quantized estimate of the plant output
to encoders as quantization centers. Finally, we present the numerical
comparison of the derived data-rate conditions with those in the earlier
studies and a time response of an inverted pendulum.Comment: 8 pages, 5 figures, to appear in Proc. IFAC WC 201
Stabilization of discrete-time piecewise affine systems with quantized signals
This paper studies quantized control for discrete-time piecewise affine
systems. For given stabilizing feedback controllers, we propose an encoding
strategy for local stability. If the quantized state is near the boundaries of
quantization regions, then the controller can recompute a better quantization
value. For the design of quantized feedback controllers, we also consider the
stabilization of piecewise affine systems with bounded disturbances. In order
to derive a less conservative design method with low computational cost, we
investigate a region to which the state belong in the next step.Comment: To be presented at IEEE CDC 201
Stabilization of continuous-time switched linear systems with quantized output feedback
In this paper, we study the problem of stabilizing continuous-time switched
linear systems with quantized output feedback. We assume that the observer and
the control gain are given for each mode. Also, the plant mode is known to the
controller and the quantizer. Extending the result in the non-switched case, we
develop an update rule of the quantizer to achieve asymptotic stability of the
closed-loop system under the average dwell-time assumption. To avoid quantizer
saturation, we adjust the quantizer at every switching time.Comment: This journal-version paper is based on the conference paper
(arXiv:1403.4670
A Characterization of the Minimal Average Data Rate that Guarantees a Given Closed-Loop Performance Level
This paper studies networked control systems closed over noiseless digital
channels. By focusing on noisy LTI plants with scalar-valued control inputs and
sensor outputs, we derive an absolute lower bound on the minimal average data
rate that allows one to achieve a prescribed level of stationary performance
under Gaussianity assumptions. We also present a simple coding scheme that
allows one to achieve average data rates that are at most 1.254 bits away from
the derived lower bound, while satisfying the performance constraint. Our
results are given in terms of the solution to a stationary signal-to-noise
ratio minimization problem and builds upon a recently proposed framework to
deal with average data rate constraints in feedback systems. A numerical
example is presented to illustrate our findings.Comment: Submitted to IEEE Transactions on Automatic Control on December 26,
201
Parametrization of completeness in symbolic abstraction of bounded input linear systems
A good state-time quantized symbolic abstraction of an already input
quantized control system would satisfy three conditions: proximity, soundness
and completeness. Extant approaches for symbolic abstraction of unstable
systems limit to satisfying proximity and soundness but not completeness.
Instability of systems is an impediment to constructing fully complete
state-time quantized symbolic models for bounded and quantized input unstable
systems, even using supervisory feedback. Therefore, in this paper we come up
with a way of parametrization of completeness of the symbolic model through the
quintessential notion of Trimmed-Input Approximate Bisimulation which is
introduced in the paper. The amount of completeness is specified by a parameter
called trimming of the set of input trajectories. We subsequently discuss a
procedure of constructing state-time quantized symbolic models which are
near-complete in addition to being sound and proximate with respect to the time
quantized models
Stabilization of uncertain systems using quantized and lossy observations and uncertain control inputs
In this paper, we consider a stabilization problem of an uncertain system in
a networked control setting. Due to the network, the measurements are quantized
to finite-bit signals and may be randomly lost in the communication. We study
uncertain autoregressive systems whose state and input parameters vary within
given intervals. We derive conditions for making the plant output to be mean
square stable, characterizing limitations on data rate, packet loss
probabilities, and magnitudes of uncertainty. It is shown that a specific class
of nonuniform quantizers can achieve stability with a lower data rate compared
with the common uniform one
Stability analysis of sampled-data switched systems with quantization
We propose a stability analysis method for sampled-data switched linear
systems with finite-level static quantizers. In the closed-loop system,
information on the active mode of the plant is transmitted to the controller
only at each sampling time. This limitation of switching information leads to a
mode mismatch between the plant and the controller, and the system may become
unstable. A mode mismatch also makes it difficult to find an attractor set to
which the state trajectory converges. A switching condition for stability is
characterized by the total time when the modes of the plant and the controller
are different. Under the condition, we derive an ultimate bound on the state
trajectories by using a common Lyapunov function computed from a randomized
algorithm. The switching condition can be reduced to a dwell-time condition.Comment: This journal-version paper is based on the conference paper
(arXiv:1403.4691
Stabilization of Networked Control Systems under DoS Attacks and Output Quantization
This paper addresses quantized output feedback stabilization under
Denial-of-Service (DoS) attacks. First, assuming that the duration and
frequency of DoS attacks are averagely bounded and that an initial bound of the
plant state is known, we propose an output encoding scheme that achieves
exponential convergence with finite data rates. Next we show that a suitable
state transformation allows us to remove the assumption on the DoS frequency.
Finally, we discuss the derivation of state bounds under DoS attacks and obtain
sufficient conditions on the bounds of DoS duration and frequency for achieving
Lyapunov stability of the closed-loop system.Comment: We have added new results in Sections 3.6 and
Disturbance-to-State Stabilization and Quantized Control for Linear Hyperbolic Systems
We consider a system of linear hyperbolic PDEs where the state at one of the
boundary points is controlled using the measurements of another boundary point.
Because of the disturbances in the measurement, the problem of designing
dynamic controllers is considered so that the closed-loop system is robust with
respect to measurement errors. Assuming that the disturbance is a locally
essentially bounded measurable function of time, we derive a
disturbance-to-state estimate which provides an upper bound on the maximum norm
of the state (with respect to the spatial variable) at each time in terms of
-norm of the disturbance up to that time. The analysis is
based on constructing a Lyapunov function for the closed-loop system, which
leads to controller synthesis and the conditions on system dynamics required
for stability. As an application of this stability notion, the problem of
quantized control for hyperbolic PDEs is considered where the measurements sent
to the controller are communicated using a quantizer of finite length. The
presence of quantizer yields practical stability only, and the ultimate bounds
on the norm of the state trajectory are also derived.Comment: Some minor errors in the derivations have been corrected, and the
references have been update
Coordination Over Multi-Agent Networks With Unmeasurable States and Finite-Level Quantization
In this note, the coordination of linear discrete-time multi-agent systems
over digital networks is investigated with unmeasurable states in agents'
dynamics. The quantized-observer based communication protocols and Certainty
Equivalence principle based control protocols are proposed to characterize the
inter-agent communication and the cooperative control in an integrative
framework. By investigating the structural and asymptotic properties of the
equations of stabilization and estimation errors nonlinearly coupled by the
finite-level quantization scheme, some necessary conditions and sufficient
conditions are given for the existence of such communication and control
protocols to ensure the inter-agent state observation and cooperative
stabilization. It is shown that these conditions come down to the simultaneous
stabilizability and the detectability of the dynamics of agents and the
structure of the communication network.Comment: 10 pages, 2 figure
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