Topic

# Multivariable calculus

About: Multivariable calculus is a research topic. Over the lifetime, 8498 publications have been published within this topic receiving 189652 citations. The topic is also known as: MV & multivariate calculus.

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19 May 1993

TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.

Abstract: Historical Survey The Modern Approach The Riemann-Liouville Fractional Integral The Riemann-Liouville Fractional Calculus Fractional Differential Equations Further Results Associated with Fractional Differential Equations The Weyl Fractional Calculus Some Historical Arguments.

7,643 citations

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01 Jan 1996

TL;DR: This book presents a rigorous, yet easily readable, introduction to the analysis and design of robust multivariable control systems and provides the reader with insights into the opportunities and limitations of feedback control.

Abstract: From the Publisher:
This is a book on practical feedback control and not on system theory in general. Feedback is used in control systems to change the dynamics of the system and to reduce the sensitivity of the system to both signal and model uncertainty. The book presents a rigorous, yet easily readable, introduction to the analysis and design of robust multivariable control systems. It provides the reader with insights into the opportunities and limitations of feedback control. Its objective is to enable the engineer to design real control systems. Important topics are: extensions and classical frequency-domain methods to multivariable systems, analysis of directions using the singular value decomposition, performance limitations and input-output controllability analysis, model uncertainty and robustness including the structured singular value, control structure design, and methods for controller synthesis and model reduction. Numerous worked examples, exercises and case studies, which make frequent use of MATLAB, are included. MATLAB files for examples and figures, solutions to selected exercises, extra problems and linear state-space models for the case studies are available on the Internet.

6,279 citations

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09 May 1995

TL;DR: The Malliavin calculus as mentioned in this paper is an infinite-dimensional differential calculus on a Gaussian space, originally developed to provide a probabilistic proof to Hormander's "sum of squares" theorem, but it has found a wide range of applications in stochastic analysis.

Abstract: The Malliavin calculus (or stochastic calculus of variations) is an infinite-dimensional differential calculus on a Gaussian space. Originally, it was developed to provide a probabilistic proof to Hormander's "sum of squares" theorem, but it has found a wide range of applications in stochastic analysis. This monograph presents the main features of the Malliavin calculus and discusses in detail its main applications. The author begins by developing the analysis on the Wiener space, and then uses this to establish the regularity of probability laws and to prove Hormander's theorem. The regularity of the law of stochastic partial differential equations driven by a space-time white noise is also studied. The subsequent chapters develop the connection of the Malliavin with the anticipating stochastic calculus, studying anticipating stochastic differential equations and the Markov property of solutions to stochastic differential equations with boundary conditions.
The second edition of this monograph includes recent applications of the Malliavin calculus in finance and a chapter devoted to the stochastic calculus with respect to the fractional Brownian motion.

3,883 citations

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TL;DR: In this article, a theoretical basis for model predictive control (MPC) has started to emerge and many practical problems like control objective prioritization and symptom-aided diagnosis can be integrated into the MPC framework by expanding the problem formulation to include integer variables yielding a mixed-integer quadratic or linear program.

Abstract: More than 15 years after model predictive control (MPC) appeared in industry as an effective means to deal with multivariable constrained control problems, a theoretical basis for this technique has started to emerge. The issues of feasibility of the on-line optimization, stability and performance are largely understood for systems described by linear models. Much progress has been made on these issues for non-linear systems but for practical applications many questions remain, including the reliability and efficiency of the on-line computation scheme. To deal with model uncertainty ‘rigorously’ an involved dynamic programming problem must be solved. The approximation techniques proposed for this purpose are largely at a conceptual stage. Among the broader research needs the following areas are identified: multivariable system identification, performance monitoring and diagnostics, non-linear state estimation, and batch system control. Many practical problems like control objective prioritization and symptom-aided diagnosis can be integrated systematically and effectively into the MPC framework by expanding the problem formulation to include integer variables yielding a mixed-integer quadratic or linear program. Efficient techniques for solving these problems are becoming available.

2,320 citations

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16 Aug 1989

TL;DR: This book discusses the development of Empirical Models from Process Data, Dynamic Behavior of First-Order and Second-Order Processes, and Dynamic Response Characteristics of More Complicated Processes.

Abstract: PART ONE: INTRODUCTORY CONCEPTS.1. Introduction to Process Control.2. Theoretical Models of Chemical Processes.PART TWO: DYNAMIC BEHAVIOR OF PROCESSES.3. Laplace Transforms.4. Transfer Function and State-Space Models.5. Dynamic Behavior of First-Order and Second-Order Processes.6. Dynamic Response Characteristics of More Complicated Processes.7. Development of Empirical Models from Process Data.PART THREE: FEEDBACK AND FEEDFORWARD CONTROL.8. Feedback Controllers.9. Control System Instrumentation.10. Overview of Control System Design.11. Dynamic Behavior and Stability of Closed-Loop Control Systems.12. PID Controller Design, Tuning, and Troubleshooting.13. Frequency Response Analysis.14. Control System Design Based on Frequency Response Analysis.15. Feedforward and Radio Control.PART FOUR: ADVANCED PROCESS CONTROL.16. Enhanced Single-Loop Control Strategies.17. Digital Sampling, Filtering, and Control.18. Multiloop and Multivariable Control.19. Real-Time Optimization.20. Model Predictive Control.21. Process Monitoring.22. Batch Process Control.23. Introduction to Plantwide Control.24. Plantwide Control System Design .Appendix A: Digital Process Control Systems: Hardware and Software.Appendix B: Review of Thermodynamics Concepts for Conservation Equations.Appendix C: Use of MATLAB in Process Control.Appendix D: Contour Mapping and the Principle of the Argument.Appendix E: Dynamic Models and Parameters Used for Plantwide Control Chapters.

2,285 citations