Mohammad Naghnaeian

Mohammad Naghnaeian, Domitilla Del Vecchio

The Chemical Master Equation (CME) is used to stochastically model biochemical reaction networks, under the Markovian assumption. The low-order statistical moments induced by the CME are often the key quantities that one is interested in. However, in most cases, the moments equation is not closed; in the sense that the first $n$ moments depend on the higher order moments, for any positive integer $n$. In this paper, we develop a moment closure technique in which the higher order moments are approximated by an affine function of the lower order moments. We refer to such functions as the affine Moment Closure Functions (MCF) and prove that they are optimal in the worst-case context, in which no a priori information on the probability distribution is available. Furthermore, we cast the problem of finding the optimal affine MCF as a linear program, which is tractable. We utilize the affine MCFs to derive a finite dimensional linear system that approximates the low-order moments. We quantify the approximation error in terms of the $% l_{\infty }$ induced norm of some linear system. Our results can be effectively used to approximate the low-order moments and characterize the noise properties of the biochemical network under study.

Mohammad Naghnaeian, Nabil Hirzallah, Petros G. Voulgaris

We consider malicious attacks on actuators and sensors of a feedback system which can be modeled as additive, possibly unbounded, disturbances at the digital (cyber) part of the feedback loop. We precisely characterize the role of the unstable poles and zeros of the system in the ability to detect stealthy attacks in the context of the sampled data implementation of the controller in feedback with the continuous (physical) plant. We show that, if there is a single sensor that is guaranteed to be secure and the plant is observable from that sensor, then there exist a class of multirate sampled data controllers that ensure that all attacks remain detectable. These dual rate controllers are sampling the output faster than the zero order hold rate that operates on the control input and as such, they can even provide better nominal performance than single rate, at the price of higher sampling of the continuous output.