Minimax Robust Decentralized Hypothesis Testing for Parallel Sensor Networks

Min-max Model Predictive Control of Nonlinear Systems: A Unifying Overview on Stability

We discuss two, in a sense extreme, kinds of nondeterministic rules in decision tables. The first kind of rules, called as inhibitory rules, are blocking only one decision value (i.e., they have all but one decisions from all possible decisions on their right hand sides). Contrary to this, any rule of the second kind, called as a bounded nondeterministic rule, can have on the right hand side only a few decisions. We show that both kinds of rules can be used for improving the quality of classification. In the paper, two lazy classification algorithms of polynomial time complexity are considered. These algorithms are based on deterministic and inhibitory decision rules, but the direct generation of rules is not required. Instead of this, for any new object the considered algorithms extract from a given decision table efficiently some information about the set of rules. Next, this information is used by a decision-making procedure. The reported results of experiments show that the algorithms based on inhibitory decision rules are often better than those based on deterministic decision rules. We also present an application of bounded nondeterministic rules in construction of rule based classifiers. We include the results of experiments showing that by combining rule based classifiers based on minimal decision rules with bounded nondeterministic rules having confidence close to 1 and sufficiently large support, it is possible to improve the classification quality.

MPC for stable linear systems with model uncertainty

This paper considers a Kullback-Leibler distance (KLD) which is asymptotically equivalent to the KLD by Goutis and Robert [1] when the reference model (in comparison to a competing fitted model) is correctly specified and that certain regularity conditions hold true (ref. Akaike [2]). We derive the asymptotic property of this Goutis-Robert-Akaike KLD under certain regularity conditions. We also examine the impact of this asymptotic property when the regularity conditions are partially satisfied. Furthermore, the connection between the Goutis-Robert-Akaike KLD and a weighted posterior predictive p-value (WPPP) is established. Finally, both the Goutis-Robert-Akaike KLD and WPPP are applied to compare models using various simulated examples as well as two cohort studies of diabetes.

Since the 2008 global economic crisis, the detection of financial instabilities has garnered extensive research attention, particularly through the application of time-series analysis. In this study, a novel time-series analysis method, integrating the Kullback-Leibler Divergence (KLD) metric with a sliding window technique, is proposed to detect instabilities in time-series data, especially in financial markets. Global financial time series from 2004 to 2022 were analyzed. The raw time series were preprocessed into return rate series and transformed into complex networks using the directed horizontal visibility graph (DHVG) algorithm, effectively preserving temporal variabilities in network topologies. The KLD method was evaluated through both retrospective analysis and real-time monitoring. It successfully identified idiosyncratic incidents in the financial market, correlating them with specific economic events. Compared to traditional metrics (e.g., moments) and econometric methods, KLD demonstrated superior performance in capturing sequence information and detecting anomalies without requiring linear regression models. Although initially designed for financial data, the KLD method is versatile and can be applied to other types of time series as well.

We consider a parallel decentralized detection system employing a bank of local detectors (LDs) to access a commonly-observed phenomenon. The system makes a binary decision about the phenomenon, accepting one of two hypotheses (H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> (“absent” ) or H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> (“present” )). The kth LD uses a local decision rule to compress its local observations y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> into a binary local decision u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> ; u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> =0 if the kth LD accepts H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> and u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> = 1 accepts H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> . The kth LD sends its decision u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> over a noiseless dedicated channel to a Data Fusion Center (DFC). The DFC combines the local decisions it receives from n LDs (u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ,u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ,...,u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> ) into a single binary global decision u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> (u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0=</sub> 0 for accepting H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> or u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> =1 for accepting H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ). If each LD uses a single deterministic local decision rule (calculating u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> from the local observations y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> ) and the DFC uses a single deterministic global decision rule (calculating u <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> from n local decisions), the team receiver operating characteristic (ROC) curve is in general non-concave. The system's performance under a Neyman-Pearson criterion may then be suboptimal in the sense that a mixed strategy may yield a higher probability of detection when the probability of false alarm is constrained not to exceed a certain value, α>0. Specifically, a “dependent randomization” detection scheme can be applied in certain circumstances to improve the system's performance by making the ROC curve concave. This scheme requires a coordinated and synchronized action between the DFC and the LDs. In this study, we specify when dependent randomization is needed, and discuss the proper response of the detection system if synchronization between the LDs and the DFC is temporarily lost.

We investigate the impact of Byzantine attacks in distributed detection under binary hypothesis testing. It is assumed that a fraction of the transmitted sensor measurements are compromised by the injected data from a Byzantine attacker, whose purpose is to confuse the decision maker at the fusion center. From the perspective of a Byzantine attacker, under the injection energy constraint, an optimization problem is formulated to maximize the asymptotic missed detection error probability, which is based on the Kullback-Leibler divergence. The properties of the optimal attack strategy are analyzed by convex optimization and parametric optimization methods. Based on the derived theoretic results, a coordinate descent algorithm is proposed to search the optimal attack solution. Simulation examples are provided to illustrate the effectiveness of the obtained attack strategy.

