In this article, we establish a comprehensive theoretical framework for remote estimation in a networked system composed of a source that is observed by a sensor, a remote monitor that needs to estimate the state of the source in real time, and a communication channel that connects the source to the monitor. The source is a partially observable dynamical process, and the communication channel is a packet-erasure channel with feedback. We consider a novel communication model that captures implicit information. Our main objective is to identify the optimal strategies and the fundamental performance limits of the underlying system in the sense of a causal tradeoff between the packet rate and the mean square error when both forward and backward channels are unreliable. We characterise an optimal coding policy profile consisting of a scheduling policy for an encoder and an estimation policy for a decoder, collocated with the source and the monitor, respectively. We derive the recursive equations that must be solved online by the encoder and the decoder. In addition, we prove that the value function, originally defined over an expanding information set, admits a lower-dimensional representation depending only on two variables. We discuss the structural properties of the optimal policies, and analyse the computational complexity of an algorithm proposed for their computation. We then examine a range of special cases derived from our main theoretical results. We complement the theoretical results with a numerical analysis, and compare the performance of different remote estimation tasks in various operating regimes.

This paper proposes a dual-aspect semantic metric in the context of a cyber-physical system and investigates a scheduling problem where a sensor and a controller communicate over an unreliable channel. In this setting, the sensor observes the state of a source at each time, and according to a scheduling policy should determine whether to transmit a compressed sampled state, transmit the uncompressed sampled state, or remain idle. Upon receiving the transmitted information, the controller executes a control action aimed at stabilizing the system, such that the effectiveness of stabilization depends on the quality of the received sensory information. Our primary objective is to derive an optimal scheduling policy that optimizes system performance subject to resource constraints, when the performance is measured by a dual-aspect metric penalizing both the frequency of transitioning to undesirable states and the continuous duration of remaining in those states. We formulate this problem as a Markov decision process, and prove that the optimal solution is a multi-threshold scheduling policy.

Pragmatic or goal-oriented communication can optimize communication decisions beyond the reliable transmission of data, instead aiming at directly affecting application performance with the minimum channel utilization. In this paper, we develop a general theoretical framework for the remote control of finite-state Markov processes, using pragmatic communication over a costly zero-delay communication channel. To that end, we model a cyber-physical system composed of an encoder, which observes and transmits the states of a process in real-time, and a decoder, which receives that information and controls the behavior of the process. The encoder and the decoder should cooperatively optimize the trade-off between the control performance (i.e., reward) and the communication cost (i.e., channel use). This scenario underscores a pragmatic (i.e., goal-oriented) communication problem, where the purpose is to convey only the data that is most valuable for the underlying task, taking into account the state of the decoder (hence, the pragmatic aspect). We investigate two different decision-making architectures: in pull-based remote control, the decoder is the only decision-maker, while in push-based remote control, the encoder and the decoder constitute two independent decision-makers, leading to a multi-agent scenario. We propose three algorithms to optimize our system (i.e., design the encoder and the decoder policies), discuss the optimality guarantees ofs the algorithms, and shed light on their computational complexity and fundamental limits.

This paper investigates denial-of-service attacks on status updates in a binary networked control system. The physical system is abstracted as a Markovian source with two states: stable and unstable. The source sends status updates over an unreliable wireless channel to a remote controller in the presence of a malicious agent. Upon receiving a new status update, the controller sends back a control signal to stabilize the source if it is in the unstable state. The vulnerability of this system is measured by theage of physical instability—the duration the system remains in the unstable state. Our objective is to design jamming policies for the malicious agent that maximize this measure subject to energy constraints. We first present our results in a single-source scenario, and then extend them to a multi-source scenario. More specifically, we explore: (i) the optimal jamming policy that makes a balance between the system performance degradation and the adversary energy expenditure in a single-source scenario; and (ii) the optimal jamming policy that maximizes the aggregate system performance degradation by selectively jamming a subset of target channels in a multi-source scenario.

