Ling Shi

Xiaoqiang Ren, Junfeng Wu, Karl H. Johansson et al.

Jointly optimal transmission power control and remote estimation over an infinite horizon is studied. A sensor observes a dynamic process and sends its observations to a remote estimator over a wireless fading channel characterized by a time-homogeneous Markov chain. The successful transmission probability depends on both the channel gains and the transmission power used by the sensor. The transmission power control rule and the remote estimator should be jointly designed, aiming to minimize an infinite-horizon cost consisting of the power usage and the remote estimation error. A first question one may ask is: Does this joint optimization problem have a solution? We formulate the joint optimization problem as an average cost belief-state Markov decision process and answer the question by proving that there exists an optimal deterministic and stationary policy. We then show that when the monitored dynamic process is scalar, the optimal remote estimates depend only on the most recently received sensor observation, and the optimal transmission power is symmetric and monotonically increasing with respect to the innovation error.

Shuang Wu, Xiaoqiang Ren, Qing-Shan Jia et al.

We consider optimal sensor scheduling with unknown communication channel statistics. We formulate two types of scheduling problems with the communication rate being a soft or hard constraint, respectively. We first present some structural results on the optimal scheduling policy using dynamic programming and assuming the channel statistics is known. We prove that the Q-factor is monotonic and submodular, which leads to the threshold-like structures in both types of problems. Then we develop a stochastic approximation and parameter learning frameworks to deal with the two scheduling problems with unknown channel statistics. We utilize their structures to design specialized learning algorithms. We prove the convergence of these algorithms. Performance improvement compared with the standard Q-learning algorithm is shown through numerical examples.

Alex S. Leong, Arunselvan Ramaswamy, Daniel E. Quevedo et al.

In many Cyber-Physical Systems, we encounter the problem of remote state estimation of geographically distributed and remote physical processes. This paper studies the scheduling of sensor transmissions to estimate the states of multiple remote, dynamic processes. Information from the different sensors have to be transmitted to a central gateway over a wireless network for monitoring purposes, where typically fewer wireless channels are available than there are processes to be monitored. For effective estimation at the gateway, the sensors need to be scheduled appropriately, i.e., at each time instant one needs to decide which sensors have network access and which ones do not. To address this scheduling problem, we formulate an associated Markov decision process (MDP). This MDP is then solved using a Deep Q-Network, a recent deep reinforcement learning algorithm that is at once scalable and model-free. We compare our scheduling algorithm to popular scheduling algorithms such as round-robin and reduced-waiting-time, among others. Our algorithm is shown to significantly outperform these algorithms for many example scenarios.

Xingkang He, Chen Hu, Yiguang Hong et al.

In this paper, we investigate a distributed estimation problem for multi-agent systems with state equality constraints (SEC). First, under a time-based consensus communication protocol, applying a modified projection operator and the covariance intersection fusion method, we propose a distributed Kalman filter with guaranteed consistency and satisfied SEC. Furthermore, we establish the relationship between consensus step, SEC and estimation error covariance in dynamic and steady processes, respectively. Employing a space decomposition method, we show the error covariance in the constraint set can be arbitrarily small by setting a sufficiently large consensus step. Besides, we propose an extended collective observability (ECO) condition based on SEC, which is milder than existing observability conditions. Under the ECO condition, through utilizing a technique of matrix approximation, we prove the boundedness of error covariance and the exponentially asymptotic unbiasedness of state estimate, respectively. Moreover, under the ECO condition for linear time-invariant systems with SEC, we provide a novel event-triggered communication protocol by employing the consistency, and give an offline design principle of triggering thresholds with guaranteed boundedness of error covariance. More importantly, we quantify and analyze the communication rate for the proposed event-triggered distributed Kalman filter, and provide optimization based methods to obtain the minimal (maximal) successive non-triggering (triggering) times. Two simulations are provided to demonstrate the developed theoretical results and the effectiveness of the filters.

Junfeng Wu, Ling Shi, Lihua Xie et al.

In this paper, we consider the peak-covariance stability of Kalman filtering subject to packet losses. The length of consecutive packet losses is governed by a time-homogeneous finite-state Markov chain. We establish a sufficient condition for peak-covariance stability and show that this stability check can be recast as a linear matrix inequality (LMI) feasibility problem. Comparing with the literature, the stability condition given in this paper is invariant with respect to similarity state transformations; moreover, our condition is proved to be less conservative than the existing results. Numerical examples are provided to demonstrate the effectiveness of our result.

