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Consensus and cluster forming of multiagent systems in the face of jamming attacks along with reactive recovery actions by a defender are discussed. The attacker is capable to disable some of the edges of the network with the objective to divide the agents into a smaller size of clusters while, in response, the defender recovers some of the edges by increasing the transmission power. We consider repeated games where the resulting optimal strategies for the two players are derived in a rolling horizon fashion. The attacker and the defender possess different computational abilities to calculate their strategies. This aspect is represented by the non-uniform values of the horizon lengths and the game periods. Theoretical and simulation based results demonstrate the effects of the horizon lengths and the game periods on the agents' states., Comment: arXiv admin note: text overlap with arXiv:2301.03302

A two-player game-theoretic problem on resilient graphs in a multiagent consensus setting is formulated. An attacker is capable to disable some of the edges of the network with the objective to divide the agents into clusters by emitting jamming signals while, in response, the defender recovers some of the edges by increasing the transmission power for the communication signals. Specifically, we consider repeated games between the attacker and the defender where the optimal strategies for the two players are derived in a rolling horizon fashion based on utility functions that take both the agents' states and the sizes of clusters (known as network effect) into account. The players' actions at each discrete-time step are constrained by their energy for transmissions of the signals, with a less strict constraint for the attacker. Necessary conditions and sufficient conditions of agent consensus are derived, which are influenced by the energy constraints. The number of clusters of agents at infinite time in the face of attacks and recoveries are also characterized. Simulation results are provided to demonstrate the effects of players' actions on the cluster forming and to illustrate the players' performance for different horizon parameters.

Evolution of agents' dynamics of multiagent systems under consensus protocol in the face of jamming attacks is discussed, where centralized parties are able to influence the control signals of the agents. In this paper we focus on a game-theoretical approach of multiagent systems where the players have incomplete information on their opponents' strength. We consider repeated games with both simultaneous and sequential player actions where players update their beliefs of each other over time. The effect of the players' optimal strategies according to Bayesian Nash Equilibrium and Perfect Bayesian Equilibrium on agents' consensus is examined. It is shown that an attacker with incomplete knowledge may fail to prevent consensus despite having sufficient resources to do so., Comment: 9 pages, 6 figures. Accepted in IFAC-WC 2023

The stability property of the loss-aversion-based noncooperative switched systems with quadratic payoffs is investigated. In this system, each agent adopts the lower sensitivity parameter in the myopic pseudo-gradient dynamics for the case of losing utility than gaining utility, and both systems' dynamics and switching events (conditions) are depending on agents' payoff functions. Sufficient conditions under which agents' state converges towards the Nash equilibrium are derived in accordance with the location of the Nash equilibrium. In the analysis, the mode transition sequence and interesting phenomena which we call flash switching instants are characterized. Finally, we present several numerical examples to illustrate the properties of our results., Comment: 8 pages, 14 figures. Accepted by IEEE Transactions on Automatic Control

A cyber security problem in a networked system formulated as a resilient graph problem based on a game-theoretic approach is considered. The connectivity of the underlying graph of the network system is reduced by an attacker who removes some of the edges whereas the defender attempts to recover them. Both players are subject to energy constraints so that their actions are restricted and cannot be performed continuously. For this two-stage game, which is played repeatedly over time, we characterize the optimal strategies for the attacker and the defender in terms of edge connectivity and the number of connected components of the graph. The resilient graph game is then applied to a multi-agent consensus problem. We study how the attacks and the recovery on the edges affect the consensus process. Finally, we also provide numerical simulation to illustrate the results., Comment: 12 pages, 13 figures

Jamming attacks on wireless networked control systems are investigated for the scenarios where the system dynamics face exogenous disturbance. In particular, the control input packets are assumed to be transmitted from a controller to a remotely located linear plant over an insecure wireless communication channel that is subject to jamming attacks. The time-varying likelihood of transmission failures on this channel depends on the power of the jamming interference signal emitted by an attacker. We show that jamming attacks can prevent stability when the system faces disturbance, even if the attacked system without disturbance is stable. We also show that stability under jamming and disturbance can be achieved if the average jamming interference power is restricted in a certain way that we characterize in the paper. We illustrate our results on an example networked control system with a fading wireless channel, where the outage probability is affected by jamming attacks., Comment: Improve wording; Correct typos

Multi-agent consensus under jamming attacks is investigated. Specifically, inter-agent communications over a network are assumed to fail at certain times due to jamming of transmissions by a malicious attacker. A new stochastic communication protocol is proposed to achieve finite-time practical consensus between agents. In this protocol, communication attempt times of agents are randomized and unknown by the attacker until after the agents make their communication attempts. Through a probabilistic analysis, we show that the proposed communication protocol, when combined with a stochastic ternary control law, allows agents to achieve consensus regardless of the frequency of attacks. We demonstrate the efficacy of our results by considering two different strategies of the jamming attacker: a deterministic attack strategy and a more malicious communication-aware attack strategy., Comment: Improved control law explanations and the numerical example