In this paper, we study the remote estimation of discrete-state Markov processes over costly point-to-point channels. We formulate this problem as an infinite-horizon optimization problem with two players, i.e., a sensor and a monitor, that have distinct information, and with a reward function that takes into account both the communication cost and the estimation quality. We show that the main challenge in solving this problem is associated with the consideration of implicit information, i.e., information that the monitor can obtain about the source when the sensor is idle. Our main objective is to develop a framework for finding exact or approximate solutions to this problem without neglecting implicit information a priori. To that end, we propose three different algorithms, and discuss their properties. The first one is an alternating optimization algorithm that converges to a Nash equilibrium. The second one optimizes both players’ policies jointly, and is guaranteed to find a globally optimal solution. The last one is a heuristic algorithm that can find a near-optimal solution. Finally, we compare the performance of these algorithms through a numerical analysis.

In this paper, we investigate denial-of-service attacks against status updating. The target system is modeled by a Markov chain along with an unreliable wireless channel, and the performance of status updating in this system is measured based on two metrics: age of information and age of incorrect information. Our objective is to devise optimal jamming policies that strike a balance between the system's performance deterioration and the adversary's energy expenditure. We model the optimal problem as a Markov decision process, and derive the optimal jamming policy. We prove rigorously that the optimal jamming policy is a threshold policy under both metrics. In addition, we provide a low-complexity algorithm for fining the optimal threshold value of the jamming policy. Our numerical results show that the networked system with the age-of-incorrect-information metric is less sensitive to jamming attacks than with the age-of-information metric.

We study feedback control of a dynamical process over a lossy channel equipped with a hybrid automatic repeat request protocol that connects a sensor to an actuator. The dynamical process is modeled by a Gauss-Markov process, and the lossy channel by a packet-erasure channel with ideal feedback. We suppose that data is communicated in the format of packets with negligible quantization error. In such a networked control system, whenever a packet loss occurs, there exists a tradeoff between transmitting new sensory information with a lower success probability and retransmitting previously failed sensory information with a higher success probability. In essence, an inherent tradeoff between freshness and reliability. To address this tradeoff, we consider a linear-quadratic-regulator performance index, which penalizes state deviations and control efforts over a finite horizon, and jointly design optimal policies for an encoder and a decoder, which are collocated with the sensor and the actuator, respectively. Our emphasis here lies specifically on designing switching and control policies, rather than error-correcting codes. We derive the structural properties of the optimal encoding and decoding policies. We show that the former is a threshold switching policy and the latter is a certainty-equivalent control policy. In addition, we specify the iterative equations that the encoder and the decoder need to solve in order to implement the optimal policies.

We study networked control of a dynamical process over a lossy channel with a hybrid automatic repeat request protocol that connects a sensor to an actuator. The dynamical process is modeled by a Gauss-Markov process, and the lossy channel by a packet-erasure channel with ideal feedback. We suppose that data is communicated in the format of packets with negligible quantization error. In such a networked control system, whenever a packet loss occurs, there exists a tradeoff between transmitting new sensory information with a lower success probability and retransmitting previously failed sensory information with a higher success probability. In essence, an inherent tradeoff between freshness and reliability. To address this tradeoff, we consider a linear-quadratic-regulator performance index, which penalizes state deviations and control efforts over a finite horizon, and jointly design optimal encoding and decoding policies for the encoder and the decoder, which are collocated with the sensor and the actuator, respectively. Our emphasis here lies specifically on designing switching and control policies, rather than error-correcting codes. We show that the optimal encoding policy is a threshold switching policy and the optimal decoding policy is a certainty-equivalent control policy. In addition, we determine the equations that the encoder and the decoder need to solve in order to implement the optimal policies. More specifically, we show that the encoder must solve the Kalman filtering equations, a mismatch linear equation, and a Bellman optimality equation, while the decoder must solve a linear filtering equation and an algebraic Riccati equation.