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  1. Although perception is an increasingly dominant portion of the overall computational cost for autonomous systems, only a fraction of the information perceived is likely to be relevant to the current task. To alleviate these perception costs, we develop a novel simultaneous perception–action design framework wherein an agent senses only the task-relevant information. This formulation differs from that of a partially observable Markov decision process, since the agent is free to synthesize not only its policy for action selection but also its belief-dependent observation function. The method enables the agent to balance its perception costs with those incurred by operating in its environment. To obtain a computationally tractable solution, we approximate the value function using a novel method of invariant finite belief sets, wherein the agent acts exclusively on a finite subset of the continuous belief space. We solve the approximate problem through value iteration in which a linear program is solved individually for each belief state in the set, in each iteration. Finally, we prove that the value functions, under an assumption on their structure, converge to their continuous state-space values as the sample density increases. 
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    Free, publicly-accessible full text available July 3, 2024
  2. Although perception is an increasingly dominant portion of the overall computational cost for autonomous systems, only a fraction of the information perceived is likely to be relevant to the current task. To alleviate these perception costs, we develop a novel simultaneous perception–action design framework wherein an agent senses only the task-relevant information. This formulation differs from that of a partially observable Markov decision process, since the agent is free to synthesize not only its policy for action selection but also its belief-dependent observation function. The method enables the agent to balance its perception costs with those incurred by operating in its environment. To obtain a computationally tractable solution, we approximate the value function using a novel method of invariant finite belief sets, wherein the agent acts exclusively on a finite subset of the continuous belief space. We solve the approximate problem through value iteration in which a linear program is solved individually for each belief state in the set, in each iteration. Finally, we prove that the value functions, under an assumption on their structure, converge to their continuous state-space values as the sample density increases. 
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    Free, publicly-accessible full text available July 3, 2024
  3. We propose an adaptive coding approach to achieve linear-quadratic-Gaussian (LQG) control with near- minimum bitrate prefix-free feedback. Our approach combines a recent analysis of a quantizer design for minimum rate LQG control with work on universal lossless source coding for sources on countable alphabets. In the aforementioned quantizer design, it was established that the quantizer outputs are an asymp- totically stationary, ergodic process. To enable LQG control with provably near-minimum bitrate, the quantizer outputs must be encoded into binary codewords efficiently. This is possible given knowledge of the probability distributions of the quantizer outputs, or of their limiting distribution. Obtaining such knowledge is challenging; the distributions do not readily admit closed form descriptions. This motivates the application of universal source coding. Our main theoretical contribution in this work is a proof that (after an invertible transformation), the quantizer outputs are random variables that fall within an exponential or power-law envelope class (depending on the plant dimension). Using ideas from universal coding on envelope classes, we develop a practical, zero-delay version of these algorithms that operates with fixed precision arithmetic. We evaluate the performance of this algorithm numerically, and demonstrate competitive results with respect to fundamental tradeoffs between bitrate and LQG control performance. 
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    Free, publicly-accessible full text available April 2, 2024
  4. In this work we consider discrete-time multiple-input multiple-output (MIMO) linear-quadratic-Gaussian (LQG) control where the feedback consists of variable length binary codewords. To simplify the decoder architecture, we enforce a strict prefix constraint on the codewords. We develop a data compression architecture that provably achieves a near minimum time-average expected bitrate for a fixed constraint on the LQG performance. The architecture conforms to the strict prefix constraint and does not require time-varying lossless source coding, in contrast to the prior art. 
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  5. We consider the scenario in which a continuous-time Gauss-Markov process is estimated by the Kalman-Bucy filter over a Gaussian channel (sensor) with a variable sensor gain. The problem of scheduling the sensor gain over a finite time interval to minimize the weighted sum of the data rate (the mutual information between the sensor output and the underlying Gauss-Markov process) and the distortion (the mean-square estimation error) is formulated as an optimal control problem. A necessary optimality condition for a scheduled sensor gain is derived based on Pontryagin’s minimum principle. For a scalar problem, we show that an optimal sensor gain control is of bang-bang type, except the possibility of taking an intermediate value when there exists a stationary point on the switching surface in the phase space of canonical dynamics. Furthermore, we show that the number of switches is at most two and the time instants at which the optimal gain must be switched can be computed from the analytical solutions to the canonical equations. 
