On the discrete linear quadratic minimum-time problem
01 Apr 1998-Journal of The Franklin Institute-engineering and Applied Mathematics (Pergamon)-Vol. 335, Iss: 3, pp 525-532
TL;DR: In this paper, the minimum-time and the control which minimizes the cost function and leads the system from a given initial state to a fixed final one are compared. But the minimum time and the optimal control are not compared.
Abstract: E. I. Verriest and F. L. Lewis have presented in (1) a new method to approximate the minimum-time control of linear continuous-time systems avoiding the Bang-Bang control. Their method relied on the optimization of a cost including time energy and precision terms. Our purpose in this article is to extend their work to discrete-time linear systems. Indeed, we consider a linear discrete-time system and a quadratic cost including time and energy term, and we look for the minimum-time and the control which minimizes the cost function and leads the system from a given initial state to a fixed final one. By selecting the magnitude of the energy term, one may balance off the requirement for minimum-time versus the one for keeping the state and inputs small over the considered interval of time. Finally we give a method to compute the minimum-time and the optimal control.
Citations
More filters
••
TL;DR: In this paper, a closed-form solution to the problem of optimally charging a Li-ion battery is presented, where a combination of three cost functions is considered as the objective function: time-to-charge, energy losses, and temperature rise index (TRI).
79 citations
••
01 Jan 2004TL;DR: In this paper, the output transition problem is formulated as a linear quadratic minimum-time (LQMT) optimal control problem, which avoids bang-bang controllers that result from solving the traditional time-optimal problem.
Abstract: This article addresses the optimal (minimum-time/energy) trajectory design for rapid output transitions, i.e. changing the output from one value to another, in linear systems. Furthermore, the output is required to be maintained constant (e.g. without vibration) outside the transition time interval. The output-transition problem is posed as a linear quadratic minimum-time (LQMT) optimal control problem, which avoids bang-bang controllers that result from solving the traditional time-optimal problem. Additionally, the LQMT approach allows the time-optimal requirement to be traded off with the energy requirement by selecting appropriated weighting factors. Current methods transform this LQMT output-transition problem into a state-transition problem by constraining the initial and final state of the output-transition interval. However, the choice of the initial and final states can be ad hoc and the resulting control law may not be optimal. In contrast, the proposed approach directly solves the LQMT output-transition problem by optimally choosing the initial and final states to minimize the output-transition cost. The novelty of the proposed approach is that inputs are not applied just during the output-transition time interval; rather, inputs are also applied before the beginning of and after the end of the output-transition time interval (these inputs are called pre- and post-actuation). The method is illustrated using a flexible structure model, and simulation results show substantial reduction in output-transition cost when compared with the cost of standard state-transition-based approaches, which do not use pre-and post-actuation.
16 citations
••
01 Jul 2015TL;DR: A closed-form solution to the problem of optimally charging a Li-ion battery as a combination of two cost functions: time-to-charge (TTC) and energy losses (EL).
Abstract: In this paper, we present a closed-form solution to the problem of optimally charging a Li-ion battery. The objective function is considered as a combination of two cost functions: time-to-charge (TTC) and energy losses (EL). For the case where cost function is a combination of TTC and EL, the optimal charging strategy is a Constant Current-Constant Voltage (CC-CV) policy with the value of the current in the CC stage being a function of the ratio of weighting on TTC and EL and of the resistance of the battery. The case where the cost function is a weighted sum of TTC, EL and a temperature rise index (TRI) is also considered and an analytical solution for the problem is derived. This analytical solution can be approximated by a CC-CV with the value of current in the CC stage being a function of ratio of weighting on TTC and EL, resistance of the battery and the effective thermal resistance. The effects of weights in the objective function on the optimal charging profile is discussed and the behavior of different kinds of commercial batteries are analyzed.
11 citations
Cites methods from "On the discrete linear quadratic mi..."
...Inspired by [19] and [4], we solve the problem in three steps as described below: Ê Given k1 (when the terminal voltage constraint becomes active), find the optimal current profile that minimizes the energy losses, and calculate the corresponding energy losses as a function of k1....
[...]
••
TL;DR: In this paper, the optimal trajectory design for changing the output from one value y to another y within a finite time interval [0, t f ] called the output-transition time interval is addressed.
Abstract: This article addresses the optimal (minimum-time/energy) trajectory design for changing the output from one value y to another y within a finite time interval [0, t f ] called the output-transition time interval. The output should be maintained constant (at the desired value) outside the output-transition time interval. The main contribution of this article is to establish the existence of a solution to the problem when preactuation (input applied during time t t f ) are allowed. The advantage of using pre- and postactuation inputs is illustrated with an experimental dual-stage actuator system.
