Characterizations of Families of Rectangular, Finite Impulse Response, Para-Unitary Systems

We here study Finite Impulse Response (FIR) rectangular, not necessarily causal, systems which are (para)-unitary on the unit circle (=the class U). First, we offer three characterizations of these systems. Then, introduce a description of all FIRs in U, as copies of a real polytope, parametrized by the dimensions and the McMillan degree of the FIRs. Finally, we present six simple ways (along with their combinations) to construct, from any FIR, a large family of FIRs, of various dimensions and McMillan degrees, so that whenever the original system is in U, so is the whole family. A key role is played by Hankel matrices

H2/H∞ controller design for input-delay and preview systems based on state decomposition approach

This thesis concentrates on the efficient solution methods of H2/H∞ optimal control problems for input-delay and preview systems. Although the problems can be reformulated to the ones for delay-free systems by augmenting the state space of the controlled systems, the numerical solution of the Riccati/KYP (Kalman-Yakubovich-Popov) equations for the augmented systems requires special efforts, and complicates controller tuning. On the other hand, it is known that the optimal control laws for certain classes of time-delay systems can be constructed without solving the augmented Riccati/KYP equations. Such design problems are called reduced-order construction problems in this thesis. The solutions of the reducedorder construction problems are still limited in theoretical and practical perspectives. The main purpose of the thesis is to propose a new approach for the reduced-order construction problems, which enables to derive the optimal output feedback controllers for input-delayed and preview systems in a unified manner. We focus on the internal dynamics of the overall systems, and decompose it toward the H^2 and H^∞ performance objectives. The fundamental idea of our approach is first introduced for the discrete-time inputdelayed H^2/H^∞ control problems. The state decomposition enables to solve the output feedback problem through the simpler ones, namely, the full information and output estimation problems. The discrete-time optimal controllers are obtained in the Smith predictor form. They are constructed from the Riccati/KYP equations for the delay-free systems. The solution procedure is further extended to the continuous-time preview H^2/H^∞ control problems in an output feedback setting. The optimal utilization of the preview information is exploited at the full information and output estimation problems. The clear structures of the optimal controllers are revealed as the combination of the finite-dimensional observers and preview-feedforward compensation. In the H^∞ control problems for the input-delayed and preview systems, the J-spectral factorization techniques in the literature are employed. Their interconnection to the augmented Riccati/KYP equations is clarified by reviewing the techniques from a view point of the internal state dynamics.首都大学東京, 2014-03-25, 博士(工学), 甲第440号首都大学東

Model Order Reduction Based on Semidefinite Programming

The main topic of this PhD thesis is complexity reduction of linear time-invariant models. The complexity in such systems is measured by the number of differential equations forming the dynamical system. This number is called the order of the system. Order reduction is typically used as a tool to model complex systems, the simulation of which takes considerable time and/or has overwhelming memory requirements. Any model reflects an approximation of a real world system. Therefore, it is reasonable to sacrifice some model accuracy in order to obtain a simpler representation. Once a low-order model is obtained, the simulation becomes computationally cheaper, which saves time and resources. A low-order model still has to be "similar" to the full order one in some sense. There are many ways of measuring "similarity" and, typically, such a measure is chosen depending on the application. Three different settings of model order reduction were investigated in the thesis. The first one is H infinity model order reduction, i.e., the distance between two models is measured by the H infinity norm. Although, the problem has been tackled by many researchers, all the optimal solutions are yet to be found. However, there are a large number of methods, which solve suboptimal problems and deliver accurate approximations. Recently, research community has devoted more attention to large-scale systems and computationally scalable extensions of existing model reduction techniques. The algorithm developed in the thesis is based on the frequency response samples matching. For a large class of systems the computation of the frequency response samples can be done very efficiently. Therefore, the developed algorithm is relatively computationally cheap. The proposed algorithm can be seen as a computationally scalable extension to the well-known Hankel model reduction, which is known to deliver very accurate solutions. One of the reasons for such an assessment is that the relaxation employed in the proposed algorithm is tightly related to the one used in Hankel model reduction. Numerical simulations also show that the accuracy of the method is comparable to the Hankel model reduction one. The second part of the thesis is devoted to parameterized model order reduction. A parameterized model is essentially a family of models which depend on certain design parameters. The model reduction goal in this setting is to approximate the whole family of models for all values of parameters. The main motivation for such a model reduction setting is design of a model with an appropriate set of parameters. In order to make a good choice of parameters, the models need to be simulated for a large set of parameters. After inspecting the simulation results a model can be picked with suitable frequency or step responses. Parameterized model reduction significantly simplifies this procedure. The proposed algorithm for parameterized model reduction is a straightforward extension of the one described above. The proposed algorithm is applicable to linear parameter-varying systems modeling as well. Finally, the third topic is modeling interconnections of systems. In this thesis an interconnection is a collection of systems (or subsystems) connected in a typical block-diagram. In order to avoid confusion, throughout the thesis the entire model is called a supersystem, as opposed to subsystems, which a supersystem consists of. One of the specific cases of structured model reduction is controller reduction. In this problem there are two subsystems: the plant and the controller. Two directions of model reduction of interconnected systems are considered: model reduction in the nu-gap metric and structured model reduction. To some extent, using the nu-gap metric makes it possible to model subsystems without considering the supersystem at all. This property can be exploited for extremely large supersystems for which some forms of analysis (evaluating stability, computing step response, etc.) are intractable. However, a more systematic way of modeling is structured model reduction. There, the objective is to approximate certain subsystems in such a way that crucial characteristics of the given supersystem, such as stability, structure of interconnections, frequency response, are preserved. In structured model reduction all subsystems are taken into account, not only the approximated ones. In order to address structured model reduction, the supersystem is represented in a coprime factor form, where its structure also appears in coprime factors. Using this representation the problem is reduced to H infinity model reduction, which is addressed by the presented framework. All the presented methods are validated on academic or known benchmark problems. Since all the methods are based on semidefinite programming, adding new constraints is a matter of formulating a constraint as a semidefinite one. A number of extensions are presented, which illustrate the power of the approach. Properties of the methods are discussed throughout the thesis while some remaining problems conclude the manuscript

