13 research outputs found
Optimal Causal Rate-Constrained Sampling for a Class of Continuous Markov Processes
Consider the following communication scenario. An encoder observes a stochastic process and causally decides when and what to transmit about it, under a constraint on bits transmitted per second. A decoder uses the received codewords to causally estimate the process in real time. The encoder and the decoder are synchronized in time. We aim to find the optimal encoding and decoding policies that minimize the end-to-end estimation mean-square error under the rate constraint. For a class of continuous Markov processes satisfying regularity conditions, we show that the optimal encoding policy transmits a 1-bit codeword once the process innovation passes one of two thresholds. The optimal decoder noiselessly recovers the last sample from the 1-bit codewords and codeword-generating time stamps, and uses it as the running estimate of the current process, until the next codeword arrives. In particular, we show the optimal causal code for the Ornstein-Uhlenbeck process and calculate its distortion-rate function
Exploiting timing information in event-triggered stabilization of linear systems with disturbances
In the same way that subsequent pauses in spoken language are used to convey
information, it is also possible to transmit information in communication
networks not only by message content, but also with its timing. This paper
presents an event-triggering strategy that utilizes timing information by
transmitting in a state-dependent fashion. We consider the stabilization of a
continuous-time, time-invariant, linear plant over a digital communication
channel with bounded delay and subject to bounded plant disturbances and
establish two main results. On the one hand, we design an encoding-decoding
scheme that guarantees a sufficient information transmission rate for
stabilization. On the other hand, we determine a lower bound on the information
transmission rate necessary for stabilization by any control policy
Analysis of Inter-Event Times in Linear Systems under Region-Based Self-Triggered Control
This paper analyzes the evolution of inter-event times (IETs) in linear
systems under region-based self-triggered control (RBSTC). In this control
method, the state space is partitioned into a finite number of conic regions
and each region is associated with a fixed IET. In this framework, studying the
steady state behavior of the IETs is equivalent to studying the existence of a
conic subregion that is positively invariant under the map that gives the
evolution of the state from one event to the next. We provide necessary
conditions and sufficient conditions for the existence of a positively
invariant subregion (PIS). We also provide necessary and sufficient conditions
for a PIS to be asymptotically stable. Indirectly, they provide necessary and
sufficient conditions for local convergence of IETs to a constant or to a given
periodic sequence. We illustrate the proposed method of analysis and results
through numerical simulations.Comment: arXiv admin note: text overlap with arXiv:2201.0209
Networked Control Under DoS Attacks:Tradeoffs Between Resilience and Data Rate
In this article, we study communication-constrained networked control problems for linear time-invariant systems in the presence of Denial-of-Service (DoS) attacks, namely attacks that prevent transmissions over the communication network. Our article aims at exploring the tradeoffs between system resilience and network bandwidth capacity. Given a class of DoS attacks, we characterize the bit-rate conditions that are dependent on the unstable eigenvalues of the dynamic matrix of the plant and the parameters of DoS attacks, under which exponential stability of the closed-loop system can be guaranteed. Our characterization clearly shows the tradeoffs between the communication bandwidth and resilience against DoS. An example is given to illustrate the proposed approach
Algorithms for Optimal Control with Fixed-Rate Feedback
We consider a discrete-time linear quadratic Gaussian networked control setting where the (full information) observer and controller are separated by a fixed-rate noiseless channel. The minimal rate required to stabilize such a system has been well studied. However, for a given fixed rate, how to quantize the states so as to optimize performance is an open question of great theoretical and practical significance. We concentrate on minimizing the control cost for first-order scalar systems. To that end, we use the Lloyd-Max algorithm and leverage properties of logarithmically-concave functions and sequential Bayesian filtering to construct the optimal quantizer that greedily minimizes the cost at every time instant. By connecting the globally optimal scheme to the problem of scalar successive refinement, we argue that its gain over the proposed greedy algorithm is negligible. This is significant since the globally optimal scheme is often computationally intractable. All the results are proven for the more general case of disturbances with logarithmically-concave distributions and rate-limited time-varying noiseless channels. We further extend the framework to event-triggered control by allowing to convey information via an additional "silent symbol", i.e., by avoiding transmitting bits; by constraining the minimal probability of silence we attain a tradeoff between the transmission rate and the control cost for rates below one bit per sample
Optimal Causal Rate-Constrained Sampling for a Class of Continuous Markov Processes
Consider the following communication scenario. An encoder observes a stochastic process and causally decides when and what to transmit about it, under a constraint on bits transmitted per second. A decoder uses the received codewords to causally estimate the process in real time. The encoder and the decoder are synchronized in time. We aim to find the optimal encoding and decoding policies that minimize the end-to-end estimation mean-square error under the rate constraint. For a class of continuous Markov processes satisfying regularity conditions, we show that the optimal encoding policy transmits a 1-bit codeword once the process innovation passes one of two thresholds. The optimal decoder noiselessly recovers the last sample from the 1-bit codewords and codeword-generating time stamps, and uses it as the running estimate of the current process, until the next codeword arrives. In particular, we show the optimal causal code for the Ornstein-Uhlenbeck process and calculate its distortion-rate function
Algorithms for Optimal Control with Fixed-Rate Feedback
We consider a discrete-time linear quadratic Gaussian networked control setting where the (full information) observer and controller are separated by a fixed-rate noiseless channel. The minimal rate required to stabilize such a system has been well studied. However, for a given fixed rate, how to quantize the states so as to optimize performance is an open question of great theoretical and practical significance. We concentrate on minimizing the control cost for first-order scalar systems. To that end, we use the Lloyd-Max algorithm and leverage properties of logarithmically-concave functions and sequential Bayesian filtering to construct the optimal quantizer that greedily minimizes the cost at every time instant. By connecting the globally optimal scheme to the problem of scalar successive refinement, we argue that its gain over the proposed greedy algorithm is negligible. This is significant since the globally optimal scheme is often computationally intractable. All the results are proven for the more general case of disturbances with logarithmically-concave distributions and rate-limited time-varying noiseless channels. We further extend the framework to event-triggered control by allowing to convey information via an additional "silent symbol", i.e., by avoiding transmitting bits; by constraining the minimal probability of silence we attain a tradeoff between the transmission rate and the control cost for rates below one bit per sample
Minimum Bitrate Neuromorphic Encoding for Continuous-Time Gauss-Markov Processes
In this work, we study minimum data rate tracking of a dynamical system under
a neuromorphic event-based sensing paradigm. We begin by bridging the gap
between continuous-time (CT) system dynamics and information theory's causal
rate distortion theory. We motivate the use of non-singular source codes to
quantify bitrates in event-based sampling schemes. This permits an analysis of
minimum bitrate event-based tracking using tools already established in the
control and information theory literature. We derive novel, nontrivial lower
bounds to event-based sensing, and compare the lower bound with the performance
of well-known schemes in the established literature