Shuang Wu, Kemi Ding, Peng Cheng et al.

This work considers the sensor scheduling for multiple dynamic processes. We consider $n$ linear dynamic processes, the state of each process is measured by a sensor, which transmits their local state estimates over wireless channels to a remote estimator with certain communication costs. In each time step, only a portion of the sensors is allowed to transmit data to the remote estimator and the packet might be lost due to unreliability of the wireless channels. Our goal is to find a scheduling policy which coordinates the sensors in a centralized manner to minimize the total expected estimation error of the remote estimator and the communication costs. We formulate the problem as a Markov decision process. We develop an algorithm to check whether there exists a deterministic stationary optimal policy. We show the optimality of monotone policies, which saves computational effort of finding an optimal policy and facilitates practical implementation. Nevertheless, obtaining an exact optimal policy still suffers from curse of dimensionality when the number of processes are large. We further provide an index-based heuristics to avoid brute force computation. Numerical examples are presented to illustrate our theoretical results.

Ye Yuan, Ling Shi, Jun Liu et al.

Fueled by applications in sensor networks, these years have witnessed a surge of interest in distributed estimation and filtering. A new approach is hereby proposed for the Distributed Kalman Filter (DKF) by integrating a local covariance computation scheme. Compared to existing well-established DKF methods, the virtue of the present approach lies in accelerating the convergence of the state estimates to those of the Centralized Kalman Filter (CKF). Meanwhile, an algorithm is proposed that allows each node to compute the averaged measurement noise covariance matrix within a minimal discrete-time running steps in a distributed way. Both theoretical analysis and extensive numerical simulations are conducted to show the feasibility and superiority of the proposed method.

Shuang Wu, Xiaoqiang Ren, Subhrakanti Dey et al.

This paper considers the problem of sensory data scheduling of multiple processes. There are $n$ independent linear time-invariant processes and a remote estimator monitoring all the processes. Each process is measured by a sensor, which sends its local state estimate to the remote estimator. The sizes of the packets are different due to different dimensions of each process, and thus it may take different lengths of time steps for the sensors to send their data. Because of bandwidth limitation, only a portion of all the sensors are allowed to transmit. Our goal is to minimize the average of estimation error covariance of the whole system at the remote estimator. The problem is formulated as a Markov decision process (MDP) with average cost over an infinite time horizon. We prove the existence of a deterministic and stationary policy for the problem. We also find that the optimal policy has a consistent behavior and threshold type structure. A numerical example is provided to illustrate our main results.

Shuang Wu, Xiaoqiang Ren, Yiguang Hong et al.

We consider the design of a fair sensor schedule for a number of sensors monitoring different linear time-invariant processes. The largest average remote estimation error among all processes is to be minimized. We first consider a general setup for the max-min fair allocation problem. By reformulating the problem as its equivalent form, we transform the fair resource allocation problem into a zero-sum game between a "judge" and a resource allocator. We propose an equilibrium seeking procedure and show that there exists a unique Nash equilibrium in pure strategy for this game. We then apply the result to the sensor scheduling problem and show that the max-min fair sensor scheduling policy can be achieved.

Lingying Huang, Alex S. Leong, Daniel E. Quevedo et al.

In this paper, we consider a remote state estimation problem in the presence of an eavesdropper. A smart sensor takes measurement of a discrete linear time-invariant (LTI) process and sends its local state estimate through a wireless network to a remote estimator. An eavesdropper can overhear the sensor transmissions with a certain probability. To enhance the system privacy level, we propose a novel encryption strategy to minimize a linear combination of the expected error covariance at the remote estimator and the negative of the expected error covariance at the eavesdropper, taking into account the cost of the encryption process. We prove the existence of an optimal deterministic and Markovian policy for such an encryption strategy over a finite time horizon. Two situations, namely, with or without knowledge of the eavesdropper estimation error covariance are studied and the optimal schedule is shown to satisfy the threshold-like structure in both cases. Numerical examples are given to illustrate the results.

Jianping He, Lin Cai, Peng Cheng et al.

