Optimal Control | Chapter 7 | Modern Control Systems: Theory, Design and Applications

This chapter provides optimal control theory for readers. In this chapter, optimal control conception and variation method were respectively narrated and explained to help readers understand optimal control problems. Furthermore, maximum principle and linear quadratic optimal control and dynamic programming were also narrated and analyzed to aid readers in correctly applying optimal control into practice. In this chapter, readers need to grasp three basic methods: variation method, minimum principle and dynamic programming.

 

Author (s) Details

 

Zhou Gaofeng
Zhongyuan University of Technology, China.

 

Zhang Qi
Zhongyuan University of Technology, China.

 

Please see the book here:- https://doi.org/10.9734/bpi/mono/978-93-49473-76-8/CH7

Modern Control Systems: Theory, Design and Applications| Book Publisher International

Relevant theories on modern control systems are narrated and explained to help readers grasp some crucial factors when a control system needs to be analyzed to realize a given action or aim. Classical examples are also provided and explained for a specific idea in detail. Deep discussion and analysis can provide an enough comprehension for readers. Review section is also added to the end of each chapter to strengthen possible consideration for some special themes.

 

This book systematically focuses on modern control systems and timely explains some available tools on control system analysis. The whole book is divided into 12 chapters and several appendices. Different chapter narrates different theme according to the whole work course of modern control system. Main contents include: introduction to classical control theory, common mathematical models of linear system, the solution of state equation for linear continuous and discrete system, steady-state error, stability analysis of control system, controllability and observability of linear system, state feedback and state observer design, optimal control, PID control and robust control, dynamic system identification and state evaluation, adaptive control and fuzzy control, modern digital control systems and overview of nonlinear control. Besides, auxiliary basic knowledge and specific examples are also added in the book or appendix section.

 

This book can be utilized as the undergraduate or graduate’s textbook or reference, also as basic technology textbook of engineer cultivation. Besides, this book can be read and applied by industrialists, engineering researcher, engineer, engineering technologist and mechanics. Of course, this book can be also taught as a textbook in the field of industry for international students or researchers or engineers. This book may help readers completely comprehend modern control systems for their possible application in reality.

 

Author (s) Details

Zhou Gaofeng
Zhongyuan University of Technology, China.

 

Zhang Qi
Zhongyuan University of Technology, China.

 

Please see the book here:- https://doi.org/10.9734/bpi/mono/978-93-49473-76-8/CH0

Determining the Sufficiency in Optimal Control without the Strengthened Condition of Legendre | Chapter 11 | Recent Advances in Mathematical Research and Computer Science Vol. 4

 In this paper, we develop a sufficiency theorem for an unconstrained Lagrange fixed-endpoint problem that provides sufficient conditions for processes that do not satisfy the traditional nonsingularity assumption, i.e., the strengthened Legendre condition is not imposed by the new sufficiency theorem. Unlike numerous generalisations of conjugate points, solutions of specific matrix Riccati equations, invariant integrals, or the Hamiltonian-Jacobi theory, the latter uses the positivity of the second variation explicitly in the demonstration of sufficiency.

Author(S) Details

Gerardo Sanchez Licea
Departamento de Matematicas, Facultad de Ciencias UNAM, Mexico D.F. 04510, Mexico.

View Book:- https://stm.bookpi.org/RAMRCS-V4/article/view/4877

Stability and Optimal Control of an Mathematical Model of Tuberculosis/AIDS Co-infection with Vaccination | Chapter 3 | New Ideas Concerning Science and Technology Vol. 11

 The analysis and control of a nonlinear mathematical epidemic model (S S_vih V E LI ) based on a system of ordinary differential equations modelling the spread of tuberculosis infectious with VIH/AIDS coinfection are the subject of this paper. The existence of both disease-free and endemic equilibrium is debated. R₀ is the reproduction number that has been calculated. We investigate the stability of epidemic systems around equilibriums using Lyapunov-Lasalle methods (Disease free and endemic equilibrium). The disease-free equilibrium's global asymptotic stability is proven whenever R_vac < 1, where R₀ is the reproduction number. We also show that Tuberculosis can be eradicated when R0 is less than one. To validate analytic data, numerical simulations are used. To achieve disease prevention by reducing the infectious group to the lowest level of vaccine coverage possible. There is a formulation of a control problem. The optimal control is defined using the Pontryagin's maximum theory. The Runge Kutta fourth method is used to extract and solve the optimality system numerically.

Author (s) Details

Leontine Nkague Nkamba
Department of Mathematics, University of Yaound´e I, Higher Teacher Training College, P.O. Box 47 Yaound´ e, Cameroon and AIDEPY Association des Ing ´enieurs Diplom´es de l’Ecole Polytechnique de Yaound´ e, Cameroon.

Thomas Timothee Manga
AIDEPY Association des Ing ´enieurs Diplom´es de l’Ecole Polytechnique de Yaound´ e, Cameroon.

View Book :- https://stm.bookpi.org/NICST-V11/article/view/677