Browsing by Author "Martins, Nuno"
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Item Certifying the Optimality of a Distributed State Estimation System via Majorization Theory(2009) Lipsa, Gabriel; Martins, Nuno; Martins, NunoConsider a first order linear time-invariant discrete time system driven by process noise, a pre-processor that accepts causal measurements of the state of the system, and a state estimator. The pre-processor and the state estimator are not co-located, and, at every time-step, the pre-processor transmits either a real number or an erasure symbol to the estimator. We seek the pre-processor and the estimator that jointly minimize a cost that combines two terms; the expected squared state estimation error and a communication cost. In our formulation, the transmission of a real number from the pre-processor to the estimator incurs a positive cost while erasures induce zero cost. This paper is the first to prove analytically that a symmetric threshold policy at the pre-processor and a Kalman-like filter at the estimator, which updates its estimate linearly in the presence of erasures, are jointly optimal for our problem.Item A convex parameterization of all stabilizing controllers for non-strongly stabilizable plants, under quadratically invariant sparsity constraints(2008) Sabau, Serban; Martins, Nuno; Rotkowitz, MichaelThis paper addresses the design of controllers, subject to sparsity constraints, for linear and timeinvariant plants. Prior results have shown that a class of stabilizing controllers, satisfying a given sparsity constraint, admits a convex representation of the Youla–type, provided that the sparsity constraints imposed on the controller are quadratically invariant with respect to the plant and that the plant is strongly stabilizable. Another important aspect of the aforementioned results is that the sparsity constraints on the controller can be recast as convex constraints on the Youla parameter, which makes this approach suitable for optimization using norm-based costs. In this paper, we extend these previous results to non-strongly stabilizable plants. Our extension also leads to a Youla-type representation for the class of controllers, under quadratically invariant sparsity constraints. In our extension, the controller class also admits a representation of the Youla–type, where the Youla parameter is subject to only convex constraints.