A delayed feedback control framework for stabilizing unstable periodic orbits of linear periodic time-varying systems is proposed. In this framework, act-and-wait approach is utilized for switching a delayed feedback controller on and off alternately at every integer multiples of the period of the system. By analyzing the monodromy matrix of the closed-loop system, we obtain conditions under which the closed-loop system's state converges towards a periodic solution under our proposed control law. We discuss the application of our results in stabilization of unstable periodic orbits of nonlinear systems and present numerical examples to illustrate the efficacy of our approach., Comment: Added a footnote, corrected typos

The control problem of a linear discrete-time dynamical system over a multi-hop network is explored. The network is assumed to be subject to packet drops by malicious and nonmalicious nodes as well as random and malicious data corruption issues. We utilize asymptotic tail-probability bounds of transmission failure ratios to characterize the links and paths of a network as well as the network itself. This probabilistic characterization allows us to take into account multiple failures that depend on each other, and coordinated malicious attacks on the network. We obtain a sufficient condition for the stability of the networked control system by utilizing our probabilistic approach. We then demonstrate the efficacy of our results in different scenarios concerning transmission failures on a multi-hop network., Comment: Correct typos in Sections 3-6. Make changes in the proofs of Theorems 3.4 and 4.3

We investigate the stability problem for discrete-time stochastic switched linear systems under the specific scenarios where information about the switching patterns and the probability of switches are not available. Our analysis focuses on the average number of times each mode becomes active in the long run and, in particular, utilizes their lower- and upper-bounds. This setup is motivated by cyber security issues for networked control systems in the presence of packet losses due to malicious jamming attacks where the attacker's strategy is not known a priori. We derive a sufficient condition for almost sure asymptotic stability of the switched systems which can be examined by solving a linear programming problem. Our approach exploits the dynamics of an equivalent system that describes the evolution of the switched system's state at every few steps; the stability analysis may become less conservative by increasing the step size. The computational efficiency is further enhanced by exploiting the structure in the stability analysis problem, and we introduce an alternative linear programming problem that has fewer variables. We demonstrate the efficacy of our results by analyzing networked control problems where communication channels face random packet losses as well as jamming attacks., Comment: Change title of Section 3; Resize figures

We study cyber security issues in networked control of a linear dynamical system. Specifically, the dynamical system and the controller are assumed to be connected through a communication channel that face malicious attacks as well as random packet losses due to unreliability of transmissions. We provide a probabilistic characterization for the link failures which allows us to study combined effects of malicious and random packet losses. We first investigate almost sure stabilization under an event-triggered control law, where we utilize Lyapunov-like functions to characterize the triggering times at which the plant and the controller attempt to exchange state and control data over the network. We then provide a look at the networked control problem from the attacker's perspective and explore malicious attacks that cause instability. Finally, we demonstrate the efficacy of our results with numerical examples.

In this paper, we study state-feedback control of Markov jump linear systems with partial information. In particular, we assume that the controller can only access the mode signals according to a hidden-Markov observation process. Our formulation generalizes various relevant cases previously studied in the literature on Markov jump linear systems, such as the cases with perfect information, no information, and cluster observations of the mode signals. In this context, we propose a Linear Matrix Inequalities (LMI) formulation to design feedback control laws for (stochastic) stabilization, $H_2$, and $H_\infty$ control of discrete-time Markov jump linear systems under hidden-Markovian observations of the mode signals. We conclude by illustrating our results with some numerical examples.

Event-triggered networked control of a linear dynamical system is investigated. Specifically, the dynamical system and the controller are assumed to be connected through a communication channel. State and control input information packets between the system and the controller are attempted to be exchanged over the network only at time instants when certain triggering conditions are satisfied. We provide a probabilistic characterization for the link failures which allows us to model random packet losses due to unreliability in transmissions as well as those caused by malicious jamming attacks. We obtain conditions for the almost sure stability of the closed-loop system, and we illustrate the efficacy of our approach with a numerical example., Comment: Presented at IEEE CDC 2015; Corrected author names in references [7],[11]; Corrected ranges of rho and tilde{p} in Lemma A.1; Corrected indices in (51)

Almost sure asymptotic stabilization of a discrete-time switched stochastic system is investigated. Information on the active operation mode of the switched system is assumed to be available for control purposes only at random time instants. We propose a stabilizing feedback control framework that utilizes the information obtained through mode observations. We first consider the case where stochastic properties of mode observation instants are fully known. We obtain sufficient asymptotic stabilization conditions for the closed-loop switched stochastic system under our proposed control law. We then explore the case where exact knowledge of the stochastic properties of mode observation instants is not available. We present a set of alternative stabilization conditions for this case. The results for both cases are predicated on the analysis of a sequence-valued process that encapsulates the stochastic nature of the evolution of active operation mode between mode observation instants. Finally, we demonstrate the efficacy of our results with numerical examples.