Control and Estimation of Systems with Input/Output Delays

Abstract

PrefaceTime delay systems exist in many engineering fields such as transportation, communication, process engineering and more recently networked control systems. In recent years, time delay systems have attracted recurring interests from research community. Much of the research work has been focused on stability analysis and stabilization of time delay systems using the so-called Lyapunov-Krasovskii functionals and linear matrix inequality (LMI) approach. While the LMI approach does provide an efficient tool for handling systems with delays in state and/or inputs, the LMI based results are mostly only sufficient and only numerical solutions are available.For systems with known single input delay, there have been rather elegant analytical solutions to various problems such as optimal tracking, linear quadratic regulation and H ∞ control. We note that discrete-time systems with delays can usually be converted into delay free systems via system augmentation, however, the augmentation approach leads to much higher computational costs, especially for systems of higher state dimension and large delays. For continuous-time systems, time delay problems can in principle be treated by the infinite-dimensional system theory which, however, leads to solutions in terms of Riccati type partial differential equations or operator Riccati equations which are difficult to understand and compute. Some attempts have been made in recent years to derive explicit and efficient solutions for systems with input/output (i/o) delays. These include the study on the H ∞ control of systems with multiple input delays based on the stable eigenspace of a Hamlitonian matrix [46]. It is worth noting that checking the existence of the stable eigenspace and finding the minimal root of the transcendent equation required for the controller design may be computationally expensive. Another approach is to split a multiple delay problem into a nested sequence of elementary problems which are then solved based on J-spectral factorizations [62].In this monograph, our aim is to present simple analytical solutions to control and estimation problems for systems with multiple i/o delays via elementary tools such as projections. We propose a re-organized innovation analysis approach which allows us to convert many complicated delay problems into delay VI Preface free ones. In particular, for linear quadratic regulation of systems with multiple input delays, the approach enables us to establish a duality between the LQR problem and a smoothing problem for a delay free system. The duality contains the well known duality between the LQR of a delay free system and Kalman filtering as a special case and allows us to derive an analytical solution via simple projections. We also consider the dual problem, i.e. the Kalman filtering for systems with multiple delayed measurements. Again, the re-organized innovation analysis turns out to be a powerful tool in deriving an estimator. A separation principle will be established for the linear quadratic Gaussian control of sys...