Moving Target Defense techniques have been proposed to increase uncertainty and apparent complexity for attackers. When more than one Moving Target Defense techniques are effective to limit opportunities of an attack, it is required to compare these techniques and select the best defense choice. In this paper, we propose a three-layer model to evaluate and compare effectiveness of different Moving Target Defenses. This model is designed as an attempt to fill a gap among existing evaluation methods and works as a systematic framework for Moving Target Defense comparison.

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This paper studies attack-resilient estimation of a class of switched nonlinear systems subject to stochastic noises. The systems are threatened by both of signal attacks and switching attacks. The problem is formulated as the joint estimation of states, attack vectors and modes of hidden-mode switched systems. We propose an estimation algorithm which is composed of a bank of state and attack vector estimators and a mode estimator. The mode estimator selects the most likely mode based on modes' posterior probabilities induced by the discrepancies between obtained outputs and predicted outputs. We formally analyze the stability of estimation errors in probability for the proposed estimator associated with the true mode when the hidden mode is time-invariant but remains unknown. For hidden-mode switched linear systems, we discuss a way to reduce computational complexity which originates from unknown signal attack locations. Lastly, we present numerical simulations on the IEEE 68-bus test system to show the estimator performance for time-varying modes with a regular mode set and a reduced mode set.We use the following definition for filter stability of nonlinear systems.Definition 1.1 Stochastic process x(t) is said to be Practically Exponentially Stable in probability (PESp) if for any γ ∈ (0, 1), there exist positive constants α, b, c, and δ such that, for any x(0) ≤ δ, the following holds for all t ≥ 0:PESp is a special case of stochastic input-to-state stability [24] when input is absent and class KL function is exponential in t and linear in x(0) . In addition, PESp is also extended from global asymptotic stability in probability (Definition 3.1 in [22]). Notice that the stability notions in [22,24] are global and PESp is local.As for linear systems, one of the sufficient conditions for filter stability is uniform observability. Definition 1.2 [3] The pair (C k , A k ) is uniformly observable if and only if there exist positive constants a, b, l, for all k ≥ 0, such that, for all kis the observability gramian and Φ k1,k0 is the state transition matrix.Uniform observability reduces to observability if the linear system is time-invariant. Motivating exampleA power network is represented by undirected graph (V, E) with the set of buses V {1, · · · , N } and the set of transmission lines E ⊆ V × V. The set of neighboring buses of i ∈ V is S i {l ∈ V \ {i}|(i, l) ∈ E}. Each bus is either a generator bus i ∈ G, or a load bus i ∈ L.

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