Privacy-preserving data aggregation in ad hoc networks is a challenging problem, considering the distributed communication and control requirement, dynamic network topology, unreliable communication links, etc. Different from the widely used cryptographic approaches, in this paper, we address this challenging problem by exploiting the distributed consensus technique. We first propose a secure consensus-based data aggregation (SCDA) algorithm that guarantees an accurate sum aggregation while preserving the privacy of sensitive data. Then, we prove that the proposed algorithm converges accurately and is $(ε, σ)$-data-privacy, and the mathematical relationship between $ε$ and $σ$ is provided. Extensive simulations have shown that the proposed algorithm has high accuracy and low complexity, and they are robust against network dynamics.

Shide Zhou, Kailong Wang, Ling Shi et al.

The widespread adoption of Large Language Models (LLMs) in critical applications has introduced severe reliability and security risks, as LLMs remain vulnerable to notorious threats such as hallucinations, jailbreak attacks, and backdoor exploits. These vulnerabilities have been weaponized by malicious actors, leading to unauthorized access, widespread misinformation, and compromised LLM-embedded system integrity. In this work, we introduce a novel approach to detecting abnormal behaviors in LLMs via hidden state forensics. By systematically inspecting layer-specific activation patterns, we develop a general framework that can efficiently identify a range of security threats in real-time without imposing prohibitive computational costs. Extensive experiments indicate detection accuracies exceeding 95% and consistently robust performance across multiple models in most scenarios, while preserving the ability to detect novel attacks effectively. Furthermore, the computational overhead remains minimal, with detector inference taking merely fractions of a second. The significance of this work lies in proposing a promising strategy to reinforce the security of LLM-integrated systems, paving the way for safer and more reliable deployment in high-stakes domains. By enabling real-time detection that can also support the mitigation of abnormal behaviors, it represents a meaningful step toward ensuring the trustworthiness of AI systems amid rising security challenges.

Yuqing Ni, Alex S. Leong, Daniel E. Quevedo et al.

We consider pricing and selection with fading channels in a Stackelberg game framework. A channel server decides the channel prices and a client chooses which channel to use based on the remote estimation quality. We prove the existence of an optimal deterministic and Markovian policy for the client, and show that the optimal policies of both the server and the client have threshold structures when the time horizon is finite. Value iteration algorithm is applied to obtain the optimal solutions for both the server and client, and numerical simulations and examples are given to demonstrate the developed result.

Shilei Li, Lijing Li, Dawei Shi et al.

This paper presents two computationally efficient algorithms for the orientation estimation of inertial measurement units (IMUs): the correntropy-based gradient descent (CGD) and the correntropy-based decoupled orientation estimation (CDOE). Traditional methods, such as gradient descent (GD) and decoupled orientation estimation (DOE), rely on the mean squared error (MSE) criterion, making them vulnerable to external acceleration and magnetic interference. To address this issue, we demonstrate that the multi-kernel correntropy loss (MKCL) is an optimal objective function for maximum likelihood estimation (MLE) when the noise follows a type of heavy-tailed distribution. In certain situations, the estimation error of the MKCL is bounded even in the presence of arbitrarily large outliers. By replacing the standard MSE cost function with MKCL, we develop the CGD and CDOE algorithms. We evaluate the effectiveness of our proposed methods by comparing them with existing algorithms in various situations. Experimental results indicate that our proposed methods (CGD and CDOE) outperform their conventional counterparts (GD and DOE), especially when faced with external acceleration and magnetic disturbances. Furthermore, the new algorithms demonstrate significantly lower computational complexity than Kalman filter-based approaches, making them suitable for applications with low-cost microprocessors.

Yuxing Zhong, Yuzhe Li, Daniel E. Quevedo et al.

This paper considers the optimal power allocation of a jamming attacker against remote state estimation. The attacker is self-sustainable and can harvest energy from the environment to launch attacks. The objective is to carefully allocate its attack power to maximize the estimation error at the fusion center. Regarding the attacker's knowledge of the system, two cases are discussed: (i) perfect channel knowledge and (ii) unknown channel model. For both cases, we formulate the problem as a Markov decision process (MDP) and prove the existence of an optimal deterministic and stationary policy. Moreover, for both cases, we develop algorithms to compute the allocation policy and demonstrate that the proposed algorithms for both cases converge to the optimal policy as time goes to infinity. Additionally, the optimal policy exhibits certain structural properties that can be leveraged to accelerate both algorithms. Numerical examples are given to illustrate the main results.