11 citations
••
TL;DR: It is shown that the resolution of the considered problem is equivalent to that of a controllability, one so-called Extended Exact Controllability with time-varying operators, and the Hilbert uniqueness method approach is extended to this case to provide an explicit form for the optimal control.
Abstract: The present work deals with the linear quadratic control problem for a discrete distributed system with terminal convex constraint. Using techniques of perturbation by feedback, it is shown that the resolution of the considered problem is equivalent to that of a controllability, one so-called Extended Exact Controllability with time-varying operators. The Hilbert uniqueness method approach is then extended to this case to provide an explicit form for the optimal control. In the same framework, the inequality constraint case is examined for which a practical numerical resolution is given. Finally, the results obtained are used to treat a minimum-time reachability problem.
3 citations
References
More filters
•
01 Oct 1972
TL;DR: In this article, the authors provide an excellent introduction to feedback control system design, including a theoretical approach that captures the essential issues and can be applied to a wide range of practical problems.
Abstract: Linear Optimal Control SystemsFeedback Control TheoryOptimal ControlLinear Optimal ControlOptimal Control SystemsThe Zeros of Linear Optimal Control Systems and Their Role in High Feedback Gain Stability DesignOptimal ControlLinear State-Space Control SystemsOptimal Control of Dynamic Systems Driven by Vector MeasuresApplied Linear Optimal Control Paperback with CD-ROMNonlinear and Optimal Control SystemsLinear SystemsLinear Control TheoryLinear Systems and Optimal ControlOptimal Control Methods for Linear Discrete-Time Economic SystemsOptimal Control Theory for Infinite Dimensional SystemsInfinite Dimensional Linear Control SystemsStochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop SolutionsApplications of Optimal Control Theory to Computer Controller DesignSwitching and Learning in Feedback SystemsContinuous Time Dynamical SystemsNew Trends in Optimal Filtering and Control for Polynomial and Time-Delay SystemsThe Theory and Application of Linear Optimal ControlTurnpike Theory of Continuous-Time Linear Optimal Control ProblemsLinear Optimal Control SystemsLinear Control TheoryCalculus of Variations and Optimal Control TheoryOptimal ControlNonlinear Controllability and Optimal ControlOptimal Control TheoryOptimal Control Of Singularly Perturbed Linear Systems And ApplicationsOptimal Control SystemsDesign criterion for improving the sensitivity of linear optimal control systemsLinear Stochastic Control SystemsConstrained Optimal Control of Linear and Hybrid SystemsOptimal Control Of Singularly Perturbed Linear Systems And ApplicationsPredictive Control for Linear and Hybrid SystemsOptimal ControlOptimal Control Theory with Applications in EconomicsNonlinear Optimal Control Theory Successfully classroom-tested at the graduate level, Linear Control Theory: Structure, Robustness, and Optimization covers three major areas of control engineering (PID control, robust control, and optimal control). It provides balanced coverage of elegant mathematical theory and useful engineering-oriented results. The first part of the book develops results relating to the design of PID and first-order controllers for continuous and discrete-time linear systems with possible delays. The second section deals with the robust stability and performance of systems under parametric and unstructured uncertainty. This section describes several elegant and sharp results, such as Kharitonov’s theorem and its extensions, the edge theorem, and the mapping theorem. Focusing on the optimal control of linear systems, the third part discusses the standard theories of the linear quadratic regulator, Hinfinity and l1 optimal control, and associated results. Written by recognized leaders in the field, this book explains how control theory can be applied to the design of real-world systems. It shows that the techniques of three term controllers, along with the results on robust and optimal control, are invaluable to developing and solving research problems in many areas of engineering.An excellent introduction to feedback control system design, this book offers a theoretical approach that captures the essential issues and can be applied to a wide range of practical problems. Its explorations of recent developments in the field emphasize the relationship of new procedures to classical control theory, with a focus on single input and output systems that keeps concepts accessible to students with limited backgrounds. The text is geared toward a single-semester senior course or a graduate-level class for students of electrical engineering. The opening chapters constitute a basic treatment of feedback design. Topics include a detailed formulation of the control design program, the fundamental issue of performance/stability robustness tradeoff, and the graphical design technique of loopshaping. Subsequent chapters extend the discussion of the loopshaping technique and connect it with notions of optimality. Concluding chapters examine controller design via optimization, offering a mathematical approach that is useful for multivariable systems.Upper-level undergraduate text introduces aspects of optimal control theory: dynamic programming, Pontryagin's minimum principle, and numerical techniques for trajectory optimization. Numerous figures, tables. Solution guide available upon request. 