This work investigates the attack strategy design problem of the false data injection attack against the cyber-physical system. Distinct from the relevant results which utilise the current intercepted data or additionally consider side information, a more universal attack model is proposed which combines historical data and side information with the current intercepted data to synergistically deteriorate the system estimation performance. In order to quantify the impact resulting from the proposed attack strategy, the optimisation objective is characterised by deriving the error covariance matrix under the attacks, which becomes more intricate since the proposed attack model introduces more decision variables and coupled terms. Take the stealthiness which is characterised by Kullback-Leibler divergence as the constraints, the problem investigated in this work is equivalently transformed into the constrained multi-variable non-convex optimisation problems, which are not able to be solved directly by the methods in the relevant results. By utilising the Lagrange multiplier method, the structural characteristic of the optimal mean and the optimal covariance which only related to the Lagrange multiplier are derived, such that the optimal distribution of the modified innovation is able to be obtained by a simple search procedure. Following that, the design of the optimal attack strategy is completed by using semi-definite programming to derive the optimal attack matrices. Finally, the simulation examples are given such that the validity of the results is verified.

In this paper, we study the metric distortion of deterministic social choice rules that choose a winning candidate from a set of candidates based on voter preferences. Voters and candidates are located in an underlying metric space. A voter has cost equal to her distance to the winning candidate. Ordinal social choice rules only have access to the ordinal preferences of the voters that are assumed to be consistent with the metric distances. Our goal is to design an ordinal social choice rule with minimum distortion, which is the worst-case ratio, over all consistent metrics, between the social cost of the rule and that of the optimal omniscient rule with knowledge of the underlying metric space. The distortion of the best deterministic social choice rule was known to be between $3$ and $5$. It had been conjectured that any rule that only looks at the weighted tournament graph on the candidates cannot have distortion better than $5$. In our paper, we disprove it by presenting a weighted tournament rule with distortion of $4.236$. We design this rule by generalizing the classic notion of uncovered sets, and further show that this class of rules cannot have distortion better than $4.236$. We then propose a new voting rule, via an alternative generalization of uncovered sets. We show that if a candidate satisfying the criterion of this voting rule exists, then choosing such a candidate yields a distortion bound of $3$, matching the lower bound. We present a combinatorial conjecture that implies distortion of $3$, and verify it for small numbers of candidates and voters by computer experiments. Using our framework, we also show that selecting any candidate guarantees distortion of at most $3$ when the weighted tournament graph is cyclically symmetric.

We consider a binary parallel decentralized detection system. It employs n local detectors (LDs) to observe a binary phenomenon in order to accept one of two hypotheses about the phenomenon (hypothesis H 0 or hypothesis H 1 ). Each LD uses a local decision rule to compress its local observations into a binary local decision. The Data Fusion Center (DFC) uses a fusion rule to combine all binary local decisions into a global binary decision. The combination of the global fusion rule and all local decision rules in the system is referred to as a decision strategy. In many scenarios, the system uses a single (deterministic) decision strategy — the DFC used a single deterministic fusion rule and each LD uses a single deterministic decision rule. A randomized strategy involves a randomized or pseudo — randomized choice between several deterministic decision strategies. In some instances, such randomized strategy is needed to ensure that the Receiver Operator Characteristic (ROC) curve of the architecture is convex. We are interested in scenarios that require that the randomized strategy be coordinated between the DFC and the LDs, maintaining synchronization between the selection scheme of local decision rules and global fusion rules. Circumstances that require such coordinated randomized selection are labeled “dependent randomization.” We present systems that use dependent randomization, and also discuss their response when synchronization is occasionally lost.

H∞ group consensus for partial-state coupled linear systems with fixed and switching topologies in the cooperation-competition networks

This paper investigates epidemic dynamics over dynamic networks via the approach of semi-tensor product of matrices. First, a formal susceptible-infected-susceptible epidemic dynamic model over dynamic networks (SISED-DN) is given. Second, based on a class of determinate co-evolutionary rule, the matrix expressions are established for the dynamics of individual states and network topologies, respectively. Then, all possible final spreading equilibria are obtained for any given initial epidemic state and network topology by the matrix expression. Third, a sufficient and necessary condition of the existence of state feedback vaccination control is presented to make every individual susceptible. The study of illustrative examples shows the effectiveness of our new results.

This paper investigates the distributed containment control problem for a class of general second-order multiagent systems with switched dynamics, which is composed of a continuous-time (CT) subsystem and a discrete-time (DT) subsystem. For this switched multiagent system under fixed directed topology, a distributed containment control protocol is proposed for each follower based on the relative local measurements of neighboring followers and leaders. Some necessary and sufficient conditions are derived under the condition that the network topology contains a directed spanning forest, and these conditions ensure that the general second-order containment control problem can be solved under arbitrary CT-DT switching. If the general second-order system is reduced to the double integrator system, some simpler containment conditions are presented. Furthermore, the similar results are also obtained under switching directed topology. Finally, some simulation examples are presented to show the efficiency of the theoretical results.

Event-triggered synchronization strategy for complex dynamical networks with the Markovian switching topologies

ABSTRACTThis paper focuses on a distributed convex optimisation problem over networks with time-varying topologies. First, an event-triggered strategy is employed to reduce computation and communication load in the networked systems. Second, the exponential convergence of event-triggered zero-gradient-sum algorithm is guaranteed if the corresponding time-varying network topology satisfies a new connected condition, called cooperatively connected condition. This condition does not require topologies constantly connected or jointly connected but only requires the integral of the Laplacian matrix of the network topology over a period of time is connected. Hence, it is suitable for more general time-varying topologies. Third, a convergence analysis technique is developed which is based on the difference of the Lyapunov function rather than its differentiation. Finally, a simulation example is provided to verify the results obtained in this paper.