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  6. In this letter, we consider a Linear Quadratic Gaussian (LQG) control system where feedback occurs over a noiseless binary channel and derive lower bounds on the minimum communication cost (quantified via the channel bitrate) required to attain a given control performance. We assume that at every time step an encoder can convey a packet containing a variable number of bits over the channel to a decoder at the controller. Our system model provides for the possibility that the encoder and decoder have shared randomness, as is the case in systems using dithered quantizers. We define two extremal prefix-free requirements that may be imposed on the message packets; such constraints are useful in that they allow the decoder, and potentially other agents to uniquely identify the end of a transmission in an online fashion. We then derive a lower bound on the rate of prefix-free coding in terms of directed information; in particular we show that a previously known bound still holds in the case with shared randomness. We generalize the bound for when prefix constraints are relaxed, and conclude with a rate-distortion formulation. 
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  7. We study the problem of synthesizing a controller that maximizes the entropy of a partially observable Markov decision process (POMDP) subject to a constraint on the expected total reward. Such a controller minimizes the predictability of an agent’s trajectories to an outside observer while guaranteeing the completion of a task expressed by a reward function. Focusing on finite-state controllers (FSCs) with deterministic memory transitions, we show that the maximum entropy of a POMDP is lower bounded by the maximum entropy of the parameteric Markov chain (pMC) induced by such FSCs. This relationship allows us to recast the entropy maximization problem as a so-called parameter synthesis problem for the induced pMC. We then present an algorithm to synthesize an FSC that locally maximizes the entropy of a POMDP over FSCs with the same number of memory states. In a numerical example, we highlight the benefit of using an entropy-maximizing FSC compared with an FSC that simply finds a feasible policy for accomplishing a task. 
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  8. This article presents a new method to solve a dynamic sensor fusion problem. We consider a large number of remote sensors which measure a common Gauss–Markov process. Each sensor encodes and transmits its measurement to a data fusion center through a resource restricted communication network. The communication cost incurred by a given sensor is quantified as the expected bitrate from the sensor to the fusion center. We propose an approach that attempts to minimize a weighted sum of these communication costs subject to a constraint on the state estimation error at the fusion center. We formulate the problem as a difference-of-convex program and apply the convex-concave procedure (CCP) to obtain a heuristic solution. We consider a 1D heat transfer model and a model for 2D target tracking by a drone swarm for numerical studies. Through these simulations, we observe that our proposed approach has a tendency to assign zero data rate to unnecessary sensors indicating that our approach is sparsity-promoting, and an effective sensor selection heuristic. 
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  9. In this article, we revisit the sequential source-coding framework to analyze fundamental performance limitations of discrete-time stochastic control systems subject to feedback data-rate constraints in finite-time horizon. The basis of our results is a new characterization of the lower bound on the minimum total-rate achieved by sequential codes subject to a total (across time) distortion constraint and a computational algorithm that allocates optimally the rate-distortion, for a given distortion level, at each instant of time and any fixed finite-time horizon. The idea behind this characterization facilitates the derivation of analytical , nonasymptotic , and finite-dimensional lower and upper bounds in two control-related scenarios: a) A parallel time-varying Gauss–Markov process with identically distributed spatial components that are quantized and transmitted through a noiseless channel to a minimum mean-squared error decoder; and b) a time-varying quantized linear quadratic Gaussian (LQG) closed-loop control system, with identically distributed spatial components and with a random data-rate allocation. Our nonasymptotic lower bound on the quantized LQG control problem reveals the absolute minimum data-rates for (mean square) stability of our time-varying plant for any fixed finite-time horizon. We supplement our framework with illustrative simulation experiments. 
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