State Estimation for Dynamic Systems
State Estimation for Dynamic Systems

Author: Felix L. Chernousko

Publisher: CRC Press

Published: 1993-11-09

Total Pages: 322

ISBN-13: 9780849344589

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State Estimation for Dynamic Systems presents the state of the art in this field and discusses a new method of state estimation. The method makes it possible to obtain optimal two-sided ellipsoidal bounds for reachable sets of linear and nonlinear control systems with discrete and continuous time. The practical stability of dynamic systems subjected to disturbances can be analyzed, and two-sided estimates in optimal control and differential games can be obtained. The method described in the book also permits guaranteed state estimation (filtering) for dynamic systems in the presence of external disturbances and observation errors. Numerical algorithms for state estimation and optimal control, as well as a number of applications and examples, are presented. The book will be an excellent reference for researchers and engineers working in applied mathematics, control theory, and system analysis. It will also appeal to pure and applied mathematicians, control engineers, and computer programmers.

Optimal State Estimation
Optimal State Estimation

Author: Dan Simon

Publisher: John Wiley & Sons

Published: 2006-06-19

Total Pages: 554

ISBN-13: 0470045337

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A bottom-up approach that enables readers to master and apply the latest techniques in state estimation This book offers the best mathematical approaches to estimating the state of a general system. The author presents state estimation theory clearly and rigorously, providing the right amount of advanced material, recent research results, and references to enable the reader to apply state estimation techniques confidently across a variety of fields in science and engineering. While there are other textbooks that treat state estimation, this one offers special features and a unique perspective and pedagogical approach that speed learning: * Straightforward, bottom-up approach begins with basic concepts and then builds step by step to more advanced topics for a clear understanding of state estimation * Simple examples and problems that require only paper and pen to solve lead to an intuitive understanding of how theory works in practice * MATLAB(r)-based source code that corresponds to examples in the book, available on the author's Web site, enables readers to recreate results and experiment with other simulation setups and parameters Armed with a solid foundation in the basics, readers are presented with a careful treatment of advanced topics, including unscented filtering, high order nonlinear filtering, particle filtering, constrained state estimation, reduced order filtering, robust Kalman filtering, and mixed Kalman/H? filtering. Problems at the end of each chapter include both written exercises and computer exercises. Written exercises focus on improving the reader's understanding of theory and key concepts, whereas computer exercises help readers apply theory to problems similar to ones they are likely to encounter in industry. With its expert blend of theory and practice, coupled with its presentation of recent research results, Optimal State Estimation is strongly recommended for undergraduate and graduate-level courses in optimal control and state estimation theory. It also serves as a reference for engineers and science professionals across a wide array of industries.

State Estimation and Stabilization of Nonlinear Systems
State Estimation and Stabilization of Nonlinear Systems

Author: Abdellatif Ben Makhlouf

Publisher: Springer Nature

Published: 2023-11-06

Total Pages: 439

ISBN-13: 3031379705

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This book presents the separation principle which is also known as the principle of separation of estimation and control and states that, under certain assumptions, the problem of designing an optimal feedback controller for a stochastic system can be solved by designing an optimal observer for the system's state, which feeds into an optimal deterministic controller for the system. Thus, the problem may be divided into two halves, which simplifies its design. In the context of deterministic linear systems, the first instance of this principle is that if a stable observer and stable state feedback are built for a linear time-invariant system (LTI system hereafter), then the combined observer and feedback are stable. The separation principle does not true for nonlinear systems in general. Another instance of the separation principle occurs in the context of linear stochastic systems, namely that an optimum state feedback controller intended to minimize a quadratic cost is optimal for the stochastic control problem with output measurements. The ideal solution consists of a Kalman filter and a linear-quadratic regulator when both process and observation noise are Gaussian. The term for this is linear-quadratic-Gaussian control. More generally, given acceptable conditions and when the noise is a martingale (with potential leaps), a separation principle, also known as the separation principle in stochastic control, applies when the noise is a martingale (with possible jumps).

Finite Dimensional Nonlinear Estimation in Continuous and Discrete Time
Finite Dimensional Nonlinear Estimation in Continuous and Discrete Time

Author: Steven I. Marcus

Publisher:

Published: 1978

Total Pages: 20

ISBN-13:

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It has been shown that, for certain classes of nonlinear stochastic systems in both continuous and discrete time, the optimal conditional mean estimator of the system state given the past observations can be computed with a recursive filter of fixed finite dimension. The typical nonlinear system in these classes consists of a linear system with linear measurements and white Gaussian noise processes, which feeds forward into a nonlinear system described by a certain type of Volterra series expansion or by a bilinear or state-linear system satisfying certain algebraic conditions. The purpose in this paper is to consider estimation problems similar to those presented before, to present simpler proofs that the estimators are indeed finite dimensional, to provide deeper insight into these problems by relating them to the homogeneous chaos of Wiener and to orthogonal polynomial expansions, to explain the similarities and differences between the continuous and discrete time cases, and to prove some extensions of previous results. The existence of polynomials in the innovations in the discrete time recursive estimator, in contrast to the continuous time estimator, is interpreted in terms of the homogeneous chaos.