16 research outputs found
Centralized Versus Decentralized Detection of Attacks in Stochastic Interconnected Systems
We consider a security problem for interconnected systems governed by linear,
discrete, time-invariant, stochastic dynamics, where the objective is to detect
exogenous attacks by processing the measurements at different locations. We
consider two classes of detectors, namely centralized and decentralized
detectors, which differ primarily in their knowledge of the system model. In
particular, a decentralized detector has a model of the dynamics of the
isolated subsystems, but is unaware of the interconnection signals that are
exchanged among subsystems. Instead, a centralized detector has a model of the
entire dynamical system. We characterize the performance of the two detectors
and show that, depending on the system and attack parameters, each of the
detectors can outperform the other. In particular, it may be possible for the
decentralized detector to outperform its centralized counterpart, despite
having less information about the system dynamics, and this surprising property
is due to the nature of the considered attack detection problem. To complement
our results on the detection of attacks, we propose and solve an optimization
problem to design attacks that maximally degrade the system performance while
maintaining a pre-specified degree of detectability. Finally, we validate our
findings via numerical studies on an electric power system.Comment: Submitted to IEEE Transactions on Automatic Control (TAC
Minimum-norm Sparse Perturbations for Opacity in Linear Systems
Opacity is a notion that describes an eavesdropper's inability to estimate a
system's 'secret' states by observing the system's outputs. In this paper, we
propose algorithms to compute the minimum sparse perturbation to be added to a
system to make its initial states opaque. For these perturbations, we consider
two sparsity constraints - structured and affine. We develop an algorithm to
compute the global minimum-norm perturbation for the structured case. For the
affine case, we use the global minimum solution of the structured case as
initial point to compute a local minimum. Empirically, this local minimum is
very close to the global minimum. We demonstrate our results via a running
example.Comment: Submitted to Indian Control Conference, 2023 (6 pages
Behavioral Feedback for Optimal LQG Control
In this work, we revisit the Linear Quadratic Gaussian (LQG) optimal control
problem from a behavioral perspective. Motivated by the suitability of
behavioral models for data-driven control, we begin with a reformulation of the
LQG problem in the space of input-output behaviors and obtain a complete
characterization of the optimal solutions. In particular, we show that the
optimal LQG controller can be expressed as a static behavioral-feedback gain,
thereby eliminating the need for dynamic state estimation characteristic of
state space methods. The static form of the optimal LQG gain also makes it
amenable to its computation by gradient descent, which we investigate via
numerical experiments. Furthermore, we highlight the advantage of this approach
in the data-driven control setting of learning the optimal LQG controller from
expert demonstrations.Comment: Submitted to CDC 202