This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material. The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the engineering properties of the regulator. Topics include degree of stability, phase and gain margin, tolerance of time delay, effect of nonlinearities, asymptotic properties, and various sensitivity problems. The third section explores state estimation and robust controller design using state-estimate feedback. Numerous examples emphasize the issues related to consistent and accurate system design. Key topics include loop-recovery techniques, frequency shaping, and controller reduction, for both scalar and multivariable systems. Self-contained appendixes cover matrix theory, linear systems, the Pontryagin minimum principle, Lyapunov stability, and the Riccati equation. Newly added to this Dover edition is a complete solutions manual for the problems appearing at the conclusion of each section.

Optimal Control: Linear Quadratic Methods

Course Description This is an advanced course in which we explore the field of Statistical Optics. Topics covered include such subjects as the statistical properties of natural (thermal) and laser light, spatial and temporal coherence, effects of partial coherence on optical imaging instruments, effects on imaging due to randomly inhomogeneous media, and a statistical treatment of the detection of light. Development of this more comprehensive model of the behavior of light draws upon the use of tools traditionally available to the electrical engineer, such as linear system theory and the theory of stochastic processes.

http://ieeexplore.ieee.org/iel5/3/23094/01073023.pdf

Statistical optics

Safe Reinforcement Learning can be defined as the process of learning policies that maximize the expectation of the return in problems in which it is important to ensure reasonable system performance and/or respect safety constraints during the learning and/or deployment processes. We categorize and analyze two approaches of Safe Reinforcement Learning. The first is based on the modification of the optimality criterion, the classic discounted finite/infinite horizon, with a safety factor. The second is based on the modification of the exploration process through the incorporation of external knowledge or the guidance of a risk metric. We use the proposed classification to survey the existing literature, as well as suggesting future directions for Safe Reinforcement Learning.

/pdf/a-comprehensive-survey-on-safe-reinforcement-learning-3p8tg32zci.pdf

A comprehensive survey on safe reinforcement learning

The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data from field measurements, experiments and large-scale simulations at multiple spatiotemporal scales. Machine learning offers a wealth of techniques to extract information from data that could be translated into knowledge about the underlying fluid mechanics. Moreover, machine learning algorithms can augment domain knowledge and automate tasks related to flow control and optimization. This article presents an overview of past history, current developments, and emerging opportunities of machine learning for fluid mechanics. It outlines fundamental machine learning methodologies and discusses their uses for understanding, modeling, optimizing, and controlling fluid flows. The strengths and limitations of these methods are addressed from the perspective of scientific inquiry that considers data as an inherent part of modeling, experimentation, and simulation. Machine learning provides a powerful information processing framework that can enrich, and possibly even transform, current lines of fluid mechanics research and industrial applications.

Machine Learning for Fluid Mechanics

1. Introduction 2. Linear Algebra Review 3. Analysis of First-order Information 4. Second-order Information in Linear Systems 5. Covariance Controllers 6.Covariance Upper Boundary Controllers 7. H-Controllers 8. Model Reduction 9. Unified Perspective 10. Projection Methods 11. Successive Centring Methods 12. A: Linear Algebra Basics 13. B: Calculus of Vectors and Matrices 14. C: Balanced Model Reduction

A unified algebraic approach to linear control design

First-order necessary conditions for quadratically optimal, steady-state,fixed-order dynamic compensation of a linear, time-invariant plant in the presence of disturbance and observation noise are derived in a new and highly simplified form. In contrast to the pair of matrix Riccati equations for the full-order LQG case, the optimal steady-state fixed-order dynamic compensator is characterized by four matrix equations (two modified Riccati equations and two modified Lyapunov equations) coupled by a projection whose rank is precisely equal to the order of the compensator and which determines the optimal compensator gains. The coupling represents a graphic portrayal of the demise of the classical separation principle for the reduced-order controller case.

/pdf/the-optimal-projection-equations-for-fixed-order-dynamic-4k6rp57ler.pdf

The optimal projection equations for fixed-order dynamic compensation

First-order necessary conditions for quadratically optimal reduced-order modeling of linear time-invariant systems are derived in the form of a pair of modified Lyapunov equations coupled by an oblique projection which determines the optimal reduced-order model. This form of the necessary conditions considerably simplifies previous results of Wilson [1] and clearly demonstrates the quadratic extremality and nonoptimality of the balancing method of Moore [2]. The possible existence of multiple solutions of the optimal projection equations is demonstrated and a relaxation-type algorithm is proposed for computing these local extrema. A component-cost analysis of the model-error criterion similar to the approach of Skelton [3] is utilized at each iteration to direct the algorithm to the global minimum.

/pdf/the-optimal-projection-equations-for-model-reduction-and-the-l64ohcw7xl.pdf

The optimal projection equations for model reduction and the relationships among the methods of Wilson, Skelton, and Moore

Active Control Technology for Large Space Structures

First-order necessary conditions for optimal, steady-state, reduced-order state estimation for a linear, time-invariant plant in the presence of correlated disturbance and nonsingular measurement noise are derived in a new and highly simplified form. In contrast to the lone matrix Riccati equation arising in the full-order (Kalman filter) case, the optimal steady-state reduced-order estimator is characterized by three matrix equations (one modified Riccati equation and two modified Lyapunov equations) coupled by a projection whose rank is precisely equal to the order of the estimator and which determines the optimal estimator gains. This coupling is a graphic reminder of the suboptimality of proposed approaches involving either model reduction followed by "full-order" estimator design or full-order estimator design followed by estimator-reduction techniques. The results given here complement recently obtained results which characterize the optimal reduced-order model by means of a pair of coupled modified Lyapunov equations [7] and the optimal fixed-order dynamic compensator by means of a coupled system of two modified Riceati equations and two modified Lyapunov equations [6].

/pdf/the-optimal-projection-equations-for-reduced-order-state-44o14oz178.pdf

The optimal projection equations for reduced-order state estimation

Compartmental models involve nonnegative state variables that exchange mass, energy, or other quantities in accordance with conservation laws. Such models are widespread in biology and economics. In this paper a connection is made between arbitrary (not necessarily nonnegative) state space systems and compartmental models. Specifically, for an arbitrary state space model with additive white noise, the nonnegative-definite second-moment matrix is characterized by a Lyapunov differential equation. Kronecker and Hadamard (Schur) matrix algebra is then used to derive an equation that characterizes the dynamics of the diagonal elements of the second-moment matrix. Since these diagonal elements are nonnegative, they can be viewed, in certain cases, as the state variables of a compartmental model. This paper examines weak coupling conditions under which the steady-state values of the diagonal elements actually satisfy a steady-state compartmental model.

/pdf/compartmental-modelling-and-second-moment-analysis-of-state-54w14sp6zz.pdf

David C. Hyland

Papers

The optimal projection equations for fixed-order dynamic compensation

The optimal projection equations for model reduction and the relationships among the methods of Wilson, Skelton, and Moore

Active Control Technology for Large Space Structures

The optimal projection equations for reduced-order state estimation

Compartmental modelling and second-moment analysis of state space systems