1977
DOI: 10.1119/1.10840
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ModernIntroductiontoClassicalMechanicsandControl

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Cited by 3 publications
(6 citation statements)
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“…In optimal control theory (see e.g. Burghes & Downs 1975; Kirk 2004), the control must maximize the so‐called objective function, J , which is written as where L is the Lagrangian which quantifies the constraints on the system and is a function of the state and control variables as shown. For a minimization, the appropriate objective function is simply the maximizing objective function multiplied by −1.…”
Section: Active Galactic Nucleus Feedback Models With Additional Comentioning
confidence: 99%
See 1 more Smart Citation
“…In optimal control theory (see e.g. Burghes & Downs 1975; Kirk 2004), the control must maximize the so‐called objective function, J , which is written as where L is the Lagrangian which quantifies the constraints on the system and is a function of the state and control variables as shown. For a minimization, the appropriate objective function is simply the maximizing objective function multiplied by −1.…”
Section: Active Galactic Nucleus Feedback Models With Additional Comentioning
confidence: 99%
“…Optimal control theory also makes use of Pontryagin's maximum principle, which states that the optimal state q *( t ), optimal control α*( t ) and corresponding costate vector y *( t ) must maximize the Hamiltonian (e.g. Burghes & Downs 1975). Therefore, the condition for optimality is For a complete solution, it is also necessary to solve the Euler–Lagrange equations of the Hamiltonian: Full solutions can then be obtained by applying the appropriate boundary conditions, which depend on the specific problem.…”
Section: Active Galactic Nucleus Feedback Models With Additional Comentioning
confidence: 99%
“…In optimal control theory (see Burghes & Downs 1975;Kirk 2004, for example), the control must maximise the socalled objective function, J, which is written as…”
Section: Optimised Agn Feedbackmentioning
confidence: 99%
“…Optimal control theory also makes use of Pontryagin's maximum principle, which states that the optimal state q * (t), optimal control α * (t) and corresponding costate vector y * (t), must maximise the Hamiltonian (e.g. Burghes & Downs 1975). Therefore, the condition for optimality is…”
Section: Optimised Agn Feedbackmentioning
confidence: 99%
“…In order to apply the results of $2 to the construction of Lagrangians for one-dimensional systems with variable mass, we first require the corresponding equation of motion. Many mechanics texts (Goodman and Warner 1964, Burghes and Downs 1975, Griffiths 1985 derive this equation in the following manner. With respect to a chosen inertial frame of reference, the momentum of the body at time t + dt is (m(?)…”
Section: Lagrangians For Simple Systems With Variable Massmentioning
confidence: 99%