Fan Zhang, Vincent K. N. Lau, Ling Shi

In this paper, we consider a networked control system (NCS) in which an dynamic plant system is connected to a controller via a temporally correlated wireless fading channel. We focus on communication power design at the sensor to minimize a weighted average state estimation error at the remote controller subject to an average transmit power constraint of the sensor. The power control optimization problem is formulated as an infinite horizon average cost Markov decision process (MDP). We propose a novel continuous-time perturbation approach and derive an asymptotically optimal closed-form value function for the MDP. Under this approximation, we propose a low complexity dynamic power control solution which has an event- driven control structure. We also establish technical conditions for asymptotic optimality, and sufficient conditions for NCS stability under the proposed scheme.

Zihao Xu, Yi Liu, Gelei Deng et al.

Security concerns for large language models (LLMs) have recently escalated, focusing on thwarting jailbreaking attempts in discrete prompts. However, the exploration of jailbreak vulnerabilities arising from continuous embeddings has been limited, as prior approaches primarily involved appending discrete or continuous suffixes to inputs. Our study presents a novel channel for conducting direct attacks on LLM inputs, eliminating the need for suffix addition or specific questions provided that the desired output is predefined. We additionally observe that extensive iterations often lead to overfitting, characterized by repetition in the output. To counteract this, we propose a simple yet effective strategy named CLIP. Our experiments show that for an input length of 40 at iteration 1000, applying CLIP improves the ASR from 62% to 83%

Huiwen Yang, Lingying Huang, Subhrakanti Dey et al.

In recent years, over-the-air aggregation has been widely considered in large-scale distributed learning, optimization, and sensing. In this paper, we propose the over-the-air federated policy gradient algorithm, where all agents simultaneously broadcast an analog signal carrying local information to a common wireless channel, and a central controller uses the received aggregated waveform to update the policy parameters. We investigate the effect of noise and channel distortion on the convergence of the proposed algorithm, and establish the complexities of communication and sampling for finding an $ε$-approximate stationary point. Finally, we present some simulation results to show the effectiveness of the algorithm.

Wei Huo, Changxin Liu, Kemi Ding et al.

This paper investigates the use of the cubic-regularized Newton method within a federated learning framework while addressing two major concerns that commonly arise in federated learning: privacy leakage and communication bottleneck. We introduce a federated learning algorithm called Differentially Private Federated Cubic Regularized Newton (DP-FCRN). By leveraging second-order techniques, our algorithm achieves lower iteration complexity compared to first-order methods. We also incorporate noise perturbation during local computations to ensure privacy. Furthermore, we employ sparsification in uplink transmission, which not only reduces the communication costs but also amplifies the privacy guarantee. Specifically, this approach reduces the necessary noise intensity without compromising privacy protection. We analyze the convergence properties of our algorithm and establish the privacy guarantee. Finally, we validate the effectiveness of the proposed algorithm through experiments on a benchmark dataset.

Xiaoxu Lyu, Guanghui Wen, Yuezu Lv et al.

This paper proposes a novel consensus-based distributed filter over directed graphs under the collectively observability condition. The distributed filter is designed using an augmented leader-following information fusion strategy, and the gain parameter is determined exclusively using local information. Additionally, the lower bound of the fusion step number is derived to ensure that the estimation error covariance remains uniformly upper-bounded. Furthermore, the lower bounds for the convergence rates of the steady-state performance gap between the proposed filter and the centralized filter are provided as the fusion step number approaches infinity. The analysis demonstrates that the convergence rate is at least as fast as exponential convergence, provided the communication topology satisfies the spectral norm condition. Finally, the theoretical results are validated through two simulation examples.

Lingying Huang, Xiaomeng Chen, Wei Huo et al.

In this paper, we surveyed the existing literature studying different approaches and algorithms for the four critical components in the general branch and bound (B&B) algorithm, namely, branching variable selection, node selection, node pruning, and cutting-plane selection. However, the complexity of the B&B algorithm always grows exponentially with respect to the increase of the decision variable dimensions. In order to improve the speed of B&B algorithms, learning techniques have been introduced in this algorithm recently. We further surveyed how machine learning can be used to improve the four critical components in B&B algorithms. In general, a supervised learning method helps to generate a policy that mimics an expert but significantly improves the speed. An unsupervised learning method helps choose different methods based on the features. In addition, models trained with reinforcement learning can beat the expert policy, given enough training and a supervised initialization. Detailed comparisons between different algorithms have been summarized in our survey. Finally, we discussed some future research directions to accelerate and improve the algorithms further in the literature.

