scispace - formally typeset

Multivariable calculus

About: Multivariable calculus is a(n) research topic. Over the lifetime, 8498 publication(s) have been published within this topic receiving 189652 citation(s). The topic is also known as: MV & multivariate calculus. more


Open accessBook
19 May 1993-
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. more

Topics: Fractional dynamics (83%), Fractional calculus (76%), Time-scale calculus (67%) more

7,229 Citations

Open accessBook
01 Jan 1996-
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. more

Topics: Instrumentation and control engineering (59%), Control theory (57%), Control system (55%) more

6,068 Citations

Open accessBook
09 May 1995-
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. more

Topics: Malliavin calculus (81%), Stochastic calculus (72%), Malliavin derivative (69%) more

3,684 Citations

Open accessJournal ArticleDOI: 10.1109/TAC.1981.1102555
John Doyle1, Gunter Stein2Institutions (2)
Abstract: This paper presents a practical design perspective on multivariable feedback control problems. It reviews the basic issue-feedback design in the face of uncertainties-and generalizes known single-input, single-output (SISO) statements and constraints of the design problem to multiinput, multioutput (MIMO) cases. Two major MIMO design approaches are then evaluated in the context of these results. more

2,247 Citations

Open accessBook
16 Aug 1989-
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. more

Topics: Model predictive control (61%), Process control (61%), Automatic control (60%) more

2,243 Citations

No. of papers in the topic in previous years

Top Attributes

Show by:

Topic's top 5 most impactful authors

B. Porter

49 papers, 580 citations

Michael J. Grimble

46 papers, 647 citations

Gang Tao

41 papers, 636 citations

Edward J. Davison

31 papers, 1.4K citations

Feng Ding

23 papers, 1.1K citations

Network Information
Related Topics (5)
Optimal control

68K papers, 1.2M citations

91% related
Linear system

59.5K papers, 1.4M citations

90% related
Robust control

42K papers, 810.5K citations

89% related
Adaptive control

60.1K papers, 1.2M citations

89% related
Model predictive control

39.6K papers, 660.4K citations

89% related