148 research outputs found
Interplay Between Transmission Delay, Average Data Rate, and Performance in Output Feedback Control over Digital Communication Channels
The performance of a noisy linear time-invariant (LTI) plant, controlled over
a noiseless digital channel with transmission delay, is investigated in this
paper. The rate-limited channel connects the single measurement output of the
plant to its single control input through a causal, but otherwise arbitrary,
coder-controller pair. An infomation-theoretic approach is utilized to analyze
the minimal average data rate required to attain the quadratic performance when
the channel imposes a known constant delay on the transmitted data. This
infimum average data rate is shown to be lower bounded by minimizing the
directed information rate across a set of LTI filters and an additive white
Gaussian noise (AWGN) channel. It is demonstrated that the presence of time
delay in the channel increases the data rate needed to achieve a certain level
of performance. The applicability of the results is verified through a
numerical example. In particular, we show by simulations that when the optimal
filters are used but the AWGN channel (used in the lower bound) is replaced by
a simple scalar uniform quantizer, the resulting operational data rates are at
most around 0.3 bits above the lower bounds.Comment: A less-detailed version of this paper has been accepted for
publication in the proceedings of ACC 201
Stabilization of Linear Systems Over Gaussian Networks
The problem of remotely stabilizing a noisy linear time invariant plant over
a Gaussian relay network is addressed. The network is comprised of a sensor
node, a group of relay nodes and a remote controller. The sensor and the relay
nodes operate subject to an average transmit power constraint and they can
cooperate to communicate the observations of the plant's state to the remote
controller. The communication links between all nodes are modeled as Gaussian
channels. Necessary as well as sufficient conditions for mean-square
stabilization over various network topologies are derived. The sufficient
conditions are in general obtained using delay-free linear policies and the
necessary conditions are obtained using information theoretic tools. Different
settings where linear policies are optimal, asymptotically optimal (in certain
parameters of the system) and suboptimal have been identified. For the case
with noisy multi-dimensional sources controlled over scalar channels, it is
shown that linear time varying policies lead to minimum capacity requirements,
meeting the fundamental lower bound. For the case with noiseless sources and
parallel channels, non-linear policies which meet the lower bound have been
identified
Stabilizing Error Correction Codes for Controlling LTI Systems over Erasure Channels
We propose (k,k') stabilizing codes, which is a type of delayless error
correction codes that are useful for control over networks with erasures. For
each input symbol, k output symbols are generated by the stabilizing code.
Receiving any k' of these outputs guarantees stability. Thus, the system to be
stabilized is taken into account in the design of the erasure codes. Our focus
is on LTI systems, and we construct codes based on independent encodings and
multiple descriptions. The theoretical efficiency and performance of the codes
are assessed, and their practical performances are demonstrated in a simulation
study. There is a significant gain over other delayless codes such as
repetition codes.Comment: Accepted and presented at the IEEE 60th Conference on Decision and
Control (CDC). arXiv admin note: substantial text overlap with
arXiv:2112.1171
Fundamental limits in Gaussian channels with feedback: confluence of communication, estimation, and control
The emerging study of integrating information theory and control systems theory has attracted tremendous attention, mainly motivated by the problems of control under communication constraints, feedback information theory, and networked systems. An often overlooked element is the estimation aspect; however, estimation cannot be studied isolatedly in those problems. Therefore, it is natural to investigate systems from the perspective of unifying communication, estimation, and control;This thesis is the first work to advocate such a perspective. To make Matters concrete, we focus on communication systems over Gaussian channels with feedback. For some of these channels, their fundamental limits for communication have been studied using information theoretic methods and control-oriented methods but remain open. In this thesis, we address the problems of characterizing and achieving the fundamental limits for these Gaussian channels with feedback by applying the unifying perspective;We establish a general equivalence among feedback communication, estimation, and feedback stabilization over the same Gaussian channels. As a consequence, we see that the information transmission (communication), information processing (estimation), and information utilization (control), seemingly different and usually separately treated, are in fact three sides of the same entity. We then reveal that the fundamental limitations in feedback communication, estimation, and control coincide: The achievable communication rates in the feedback communication problems can be alternatively given by the decay rates of the Cramer-Rao bounds (CRB) in the associated estimation problems or by the Bode sensitivity integrals in the associated control problems. Utilizing the general equivalence, we design optimal feedback communication schemes based on the celebrated Kalman filtering algorithm; these are the first deterministic, optimal communication schemes for these channels with feedback (except for the degenerated AWGN case). These schemes also extend the Schalkwijk-Kailath (SK) coding scheme and inherit its useful features, such as reduced coding complexity and improved performance. Hence, this thesis demonstrates that the new perspective plays a significant role in gaining new insights and new results in studying Gaussian feedback communication systems. We anticipate that the perspective could be extended to more general problems and helpful in building a theoretically and practically sound paradigm that unifies information, estimation, and control
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