Yik Ben Wong, Yawen Chen, Kam Fai Elvis Tsang et al.

Recently, the lower limb exoskeletons which providemobility for paraplegic patients to support their daily life havedrawn much attention. However, the pilots are required to applyexcessive force through a pair of crutches to maintain balanceduring walking. This paper proposes a novel gait trajectorygeneration algorithm for exoskeleton locomotion on flat groundand stair which aims to minimize the force applied by the pilotwithout increasing the degree of freedom (DoF) of the system.First, the system is modelled as a five-link mechanism dynam-ically for torque computing. Then, an optimization approachis used to generate the trajectory minimizing the ankle torquewhich is correlated to the supporting force. Finally, experimentis conducted to compare the different gait generation algorithmsthrough measurement of ground reaction force (GRF) appliedon the crutches

Wulin Zou, Pu Duan, Yawen Chen et al.

Variable impedance control is advantageous for physical human-robot interaction to improve safety, adaptability and many other aspects. This paper presents a gain-scheduled variable stiffness control approach under strict frequency-domain constraints. Firstly, to reduce conservativeness, we characterize and constrain the impedance rendering, actuator saturation, disturbance/noise rejection and passivity requirements into their specific frequency bands. This relaxation makes sense because of the restricted frequency properties of the interactive robots. Secondly, a gain-scheduled method is taken to regulate the controller gains with respect to the desired stiffness. Thirdly, the scheduling function is parameterized via a nonsmooth optimization method. Finally, the proposed approach is validated by simulations, experiments and comparisons with a gain-fixed passivity-based PID method.

Ziyang Guo, Yuqing Ni, Wing Shing Wong et al.

We consider time synchronization attack against multi-system scheduling in a remote state estimation scenario where a number of sensors monitor different linear dynamical processes and schedule their transmissions through a shared collision channel. We show that by randomly injecting relative time offsets on the sensors, the malicious attacker is able to make the expected estimation error covariance of the overall system diverge without any system knowledge. For the case that the attacker has full system information, we propose an efficient algorithm to calculate the optimal attack, which spoofs the least number of sensors and leads to unbounded average estimation error covariance. To mitigate the attack consequence, we further propose a countermeasure by constructing shift invariant transmission policies and characterize the lower and upper bounds for system estimation performance. Simulation examples are provided to illustrate the obtained results.

Jiahu Qin, Jie Wang, Ling Shi et al.

This paper is concerned with developing a novel distributed Kalman filtering algorithm over wireless sensor networks based on randomized consensus strategy. Compared with the centralized algorithm, distributed filtering techniques require less computation per sensor and lead to more robust estimation since they simply use the information from the neighboring nodes in the network. However, poor local sensor estimation caused by limited observability and network topology changes which interfere the global consensus are challenging issues. Motivated by this observation, we propose a novel randomized gossip-based distributed Kalman filtering algorithm. Information exchange and computation in the proposed algorithm can be carried out in an arbitrarily connected network of nodes. In addition, the computational burden can be distributed for a sensor which communicates with a stochastically selected neighbor at each clock step under schemes of gossip algorithm. In this case, the error covariance matrix changes stochastically at every clock step, thus the convergence is considered in a probabilistic sense. We provide the mean square convergence analysis of the proposed algorithm. Under a sufficient condition, we show that the proposed algorithm is quite appealing as it achieves better mean square error performance theoretically than the noncooperative decentralized Kalman filtering algorithm. Besides, considering the limited computation, communication, and energy resources in the wireless sensor networks, we propose an optimization problem which minimizes the average expected state estimation error based on the proposed algorithm. To solve the proposed problem efficiently, we transform it into a convex optimization problem. And a sub-optimal solution is attained. Examples and simulations are provided to illustrate the theoretical results.

Jiahu Qin, Menglin Li, Ling Shi et al.

