Indefinite metric spaces in estimation, control and adaptive filtering

The goal of this thesis is two-fold: first to present a unified mathematical framework (based upon optimization in indefinite metric spaces) for a wide range of problems in estimation and control, and second, to motivate and introduce the problem of robust estimation and control, and to study its implications to the area of adaptive signal processing. Robust estimation (and control) is concerned with the design of estimators (and controllers that have acceptable performance in the face of model uncertainties and lack of statistical information, and can be considered an outgrowth and extension of (the now classical) LQG theory, developed in the 1950's and 1960's which assumed perfect models and complete statistical knowledge. It has particular significance in adaptive signal processing where one needs to cope with time-variations of system parameters and to compensate for lack of a priori knowledge of the statistics of the input data and disturbances. One method of addressing the above problem is the so-called H∞ approach, which was introduced by G. Zames in 1980 and that has been recently solved by various authors. Despite the "fundamental differences" between the philosophies of the H∞ and LQG approaches to control and estimation, there are striking "formal similarities" between the controllers and estimators obtained from these two methodologies. In an attempt to explain these similarities, we shall describe a new approach to H∞ estimation (and control), different from the existing (e.g., interpolation-theoretic-based, game-theoretic-based, etc) approaches, that is based upon setting up estimation (and control problems) not in the usual Hilbert space of random variables, but in an indefinite (so-called Krein) space

Differential-Algebraic Equations

Differential-Algebraic Equations (DAE) are today an independent field of research, which is gaining in importance and becoming of increasing interest for applications and mathematics itself. This workshop has drawn the balance after about 25 years investigations of DAEs and the research aims of the future were intensively discussed

Control and Estimation Oriented Model Order Reduction for Linear and Nonlinear Systems

Optimization based controls are advantageous in meeting stringent performance requirements and accommodating constraints. Although computers are becoming more powerful, solving optimization problems in real-time remains an obstacle because of associated computational complexity. Research efforts to address real-time optimization with limited computational power have intensified over the last decade, and one direction that has shown some success is model order reduction. This dissertation contains a collection of results relating to open- and closed-loop reduction techniques for large scale unconstrained linear descriptor systems, constrained linear systems, and nonlinear systems. For unconstrained linear descriptor systems, this dissertation develops novel gramian and Riccati solution approximation techniques. The gramian approximation is used for an open-loop reduction technique following that of balanced truncation proposed by (Moore, 1981) for ordinary linear systems and (Stykel, 2004) for linear descriptor systems. The Riccati solution is used to generalize the Linear Quadratic Gaussian balanced truncation (LQGBT) of (Verriest, 1981) and (Jonckheere and Silverman, 1983). These are applied to an electric machine model to reduce the number of states from $>$100000 to 8 while improving accuracy over the state-of-the-art modal truncation of (Zhou, 2015) for the purpose of condition monitoring. Furthermore, a link between unconstrained model predictive control (MPC) with a terminal penalty and LQG of a linear system is noted, suggesting an LQGBT reduced model as a natural model for reduced MPC design. The efficacy of such a reduced controller is demonstrated by the real-time control of a diesel airpath. Model reduction generally introduces modeling errors, and controlling a constrained plant subject to modeling errors falls squarely into robust control. A standard assumption of robust control is that inputs/states/outputs are constrained by convex sets, and these sets are ``tightened'' for robust constraint satisfaction. However, robust control is often overly conservative, and resulting control strategies cannot take advantage of the true admissible sets. A new reduction problem is proposed that considers the reduced order model accuracy and constraint conservativeness. A constant tube methodology for reduced order constrained MPC is presented, and the proposed reduced order model is found to decrease the constraint conservativeness of the reduced order MPC law compared to reduced order models obtained by gramian and LQG reductions. For nonlinear systems, a reformulation of the empirical gramians of (Lall et al., 1999) and (Hahn et al., 2003) into simpler, yet more general forms is provided. The modified definitions are used in the balanced truncation of a nonlinear diesel airpath model, and the reduced order model is used to design a reduced MPC law for tracking control. Further exploiting the link between the gramian and Riccati solution for linear systems, the new empirical gramian formulation is extended to obtain empirical Riccati covariance matrices used for closed-loop model order reduction of a nonlinear system. Balanced truncation using the empirical Riccati covariance matrices is demonstrated to result in a closer-to-optimal nonlinear compensator than the previous balanced truncation techniques discussed in the dissertation.PHDNaval Architecture & Marine EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/140839/1/riboch_1.pd

Design of of model-based controllers via parametric programming

Imperial Users onl

MIT Space Engineering Research Center

The Space Engineering Research Center (SERC) at MIT, started in Jul. 1988, has completed two years of research. The Center is approaching the operational phase of its first testbed, is midway through the construction of a second testbed, and is in the design phase of a third. We presently have seven participating faculty, four participating staff members, ten graduate students, and numerous undergraduates. This report reviews the testbed programs, individual graduate research, other SERC activities not funded by the Center, interaction with non-MIT organizations, and SERC milestones. Published papers made possible by SERC funding are included at the end of the report

Discrete Time Systems

Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area