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16.323 Principles of Optimal Control (MIT) 16.323 Principles of Optimal Control (MIT)

Description

This course studies the principles of deterministic optimal control. It uses variational calculus and Pontryagin's maximum principle. It focuses on applications of the theory, including optimal feedback control, time-optimal control, and others. Dynamic programming and numerical search algorithms are introduced briefly. This course studies the principles of deterministic optimal control. It uses variational calculus and Pontryagin's maximum principle. It focuses on applications of the theory, including optimal feedback control, time-optimal control, and others. Dynamic programming and numerical search algorithms are introduced briefly.

Subjects

nonlinear optimization | nonlinear optimization | linear quadratic regulators | linear quadratic regulators | MATLAB implementation | MATLAB implementation | dynamic programming | dynamic programming | calculus of variations | calculus of variations | LQR | LQR | LQG | LQG | stochastic optimization | stochastic optimization | on-line optimization and control | on-line optimization and control | constrained optimization | constrained optimization | signals | signals | system norms | system norms | Model Predictive Behavior | Model Predictive Behavior | quadratic programming | quadratic programming | mixed-integer linear programming | mixed-integer linear programming | linear programming | linear programming

License

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2.035 Special Topics in Mathematics with Applications: Linear Algebra and the Calculus of Variations (MIT) 2.035 Special Topics in Mathematics with Applications: Linear Algebra and the Calculus of Variations (MIT)

Description

This course forms an introduction to a selection of mathematical topics that are not covered in traditional mechanical engineering curricula, such as differential geometry, integral geometry, discrete computational geometry, graph theory, optimization techniques, calculus of variations and linear algebra. The topics covered in any particular year depend on the interest of the students and instructor. Emphasis is on basic ideas and on applications in mechanical engineering. This year, the subject focuses on selected topics from linear algebra and the calculus of variations. It is aimed mainly (but not exclusively) at students aiming to study mechanics (solid mechanics, fluid mechanics, energy methods etc.), and the course introduces some of the mathematical tools used in these subjects. App This course forms an introduction to a selection of mathematical topics that are not covered in traditional mechanical engineering curricula, such as differential geometry, integral geometry, discrete computational geometry, graph theory, optimization techniques, calculus of variations and linear algebra. The topics covered in any particular year depend on the interest of the students and instructor. Emphasis is on basic ideas and on applications in mechanical engineering. This year, the subject focuses on selected topics from linear algebra and the calculus of variations. It is aimed mainly (but not exclusively) at students aiming to study mechanics (solid mechanics, fluid mechanics, energy methods etc.), and the course introduces some of the mathematical tools used in these subjects. App

Subjects

calculus of variations | calculus of variations | linear algebra | linear algebra | solid mechanics | solid mechanics | fluid mechanics | fluid mechanics | energy methods | energy methods | microstructures of crystalline | microstructures of crystalline

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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14.451 Dynamic Optimization Methods with Applications (MIT) 14.451 Dynamic Optimization Methods with Applications (MIT)

Description

This course focuses on dynamic optimization methods, both in discrete and in continuous time. We approach these problems from a dynamic programming and optimal control perspective. We also study the dynamic systems that come from the solutions to these problems. The course will illustrate how these techniques are useful in various applications, drawing on many economic examples. However, the focus will remain on gaining a general command of the tools so that they can be applied later in other classes. This course focuses on dynamic optimization methods, both in discrete and in continuous time. We approach these problems from a dynamic programming and optimal control perspective. We also study the dynamic systems that come from the solutions to these problems. The course will illustrate how these techniques are useful in various applications, drawing on many economic examples. However, the focus will remain on gaining a general command of the tools so that they can be applied later in other classes.

Subjects

vector spaces | vector spaces | principle of optimality | principle of optimality | concavity of the value function | concavity of the value function | differentiability of the value function | differentiability of the value function | Euler equations | Euler equations | deterministic dynamics | deterministic dynamics | models with constant returns to scale | models with constant returns to scale | nonstationary models | nonstationary models | stochastic dynamic programming | stochastic dynamic programming | stochastic Euler equations | stochastic Euler equations | stochastic dynamics | stochastic dynamics | calculus of variations | calculus of variations | the maximum principle | the maximum principle | discounted infinite-horizon optimal control | discounted infinite-horizon optimal control | saddle-path stability | saddle-path stability

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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16.323 Principles of Optimal Control (MIT) 16.323 Principles of Optimal Control (MIT)

Description

This course studies basic optimization and the principles of optimal control. It considers deterministic and stochastic problems for both discrete and continuous systems. The course covers solution methods including numerical search algorithms, model predictive control, dynamic programming, variational calculus, and approaches based on Pontryagin's maximum principle, and it includes many examples and applications of the theory. This course studies basic optimization and the principles of optimal control. It considers deterministic and stochastic problems for both discrete and continuous systems. The course covers solution methods including numerical search algorithms, model predictive control, dynamic programming, variational calculus, and approaches based on Pontryagin's maximum principle, and it includes many examples and applications of the theory.

