2 edition of **Optimal Liapunov functions** found in the catalog.

Optimal Liapunov functions

R. C. Breen

- 290 Want to read
- 6 Currently reading

Published
**1970**
.

Written in English

**Edition Notes**

Thesis(M.Sc.) - Course project in the Department of Mathematics, Loughborough University of Technology 1970.

Statement | by R.C. Breen. |

ID Numbers | |
---|---|

Open Library | OL21505859M |

The main purpose of this work is to prove a converse theorem for bounded-input bounded-state stability of nonlinear systems in the framework of Liapunov's second method. The construction gives rise to an upper semicontinuous time-dependent Liapunov function. In certain cases, the monotonicity conditions can be checked by means of contingent directional :// () Outline of the liapunov stability theory in general. In: Grujić L.T., Martynyuk A.A., Ribbens-Pavella M. (eds) Large Scale Systems Stability under Structural and Singular Perturbations. Lecture Notes in Control and Information Sciences, vol

Liapunov Functions and Stability in Control Theory, Communication and Control EngineeringR-composition of Lyapunov FunctionsStability Analysis of Dynamical Systems via R-functions /_Logical_composition_of_Lyapunov_functions. Vector and Matrix Liapunov Functions A Functional Differential Equation Brief Comments on the Start and Evolution of the Comparison Method in Stability Bibliographical Notes 4 Oscillatory Motion, with Special Regard to the Almost Periodic Case Trigonometric Polynomials and APr-Spaces › Home › Subjects › Mathematics & Statistics › Calculus › Differential Equations.

This paper is concerned with the problem of uniform persistence in population dynamics. We consider systems of reaction--diffusion equations which model ecosystems in bounded habitats with diffusion. It is shown that a system is persistent if every chain-recurrent set in the boundary of the positive cone does not attract trajectories from the interior of the positive cone, and this property Frequently, optimal control of engineering processes is difficult to achieve, or the resulting structure of the optimal control policy may not be in an appropriate form for application. This leads us to make certain approximations to the formulation of the problem, to simplify the model describing the process, or to impose some structure on the

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The optimal control system is formulated by considering a control system whose state at any time Optimal Liapunov functions book is described by an n This chapter highlights Liapunov functions and comparison theorems.

nonlinear mechanics, control theory, and other related topics. This book discusses the properties of solutions of equations in standard form in the In Stochastic Processes, Lyapunov Approach.

Lyapunov functions have been used in various contexts (stability, convergence analysis, design of model reference adaptive systems, etc.). The Lyapunov approach is based on the physical idea that the energy of an isolated system :// In [9] the definition of a liapunov function was confined to cylinders Γ = R + x G, G ⊂ G *.In this case we will say that V is a liapunov function of (1) on G.

Next we generalize the notion of the set E associated with a liapunov function V of (1) on Γ. The set E Optimal Liapunov functions book defined by x ∈ E if there is a sequence (t n,x n) ∈ Γ such that (t n,x n) → (∞,x) and V • (t n, x n) → 0 as n In the 2nd edition of this successful book several new sections were added and old sections have been improved, e.g., about the Zubovs method, Liapunov functions for discontinuous systems and The paper considers the control of a complex system consisting of distributed and lumped components.

A method involving the Liapunov function and the Laplace transformation is used to solve the problem of stabilization and quasi-optimal control. Equations for controlling functions are :// 15A/abstract. Liapunov Functions and Stability in Control Theory: Edition 2 - Ebook written by Andrea Bacciotti, Lionel Rosier.

Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Liapunov Functions and Stability in Control Theory: Edition :// The Liapunov functions define a metric or distance function with respect to the origin in the phase space.

This can also be used to define velocities. With this in mind it is now possible to develop a very important property of the isochronal surfaces. Along the optimal trajectory the following equation holds: (7) d T 0 d t Some stability deﬁnitions we consider nonlinear time-invariant system x˙ = f(x), where f: Rn → Rn a point xe ∈ R n is an equilibrium point of the system if f(xe) = 0 xe is an equilibrium point ⇐⇒ x(t) = xe is a trajectory suppose xe is an equilibrium point • system is globally asymptotically stable (G.A.S.) if for every trajectory Liapunov functions Differential equations and difference equations in ecosystem modeling Selected references Chapter 2.

Optimization techniques Introduction Static optimization problems Relaxed optimization problem method Multiple objectives decision problems Continuous time optimal control Discrete time Part of Z-Library project.

The world's largest scientific articles store. 70,+ articles for :// Liapunov‟s Stability Analysis: Introduction, Liapunov‟s Stability Criterion, The Direct Method of Liapunov and the Linear System, Methods of Constructing Liapunov Functions for Nonlinear Systems, Popov‟s Criterion.

MODULE-IV (10 HOURS) Optimal Control Systems: Introduction, Parameter Optimization: Servomechanisms, Optimal Optimal Control Applications and Methods() Global finite-time control for a class of switched nonlinear systems with different powers via output feedback.

International Journal of Systems Science This book presents different methods for generating Liapunov functions, which is important in the analysis of nonlinear systems. Organized into five chapters, this volume begins with an overview of the reduction of the important method of Liapunov to a practical working tool for the analysis of complex nonlinear :// $\begingroup$ E.g.

the book: Malisoff, M. and Mazenc, F. Constructions of Strict Lyapunov Functions. Springer, Springer, However, the best way to find a LF is experience in stability analysis $\endgroup$ – Carlos Feb 17 '18 at In the 2nd edition of this successful book several new sections were added and old sections have been improved, e.g about the Zubovs method, Liapunov functions for discontinuous systems and cascaded systems.

Many new examples, explanations and figures were added making this book accessible and well readable for engineers as well as :// Search in this book series. Edited by C.T. LEONDES. Volume 2, Pages () Download full volume. Previous volume. Next volume. Actions for selected chapters. Select all / Deselect all.

Download PDFs Export citations. Show all chapter previews Show all chapter :// Optimal Lyapunov function selection for reaching time estimation of Super Twisting algorithm and a formula to estimate the convergence time for the considered family of Lyapunov functions is perturbed Liapunov functions, local contraction, invariant set, stochastic invariant set, martingales, supermartingales, convergence with probability one, asymptotic and New York: Springer-Verlag.

[A comprehensive book on all aspects of stochastic recursive nearly optimal control and filtering for non-Markovian systems, and algorithms We also investigate the optimal stochastic control of the controlled semi-Markov processes.

The Bellman equation for semi-Markov risk processes is derived. Analogue of Dynkin formulae and boundary value problem for semi-Markov random evolutions, and properties of the respected stochastic Liapunov functions are :// Purchase International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics - 1st Edition.

Print Book & E-Book. ISBN. The groundbreaking work of Russian mathematician A. M. Liapunov on the analysis of stability of dynamical systems was overlooked for decades because of political turmoil. During the Cold War, when it was discovered that his method was applicable to the stability of aerospace guidance systems, interest in his research was rekindled and has remained high ever ://The mathematical pendulum is used to provide a survey of free and forced oscillations in damped and undamped systems.

This simple model is employed to present illustrations for and comparisons between the various approximation schemes. A summary of the Liapunov stability theory is provided.

The first and the second method of Liapunov are explained for autonomous as well as for nonautonomous The book covers important tools such as linearization, feedback concepts, the use of Liapunov functions, and optimal control.

This new edition is a valuable tool for understanding and teaching a rapidly growing field. Practitioners and researchers may also find this book of › Books › Science & Math › Mathematics.