Ahmet Cetinkaya

Event-triggered control over unreliable networks subject to jamming attacks

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.

Networked Control Under Random and Malicious Packet Losses

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 attackers perspective and explore malicious attacks that cause instability. Finally, we demonstrate the efficacy of our results with numerical examples.

Stabilizing discrete-time switched linear stochastic systems using periodically available imprecise mode information

A feedback control framework is developed for stabilizing discrete-time switched linear stochastic dynamical systems for the case where the mode of the switched system is not observable at all time instants. We propose a feedback control law that depends only on the periodically obtained imprecise mode information. Specifically, the modes of the switched system are assumed to be divided into a number of groups, and the periodically available mode information indicates only the group that contains the active mode. We obtain sufficient conditions for second-moment asymptotic stability of the closed-loop system under our proposed control law. We demonstrate the efficacy of our approach through an illustrative numerical example.

Feedback control of switched stochastic systems using uniformly sampled mode information

Feedback stabilization of continuous-time switched linear stochastic dynamical systems is explored. The mode signal, which characterizes the switching between subsystems, is modeled as a Markov chain. We propose a feedback control law that depends only on the uniformly sampled mode information rather than the actual mode signal. We analyze the probabilistic dynamics of the sampled mode information, and develop a form of strong law of large numbers to show the almost sure asymptotic stability of the closed-loop system under the proposed control law. Finally, we present a numerical example to illustrate the efficacy of our approach.

Stabilization of switched linear stochastic dynamical systems under limited mode information

Almost sure asymptotic stabilization problem of continuous-time switched linear stochastic dynamical systems is considered. The mode signal, which manages the transition between subsystems, is modeled as a Markov chain. Mode information is assumed to be only available at certain time instances. We propose a control law that depends on the sampled information of the mode signal, which is constructed from the available mode samples. Based on our stability analysis for switched linear stochastic systems, we obtain sufficient conditions under which the proposed control law guarantees stability of the zero solution. Finally, we present an illustrative numerical example to demonstrate the efficacy of our results.

Stability and stabilization of switching stochastic differential equations subject to probabilistic state jumps

Stability conditions of continuous-time mode switching stochastic systems with probabilistic state jumps are provided. The mode signal, which manages the transition between subsystems, is modeled as a piecewise constant stochastic process. The state variables of the stochastic switching system is subject to jumps of random size occurring at random instances. The proposed piecewise continuous control law guarantees exponential moment stability of the zero solution by using multiple Lyapunov functions. Finally, an illustrative numerical example is presented to demonstrate the efficacy of our results.

Stability of stochastic systems with probabilistic mode switchings and state jumps

In this paper, we discuss the stability of continuous-time stochastic systems with probabilistic mode switchings and state jumps. Occurrences of mode transitions and state jumps are modeled with independent Poisson processes. We use multiple Lyapunov functions to derive sufficient conditions for stability in probability and moment exponential stability both for linear and nonlinear stochastic switching systems. Furthermore, we provide numerical examples to demonstrate the efficacy of our results.

Feedback control of switched stochastic systems using randomly available active mode information

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.

One-dimensional heat diffusion modelling and random walks on non-uniform grids

A probabilistic model for the diffusion of heat on one-dimensional spaces is developed. Specifically, grid points are arbitrarily placed on the real line and the heat particles are assumed to jump between these grid points in continuous time. This random walk by the heat particles is represented by a continuous-time Markov chain and state-transition intensities depends on the underlying, possibly non-uniform, spacing of the grid points to characterize the Markov chain. Several numerical examples are demonstrated to show the efficacy of the proposed framework for exemplary non-uniform grids.

Sampled-mode-dependent time-varying control strategy for stabilizing discrete-time switched stochastic systems

Second-moment asymptotic stabilization of a discrete-time switched stochastic system is investigated. Active operation mode of the switched system is assumed to be only periodically observed (sampled). We develop a stabilizing feedback control framework that incorporates sampled-mode-dependent time-varying feedback gains, which allow stabilization despite the uncertainty of the active operation mode between consecutive mode observation instants. We utilize the periodicity induced in the closed-loop system dynamics due to periodic mode observations, and employ discrete-time Floquet theory to obtain necessary and sufficient conditions for second-moment asymptotic stabilization of the zero solution. Furthermore, we use Lyapunov-like functions with periodic coefficients to obtain alternative stabilization conditions, which we then employ for designing feedback gains. Finally, we demonstrate the efficacy of our results with a numerical example.