Subjects

nonlinear optimization | nonlinear optimization | dynamic programming | dynamic programming | HJB Equation | HJB Equation | calculus of variations | calculus of variations | constrained optimal control | constrained optimal control | singular arcs | singular arcs | stochastic optimal control | stochastic optimal control | LQG robustness | LQG robustness | feedback control systems | feedback control systems | model predictive control | model predictive control | line search methods | line search methods | Lagrange multipliers | Lagrange multipliers | discrete LQR | discrete LQR

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.354J Nonlinear Dynamics II: Continuum Systems (MIT) 18.354J Nonlinear Dynamics II: Continuum Systems (MIT)

Description

This course introduces the basic ideas for understanding the dynamics of continuum systems, by studying specific examples from a range of different fields. Our goal will be to explain the general principles, and also to illustrate them via important physical effects. A parallel goal of this course is to give you an introduction to mathematical modeling. This course introduces the basic ideas for understanding the dynamics of continuum systems, by studying specific examples from a range of different fields. Our goal will be to explain the general principles, and also to illustrate them via important physical effects. A parallel goal of this course is to give you an introduction to mathematical modeling.

Subjects

continuum systems | continuum systems | mathematical modeling | mathematical modeling | diffusion equation | diffusion equation | equations of motion | equations of motion | nonlinear partial differential equations | nonlinear partial differential equations | calculus of variations | calculus of variations | Brachistochrone curve | Brachistochrone curve | soap films | soap films | hydrodynamics | hydrodynamics | Navier-Stokes | Navier-Stokes | solitons | solitons | surface tension | surface tension | waves | waves | conformal maps | conformal maps | airfoils | airfoils

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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16.323 Principles of Optimal Control (MIT)

Description

This course studies the principles of deterministic optimal control. It uses variational calculus and Pontryagin's maximum principle. It focuses on applications of the theory, including optimal feedback control, time-optimal control, and others. Dynamic programming and numerical search algorithms are introduced briefly.

Subjects

nonlinear optimization | linear quadratic regulators | MATLAB implementation | dynamic programming | calculus of variations | LQR | LQG | stochastic optimization | on-line optimization and control | constrained optimization | signals | system norms | Model Predictive Behavior | quadratic programming | mixed-integer linear programming | linear programming

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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2.035 Special Topics in Mathematics with Applications: Linear Algebra and the Calculus of Variations (MIT)

Description

This course forms an introduction to a selection of mathematical topics that are not covered in traditional mechanical engineering curricula, such as differential geometry, integral geometry, discrete computational geometry, graph theory, optimization techniques, calculus of variations and linear algebra. The topics covered in any particular year depend on the interest of the students and instructor. Emphasis is on basic ideas and on applications in mechanical engineering. This year, the subject focuses on selected topics from linear algebra and the calculus of variations. It is aimed mainly (but not exclusively) at students aiming to study mechanics (solid mechanics, fluid mechanics, energy methods etc.), and the course introduces some of the mathematical tools used in these subjects. App

Subjects

calculus of variations | linear algebra | solid mechanics | fluid mechanics | energy methods | microstructures of crystalline

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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14.451 Dynamic Optimization Methods with Applications (MIT)

Description

This course focuses on dynamic optimization methods, both in discrete and in continuous time. We approach these problems from a dynamic programming and optimal control perspective. We also study the dynamic systems that come from the solutions to these problems. The course will illustrate how these techniques are useful in various applications, drawing on many economic examples. However, the focus will remain on gaining a general command of the tools so that they can be applied later in other classes.

Subjects

vector spaces | principle of optimality | concavity of the value function | differentiability of the value function | Euler equations | deterministic dynamics | models with constant returns to scale | nonstationary models | stochastic dynamic programming | stochastic Euler equations | stochastic dynamics | calculus of variations | the maximum principle | discounted infinite-horizon optimal control | saddle-path stability

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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16.323 Principles of Optimal Control (MIT)

Description

This course studies basic optimization and the principles of optimal control. It considers deterministic and stochastic problems for both discrete and continuous systems. The course covers solution methods including numerical search algorithms, model predictive control, dynamic programming, variational calculus, and approaches based on Pontryagin's maximum principle, and it includes many examples and applications of the theory.

Subjects

nonlinear optimization | dynamic programming | HJB Equation | calculus of variations | constrained optimal control | singular arcs | stochastic optimal control | LQG robustness | feedback control systems | model predictive control | line search methods | Lagrange multipliers | discrete LQR

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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18.354J Nonlinear Dynamics II: Continuum Systems (MIT)

Description

This course introduces the basic ideas for understanding the dynamics of continuum systems, by studying specific examples from a range of different fields. Our goal will be to explain the general principles, and also to illustrate them via important physical effects. A parallel goal of this course is to give you an introduction to mathematical modeling.

Subjects

continuum systems | mathematical modeling | diffusion equation | equations of motion | nonlinear partial differential equations | calculus of variations | Brachistochrone curve | soap films | hydrodynamics | Navier-Stokes | solitons | surface tension | waves | conformal maps | airfoils

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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