34th Midwest Symposium on Circuits and Systems-Final Program

Organized by the Naval Postgraduate School Monterey California. Cosponsored by the IEEE Circuits and Systems Society. Symposium Organizing Committee: General Chairman-Sherif Michael, Technical Program-Roberto Cristi, Publications-Michael Soderstrand, Special Sessions- Charles W. Therrien, Publicity: Jeffrey Burl, Finance: Ralph Hippenstiel, and Local Arrangements: Barbara Cristi

Automatic Flight Control Systems

The history of flight control is inseparably linked to the history of aviation itself. Since the early days, the concept of automatic flight control systems has evolved from mechanical control systems to highly advanced automatic fly-by-wire flight control systems which can be found nowadays in military jets and civil airliners. Even today, many research efforts are made for the further development of these flight control systems in various aspects. Recent new developments in this field focus on a wealth of different aspects. This book focuses on a selection of key research areas, such as inertial navigation, control of unmanned aircraft and helicopters, trajectory control of an unmanned space re-entry vehicle, aeroservoelastic control, adaptive flight control, and fault tolerant flight control. This book consists of two major sections. The first section focuses on a literature review and some recent theoretical developments in flight control systems. The second section discusses some concepts of adaptive and fault-tolerant flight control systems. Each technique discussed in this book is illustrated by a relevant example

Study of numeric Saturation Effects in Linear Digital Compensators

Saturation arithmetic is often used in finite precision digital compensators to circumvent instability due to radix overflow. The saturation limits in the digital structure lead to nonlinear behavior during large state transients. It is shown that if all recursive loops in a compensator are interrupted by at least one saturation limit, then there exists a bounded external scaling rule which assures against overflow at all nodes in the structure. Design methods are proposed based on the generalized second method of Lyapunov, which take the internal saturation limits into account to implement a robust dual-mode suboptimal control for bounded input plants. The saturating digital compensator provides linear regulation for small disturbances, and near-time-optimal control for large disturbances or changes in the operating point. Computer aided design tools are developed to facilitate the analysis and design of this class of digital compensators

Statistical Learning Theory for Control: A Finite Sample Perspective

This tutorial survey provides an overview of recent non-asymptotic advances in statistical learning theory as relevant to control and system identification. While there has been substantial progress across all areas of control, the theory is most well-developed when it comes to linear system identification and learning for the linear quadratic regulator, which are the focus of this manuscript. From a theoretical perspective, much of the labor underlying these advances has been in adapting tools from modern high-dimensional statistics and learning theory. While highly relevant to control theorists interested in integrating tools from machine learning, the foundational material has not always been easily accessible. To remedy this, we provide a self-contained presentation of the relevant material, outlining all the key ideas and the technical machinery that underpin recent results. We also present a number of open problems and future directions.Comment: Survey Paper, Submitted to Control Systems Magazine. Second version contains additional motivation for finite sample statistics and more detailed comparison with classical literatur