Practical Methods For Optimal Control Using Nonlinear Programming Third Edition

"The third edition focuses on the direct transcription method for optimal control and includes new material on implicit Runge-Kutta discretization techniques, new chapters on partial differential equations and delay equations, and over seventy test problems and open source FORTRAN code for all of the problems"--

The book describes how sparse optimization methods can be combined with discretization techniques for differential-algebraic equations and used to solve optimal control and estimation problems. The interaction between optimization and integration is emphasized throughout the book.

How do you fly an airplane from one point to another as fast as possible? What is the best way to administer a vaccine to fight the harmful effects of disease? What is the most efficient way to produce a chemical substance? This book presents practical methods for solving real optimal control problems such as these. Practical Methods for Optimal Control Using Nonlinear Programming, Third Edition focuses on the direct transcription method for optimal control. It features a summary of relevant material in constrained optimization, including nonlinear programming; discretization techniques appropriate for ordinary differential equations and differential-algebraic equations; and several examples and descriptions of computational algorithm formulations that implement this discretize-then-optimize strategy. The third edition has been thoroughly updated and includes new material on implicit Runge–Kutta discretization techniques, new chapters on partial differential equations and delay equations, and more than 70 test problems and open source FORTRAN code for all of the problems. This book will be valuable for academic and industrial research and development in optimal control theory and applications. It is appropriate as a primary or supplementary text for advanced undergraduate and graduate students.

This self-contained book presents in a unified, systematic way the basic principles of optimal control governed by ODEs. Using a variational perspective, the author incorporates important restrictions like constraints for control and state, as well as the state system itself, into the equivalent variational reformulation of the problem. The fundamental issues of existence of optimal solutions, optimality conditions, and numerical approximation are then examined from this variational viewpoint. Inside, readers will find a unified approach to all the basic issues of optimal control, academic and real-world examples testing the book’s variational approach, and a rigorous treatment stressing ideas and arguments rather than the underlying mathematical formalism. A Variational Approach to Optimal Control of ODEs is mainly for applied analysts, applied mathematicians, and control engineers, but will also be helpful to other scientists and engineers who want to understand the basic principles of optimal control governed by ODEs. It requires no prerequisites in variational problems or expertise in numerical approximation. It can be used for a first course in optimal control.

This book introduces optimal control methods, formulated as optimization problems, applied to business dynamics problems. Business dynamics refers to a combination of business management and financial objectives embedded in a dynamical system model. The model is subject to a control that optimizes a performance index and takes both management and financial aspects into account. Business Dynamics Models: Optimization-Based One Step Ahead Optimal Control includes solutions that provide a rationale for the use of optimal control and guidelines for further investigation into more complex models, as well as formulations that can also be used in a so-called flight simulator mode to investigate different complex scenarios. The text offers a modern programming environment (Jupyter notebooks in JuMP/Julia) for modeling, simulation, and optimization, and Julia code and notebooks are provided on a website for readers to experiment with their own examples. This book is intended for students majoring in applied mathematics, business, and engineering. The authors use a formulation-algorithm-example approach, rather than the classical definition-theorem-proof, making the material understandable to senior undergraduates and beginning graduates.

Extremum Seeking through Delays and PDEs, the first book on the topic, expands the scope of applicability of the extremum seeking method, from static and finite-dimensional systems to infinite-dimensional systems. Readers will find numerous algorithms for model-free real-time optimization are developed and their convergence guaranteed, extensions from single-player optimization to noncooperative games, under delays and PDEs, are provided, the delays and PDEs are compensated in the control designs using the PDE backstepping approach, and stability is ensured using infinite-dimensional versions of averaging theory, and accessible and powerful tools for analysis. This book is intended for control engineers in all disciplines (electrical, mechanical, aerospace, chemical), mathematicians, physicists, biologists, and economists. It is appropriate for graduate students, researchers, and industrial users.

This book introduces transfinite interpolation as a generalization of interpolation of data prescribed at a finite number of points to data prescribed on a geometrically structured set, such as a piece of curve, surface, or submanifold. The time-independent theory is readily extended to a moving/deforming data set whose dynamics is specified in a Eulerian or Lagrangian framework. The resulting innovative tools cover a very broad spectrum of applications in fluid mechanics, geometric optimization, and imaging. The authors chose to focus on the dynamical mesh updating in fluid mechanics and the construction of velocity fields from the boundary expression of the shape derivative. Transfinite Interpolations and Eulerian/Lagrangian Dynamics is a self-contained graduate-level text that integrates theory, applications, numerical approximations, and computational techniques. It applies transfinite interpolation methods to finite element mesh adaptation and ALE fluid-structure interaction. Specialists in applied mathematics, physics, mechanics, computational sciences, imaging sciences, and engineering will find this book of interest.

This book is about nonlinear observability. It provides a modern theory of observability based on a new paradigm borrowed from theoretical physics and the mathematical foundation of that paradigm. In the case of observability, this framework takes into account the group of invariance that is inherent to the concept of observability, allowing the reader to reach an intuitive derivation of significant results in the literature of control theory. The book provides a complete theory of observability and, consequently, the analytical solution of some open problems in control theory. Notably, it presents the first general analytic solution of the nonlinear unknown input observability (nonlinear UIO), a very complex open problem studied in the 1960s. Based on this solution, the book provides examples with important applications for neuroscience, including a deep study of the integration of multiple sensory cues from the visual and vestibular systems for self-motion perception. Observability: A New Theory Based on the Group of Invariance is the only book focused solely on observability. It provides readers with many applications, mostly in robotics and autonomous navigation, as well as complex examples in the framework of vision-aided inertial navigation for aerial vehicles. For these applications, it also includes all the derivations needed to separate the observable part of the system from the unobservable, an analysis with practical importance for obtaining the basic equations for implementing any estimation scheme or for achieving a closed-form solution to the problem. This book is intended for researchers in robotics and automation, both in academia and in industry. Researchers in other engineering disciplines, such as information theory and mechanics, will also find the book useful.