1970 edition.Infinite dimensional systems can be used to describe many phenomena in the real world. As is well known, heat conduction, properties of elastic plastic material, fluid dynamics, diffusion-reaction processes, etc., all lie within this area. The object that we are studying (temperature, displace ment, concentration, velocity, etc.) is usually referred to as the state. We are interested in the case where the state satisfies proper differential equa tions that are derived from certain physical laws, such as Newton's law, Fourier's law etc. The space in which the state exists is called the state space, and the equation that the state satisfies is called the state equation. By an infinite dimensional system we mean one whose corresponding state space is infinite dimensional. In particular, we are interested in the case where the state equation is one of the following types: partial differential equation, functional differential equation, integro-differential equation, or abstract evolution equation. The case in which the state equation is being a stochastic differential equation is also an infinite dimensional problem, but we will not discuss such a case in this book.For more than forty years, the equation y’(t) = Ay(t) + u(t) in Banach spaces has been used as model for optimal control processes described by partial differential equations, in particular heat and diffusion processes. Many of the outstanding open problems, however, have remained open until recently, and some have never been solved. This book is a survey of all results know to the author, with emphasis on very recent results (1999 to date). The book is restricted to linear equations and two particular problems (the time optimal problem, the norm optimal problem) which results in a more focused and concrete treatment. As experience shows, results on linear equations are the basis for the treatment of their semilinear counterparts, and techniques for the time and norm optimal problems can often be generalized to more general cost functionals. The main object of this book is to be a state-of-the-art monograph on the theory of the time and norm optimal controls for y’(t) = Ay(t) + u(t) that ends at the very latest frontier of research, with open problems and indications for future research. Key features: · Applications to optimal diffusion processes. · Applications to optimal heat propagation processes. · Modelling of optimal processes governed by partial differential equations. · Complete bibliography. · Includes the latest research on the subject. · Does not assume anything from the reader except basic functional analysis. · Accessible to researchers and advanced graduate students alike · Applications to optimal diffusion processes. · Applications to optimal heat propagation processes. · Modelling of optimal processes governed by partial differential equations. · Complete bibliography. · Includes the latest research on the subject. · Does not assume anything from the reader except basic functional analysis. · Accessible to researchers and advanced graduate students alikeLinear Stochastic Control Systems presents a thorough description of the mathematical theory and fundamental principles of linear stochastic control systems. Both continuous-time and discrete-time systems are thoroughly covered. Reviews of the modern probability and random processes theories and the Itô stochastic differential equations are provided. Discrete-time stochastic systems theory, optimal estimation and Kalman filtering, and optimal stochastic control theory are studied in detail. A modern treatment of these same topics for continuous-time stochastic control systems is included. The text is written in an easy-to-understand style, and the reader needs only to have a background of elementary real analysis and linear deterministic systems theory to comprehend the subject matter. This graduate textbook is also suitable for self-study, professional training, and as a handy research reference. Linear Stochastic Control Systems is self-contained and provides a step-by-step development of the theory, with many illustrative examples, exercises, and engineering applications.This outstanding reference presents current, state-of-the-art research on importantproblems of finite-dimensional nonlinear optimal control and controllability theory. Itpresents an overview of a broad variety of new techniques useful in solving classicalcontrol theory problems.Written and edited by renowned mathematicians at the forefront of research in thisevolving field, Nonlinear Controllability and Optimal Control providesdetailed coverage of the construction of solutions of differential inclusions by means ofdirectionally continuous sections Lie algebraic conditions for local controllability the use of the Campbell-Hausdorff series to derive properties of optimal trajectories the Fuller phenomenon the theory of orbits and more.Containing more than 1,300 display equations, this exemplary, instructive reference is aninvaluable source for mathematical researchers and applied mathematicians, electrical andelectronics, aerospace, mechanical, control, systems, and computer engineers, and graduatestudents in these disciplines .This book is based on lectures from a one-year course at the Far Eastern Federal University (Vladivostok, Russia) as well as on workshops on optimal control offered to students at various mathematical departments at the university level. The main themes of the theory of linear and nonlinear systems are considered, including the basic problem of establishing the necessary and sufficient conditions of optimal processes. In the
4,294 citations
•
[...]
13 Feb 1986
TL;DR: Reading optimal control frank l lewis solution manual ebook pdf 2019 is extremely useful because you could get enough detailed information in the book technology has.
