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We study autocovariance least squares (ALS) estimation methods for covariance estimation for linear time-invariant systems. Previous works have posited that calculation of the ALS weighting matrix is intractable unless the number of data points $N_d$ is small because it requires storage of a matrix whose number of elements scales as $N_d^4$. We derive a novel way to compute the weight that avoids this difficulty. In practice, the true optimal weight cannot be calculated because it is a function of the sought covariance matrices. However, our work enables implementation of two novel ALS algorithms that estimate the weight from data. For the purpose of comparison, we also discuss ALS with an arbitrary weight (such as an identity matrix) and present a previously published method for estimating the ALS weight. ALS with an identity weight guarantees unbiased and consistent covariance estimates, but algorithms that estimate the weight from data do not inherit these guarantees. Despite this drawback, we present a numerical example for which the best performing algorithm, iterative estimation of the covariances and the ALS weight, produces covariance estimates with a small amount of bias and a significantly reduced variance compared to all other algorithms. [ABSTRACT FROM AUTHOR]

This note studies the linear quadratic (LQ) optimal control of continuous-time linear time-invariant systems with random gains imposed on the input channels. We start from the indefinite LQ problem, in which the cost weighting matrix can be indefinite. The definite LQ problem is discussed as a special case. The main novelty originates from the point of view that in networked control, designing the channels and controller jointly often leads to an easier problem and achieves better performance than designing them separately. Specifically, we formulate the LQ problem as a channel/controller co-design problem assuming that the channel capacities can be allocated among the input channels subject to an overall capacity constraint. Necessary and sufficient conditions are obtained for the well-posedness and the attainability of the indefinite LQ problem under a given channel capacity allocation satisfying the stabilization requirement. The optimal controller is given by a linear state feedback associated with the mean-square stabilizing solution of a modified algebraic Riccati equation. [ABSTRACT FROM PUBLISHER]

This paper presents a receding horizon control (RHC) for an unconstrained input-delayed system. To begin with, we derive a finite horizon optimal control for a quadratic cost function including two final weighting terms. The RHC is easily obtained by changing the initial and final times of the finite horizon optimal control. A linear matrix inequality (LMI) condition on two final weighting matrices is proposed to meet the cost monotonicity, under which the optimal cost on the horizon is monotonically nonincreasing with time and hence the asymptotical stability is guaranteed only if an observability condition is met. It is shown through simulation that the proposed RHC stabilizes the input-delayed system effectively and its performance can be tuned by adjusting weighting matrices with respect to the state and the input. [ABSTRACT FROM AUTHOR]