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Co-design for Security and Performance: LMI Tools

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 Added by Navid Hashemi
 Publication date 2019
and research's language is English




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We present a convex optimization to reduce the impact of sensor falsification attacks in linear time invariant systems controlled by observer-based feedback. We accomplish this by finding optimal observer and controller gain matrices that minimize the size of the reachable set of attack-induced states. To avoid trivial solutions, we integrate a covariance-based $|H|_2$ closed-loop performance constraint, for which we develop a novel linearization for this typically nonlinear, non-convex problem. We demonstrate the effectiveness of this linear matrix inequality framework through a numerical case study.

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80 - Lanlan Su 2020
This work investigates robust monotonic convergent iterative learning control (ILC) for uncertain linear systems in both time and frequency domains, and the ILC algorithm optimizing the convergence speed in terms of $l_{2}$ norm of error signals is derived. Firstly, it is shown that the robust monotonic convergence of the ILC system can be established equivalently by the positive definiteness of a matrix polynomial over some set. Then, a necessary and sufficient condition in the form of sum of squares (SOS) for the positive definiteness is proposed, which is amendable to the feasibility of linear matrix inequalities (LMIs). Based on such a condition, the optimal ILC algorithm that maximizes the convergence speed is obtained by solving a set of convex optimization problems. Moreover, the order of the learning function can be chosen arbitrarily so that the designers have the flexibility to decide the complexity of the learning algorithm.
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