Abstract: optimal control frank l lewis solution manual optimal control frank l lewis solution manual download optimal control frank l lewis solution manual document on this page you can read or download optimal control frank l lewis solution manual in pdf format if you don t see any interesting for you use our search form on bottom optimal feature selection for support vector machines, optimal control frank l lewis solution manual obtain optimal control frank l lewis solution manual guide pdf and others format obtainable from this web site may not be reproduced in any form in whole or in part except for brief quotation in critical articles or comments without prior written authorization from optimal control frank l lewis solution manual, download optimal control frank l lewis solution manual pdf there are a lot of books literatures user manuals and guidebooks that are related to optimal control frank l lewis solution manual such as promo code for bikini body guide journal of sports training central air conditioner troubleshooting guide tv guide free movies 2005, optimal control frank l lewis solution manual optimal control frank l lewis 9781118122709 telegraph frank l lewis is the moncrief o donnell professor and head of the advanced controls sensors and mems group in the automation and robotics research institute of the university of texas at arlington optimal control frank l lewis draguna vrabie vassilis, optimal control frank l lewis solution manual wsntech net optimal control frank l lewis solution manual 1999 repair optimal control third edition lewis wiley tata novus 5542 workshop manual cooperative control of multi agent systems instron 4443 lewis vrabie syrmos optimal control 3rd celebrity boats manuals optimal control frank l lewis draguna vrabie, optimal control frank l lewis solution manual pdf format optimal control frank l lewis solution manual pdf format related book pdf book optimal control frank l lewis solution manual honda crv user manual 2005 honda gx 200 repair manual honda gx 160 owners manual honda cr z manual for sale honda dio 1, optimal control frank l lewis solution manual polyurea com optimal control frank l lewis solution manual sun 31 mar 2019 09 06 00 gmt optimal control frank l lewis pdf use of microbes for control and eradication of invasive arthropods 2009 ann hajek download with google download with facebook or download with email fri 05 apr 2019 14 01 00 gmt pdf invasive arthropods and approaches for their, optimal control frank l lewis solution manual pdf download optimal control frank l lewis solution manual twitpic dear twitpic community thank you for all the wonderful photos you have taken over the years we have now placed twitpic in an archived state, optimal control frank l lewis solution manual ebook pdf optimal control frank l lewis solution manual ebook pdf 2019 zsoi4 net free download pdf books optimal control frank l lewis solution manual ebook pdf 2019 everybody knows that reading optimal control frank l lewis solution manual ebook pdf 2019 is extremely useful because we could get enough detailed information in the book technology has, l lewis draguna vrabie s solutions manual optimal control l lewis draguna vrabie s solutions manual optimal control 3rd ed by frank l lewis draguna vrabie vassilis l syrmos ism pdf review your past material prepare for future material and get full marks with these supplemental ism pdfs, solution manual optimal control frank lewis locklines org uk solution manual optimal control frank lewis optimal control frank l lewis solution manual ebook optimal control frank l lewis solution manual currently available at
3,133 citations
•
01 Jan 1971
TL;DR: The relationship between state variable and transfer function descriptions of linear feedback control systems is discussed in this paper, along with the relationship between the Cayley Hamilton Theorem and state variable descriptions of systems.
Abstract: 1. Background and Preview. 2. Highlights of Classical Control Theory. 3. State Variables and the State Space Description of Dynamic Systems. 4. Fundamentals of Matrix Algebra. 5. Vectors and Linear Vector Spaces. 6. Simultaneous Linear Equations. 7. Eigenvalues and Eigenvectors. 8. Functions of Square Matrices and the Cayley-Hamilton Theorem. 9. Analysis of Continuous and Discrete Time State Equations. 10. Stability. 11. Controllability and Observability for Linear Systems. 12. The Relationship between State Variable and Transfer Function Descriptions of Systems. 13. Design of Linear Feedback Control Systems. 14. An Introduction to Optimal Control Theory. 15. An Introduction to Nonlinear Control Systems.
1,419 citations
••
TL;DR: In this paper, a nontraditional minimum-time problem that includes quadratic-state and control-weighting terms in the performance index is investigated, and a convenient solution to the problem that uses the solution of the Riccati equation to compute the optimal feedback gain and the optimal time is provided.
Abstract: A nontraditional minimum-time problem that includes quadratic-state and control-weighting terms in the performance index is investigated. This formulation provides a convenient solution to the problem that uses the solution of the Riccati equation to compute the optimal feedback gain and the optimal time. In some cases the latter is simply found using the derivative of the Riccati equation solution. >
48 citations
•
01 Jan 1986
TL;DR: In this article, a commande optimale avec critere quadratique des systemes bilineaires distribues ainsi qu'a l'elaboration d'algorithmes numeriques.
Abstract: Etude consacree a l'analyse et a la commande optimale avec critere quadratique des systemes bilineaires distribues ainsi qu'a l'elaboration d'algorithmes numeriques. Deux applications sont developpees: commande d'un systeme de stockage thermique par chaleur sensible en milieu poreux, et le controle d'une pompe a chaleur (reacteurs solide/gaz).
18 citations