Search

The repetitive tracking task for time‐varying systems (TVSs) with non‐repetitive time‐varying parameters at each trial, which is also called non‐repetitive TVSs, is realized in this article using iterative learning control (ILC). A machine learning (ML) based nominal model update mechanism, which utilizes the linear regression technique to update the nominal model at each ILC trial using only the current trial information, is proposed for non‐repetitive TVSs in order to enhance the ILC performance. Given that the ML mechanism forces the model uncertainties to remain within the ILC robust tolerance, an ILC update law is proposed to deal with non‐repetitive TVSs. How to tune parameters inside ML and ILC algorithms to achieve the desired aggregate performance is also provided. The robustness and reliability of the proposed method are verified by real experiments. Real data comparison with current state‐of‐the‐art methods demonstrates its superior control performance in terms of controlling precision. This article broadens ILC applications from time‐invariant systems to non‐repetitive TVSs, adopts ML regression technique to estimate non‐repetitive time‐varying parameters between two ILC trials and proposes a detailed parameter tuning mechanism to achieve desired performance, which are the main contributions. [ABSTRACT FROM AUTHOR]

This paper derives the optimal test channel distribution and the complete characterization of the classical Gorbunov and Pinsker (1973), Gorbunov and Pinsker (1974) nonanticipatory epsilon entropy of multivariate Gaussian Markov sources with square-error fidelity, which remained an open problem since 1974. The paper also formulates a state dependent nonanticipatory epsilon entropy, in which past reproductions are available to the decoder and not to the encoder, the test channel is specified with respect to an auxiliary (state) random process, and the reproduction process is a causal function of past reproduction and the auxiliary random process. This variation is analogous to the Wyner and Ziv (1976) and Wyner (1978) rate distortion function (RDF), of memoryless sources. It is shown that the operational rate of zero-delay codes, with past reproductions available to the decoder but not to the encoder is bounded below by the state dependent nonanticipatory epsilon entropy rate. For the case of multivariate Gaussian Markov sources with square-error fidelity, the optimal test channel distribution and the complete characterization of the state dependent of nonanticipatory epsilon entropy are derived, and also shown that that the two nonanticipatory epsilon entropies coincide. The derivations are new; they are based on structural properties of the stochastic realizations of the reproduction process that induce the optimal test channel distributions. They are derived using, achievable lower bounds on information theoretic measures, properties of mean-square estimation theory, Hadamard’s inequality, and canonical correlation coefficients of a tuple of multivariate jointly Gaussian random processes. Applications of the nonanticipatory epsilon entropy and its state dependent variation are discussed to the areas of control of unstable Gaussian systems over limited memory channels, design of causal estimators for Gaussian Markov sources with a fidelity criterion, computation of the rate loss of causal and zero-delay codes of Gaussian Markov sources with respect to non-causal codes. [ABSTRACT FROM AUTHOR]

• Accelerated first-order method for solving large-scale optimization problems with composite objective structure. • New composite estimating functions constructed by using the gradient mapping technique and a tighter lower bound on the objective function. • Efficient line-search strategy and novel convergence analysis results. • Initialization of the proposed method can be made robust to the imperfect knowledge of the strong convexity parameter. A plethora of problems arising in signal processing, machine learning and statistics can be cast as large-scale optimization problems with a composite objective structure. Such problems are typically solved by utilizing iterative first-order algorithms. In this work, we devise a new accelerated gradient-based estimating sequence technique for solving large-scale optimization problems with composite objective structure. Specifically, we introduce a new class of estimating functions, which are obtained by utilizing both a tight lower bound on the objective function, as well as the gradient mapping technique. Then, using the proposed estimating functions, we construct a class of Composite Objective Multi-step Estimating-sequence Techniques (COMET), which are endowed with an efficient line-search procedure. We prove that our proposed COMET enjoys the accelerated convergence rate, and our newly established convergence results allow for step-size adaptation. Our theoretical findings are supported by extensive computational experiments on various problem types and real-world datasets. Moreover, our numerical results show evidence of the robustness of the proposed method to the imperfect knowledge of the smoothness and strong convexity parameters. [ABSTRACT FROM AUTHOR]