We consider a scenario in which a DoS attacker with the limited power resource jams a wireless network through which the packet from a sensor is sent to a remote estimator to estimate the system state. To degrade the estimation quality with power constraint, the attacker aims to solve how much power to obstruct the channel each time, which is the recently proposed optimal attack energy management problem. The existing works are built on an ideal link model in which the packet dropout never occurs without attack. To encompass wireless transmission losses, we introduce the SINR-based link. First, we focus on the case when the attacker employs the constant power level. To maximize the terminal error at the remote estimator, we provide some sufficient conditions for the existence of an explicit solution to the optimal static attack energy management problem and the solution is constructed. Compared with the existing result in which corresponding sufficient conditions work only when the system matrix is normal, the obtained conditions in this paper are viable for a general system and shown to be more relaxed. For the other system index, the average error, the associated sufficient conditions are also derived based on different analysis with the existing work. And a feasible method is presented for both indexes when the system cannot meet the sufficient conditions. Then when the real-time ACK information can be acquired, an MDP based algorithm is designed to solve the optimal dynamic attack energy management problem. We further study the optimal tradeoff between attack power and system degradation. By moving power constraint into the objective function to maximize system index and minimize energy consumption, the other MDP based algorithm is proposed to find the optimal attack policy which is further shown to have a monotone structure. The theoretical results are illustrated by simulations.

Kemi Ding, Subhrakanti Dey, Daniel E. Quevedo et al.

This paper studies remote state estimation under denial-of-service (DoS) attacks. A sensor transmits its local estimate of an underlying physical process to a remote estimator via a wireless communication channel. A DoS attacker is capable to interfere the channel and degrades the remote estimation accuracy. Considering the tactical jamming strategies played by the attacker, the sensor adjusts its transmission power. This interactive process between the sensor and the attacker is studied in the framework of a zero-sum stochastic game. To derive their optimal power schemes, we first discuss the existence of stationary Nash equilibrium (SNE) for this game. We then present the monotone structure of the optimal strategies, which helps reduce the computational complexity of the stochastic game algorithm. Numerical examples are provided to illustrate the obtained results.

Xiaoqiang Ren, Junfeng Wu, Subhrakanti Dey et al.

This paper considers optimal attack attention allocation on remote state estimation in multi-systems. Suppose there are $\mathtt{M}$ independent systems, each of which has a remote sensor monitoring the system and sending its local estimates to a fusion center over a packet-dropping channel. An attacker may generate noises to exacerbate the communication channels between sensors and the fusion center. Due to capacity limitation, at each time the attacker can exacerbate at most $\mathtt{N}$ of the $\mathtt{M}$ channels. The goal of the attacker side is to seek an optimal policy maximizing the estimation error at the fusion center. The problem is formulated as a Markov decision process (MDP) problem, and the existence of an optimal deterministic and stationary policy is proved. We further show that the optimal policy has a threshold structure, by which the computational complexity is reduced significantly. Based on the threshold structure, a myopic policy is proposed for homogeneous models and its optimality is established. To overcome the curse of dimensionality of MDP algorithms for general heterogeneous models, we further provide an asymptotically (as $\mathtt{M}$ and $\mathtt{N}$ go to infinity) optimal solution, which is easy to compute and implement. Numerical examples are given to illustrate the main results.

Junfeng Wu, Yuzhe Li, Daniel E. Quevedo et al.

We consider sensor transmission power control for state estimation, using a Bayesian inference approach. A sensor node sends its local state estimate to a remote estimator over an unreliable wireless communication channel with random data packet drops. As related to packet dropout rate, transmission power is chosen by the sensor based on the relative importance of the local state estimate. The proposed power controller is proved to preserve Gaussianity of local estimate innovation, which enables us to obtain a closed-form solution of the expected state estimation error covariance. Comparisons with alternative non data-driven controllers demonstrate performance improvement using our approach.

Xiaoqiang Ren, Jiming Chen, Karl H. Johansson et al.

The problem of quickest change detection with a wireless sensor node is studied in this paper. The sensor that is deployed to monitor the environment has limited energy constraint to the classical quickest change detection problem. We consider the "censoring" strategy at the sensor side, i.e., the sensor selectively sends its observations to the decision maker. The quickest change detection problem is formulated in a minimax way. In particular, our goal is to find the optimal censoring strategy and stopping time such that the detection delay is minimized subject to constraints on both average run length (ARL) and average energy cost before the change. We show that the censoring strategy that has the maximal post-censoring Kullback-Leibler (K-L) divergence coupled with Cumulative Sum (CuSum) and Shiryaev-Roberts-Pollak (SRP) detection procedure is asymptotically optimal for the Lorden's and Pollak's problem as the ARL goes to infinity, respectively. We also show that the asymptotically optimal censoring strategy should use up the available energy and has a very special structure, i.e., the likelihood ratio of the no send region is a single interval, which can be utilized to significantly reduce the computational complexity. Numerical examples are shown to illustrate our results.