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Pseudospectral Optimal Control
Pseudospectral optimal control is a joint theoretical-computational method for solving optimal control problems. It combines pseudo-spectral method, pseudospectral (PS) theory with optimal control theory to produce a PS optimal control theory. PS optimal control theory has been used in ground and flight systems in military and industrial applications. The techniques have been extensively used to solve a wide range of problems such as those arising in UAV trajectory generation, missile guidance, control of robotic arms, vibration damping, lunar guidance, magnetic control, swing-up and stabilization of an inverted pendulum, orbit transfers, tether libration control, ascent guidance and quantum control. Overview There are a very large number of ideas that fall under the general banner of pseudospectral optimal control. Examples of these are the Legendre pseudospectral method, the Chebyshev pseudospectral method, the Gauss pseudospectral method, the Ross-Fahroo pseudospectral metho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Optimal Control
Optimal control theory is a branch of control theory that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the Moon with minimum fuel expenditure. Or the dynamical system could be a nation's economy, with the objective to minimize unemployment; the controls in this case could be fiscal and monetary policy. A dynamical system may also be introduced to embed operations research problems within the framework of optimal control theory. Optimal control is an extension of the calculus of variations, and is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and Richard Bellman in the 1950s, after contributions to calculus of v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Dual Number
In algebra, the dual numbers are a hypercomplex number system first introduced in the 19th century. They are expressions of the form , where and are real numbers, and is a symbol taken to satisfy \varepsilon^2 = 0 with \varepsilon\neq 0. Dual numbers can be added component-wise, and multiplied by the formula : (a+b\varepsilon)(c+d\varepsilon) = ac + (ad+bc)\varepsilon, which follows from the property and the fact that multiplication is a bilinear operation. The dual numbers form a commutative algebra of dimension two over the reals, and also an Artinian local ring. They are one of the simplest examples of a ring that has nonzero nilpotent elements. History Dual numbers were introduced in 1873 by William Clifford, and were used at the beginning of the twentieth century by the German mathematician Eduard Study, who used them to represent the dual angle which measures the relative position of two skew lines in space. Study defined a dual angle as , where is the angle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
GPOPS-II
GPOPS-II (pronounced "GPOPS 2") is a general-purpose MATLAB software for solving continuous optimal control problems using hp-adaptive Gaussian quadrature collocation and sparse nonlinear programming. The acronym GPOPS stands for "General Purpose OPtimal Control Software", and the Roman numeral "II" refers to the fact that GPOPS-II is the second software of its type (that employs Gaussian quadrature integration). Problem Formulation GPOPS-II is designed to solve multiple-phase optimal control problems of the following mathematical form (where P is the number of phases): ::: \min J = \phi(\mathbf^,\ldots,\mathbf^) :subject to the dynamic constraints ::: \dot^(t)=\mathbf^(\mathbf^(t),\mathbf^(t),t,\mathbf),\quad (p=1,\ldots,P), :the event constraints ::: \mathbf_\leq\mathbf(\mathbf^,\ldots,\mathbf^,\mathbf)\leq\mathbf_, :the inequality path constraints ::: \mathbf_^\leq\mathbf(\mathbf^(t),\mathbf^(t),t,\mathbf)\leq\mathbf_^,\quad (p=1,\ldots,P), :the static parameter constraints ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Dido (Queen Of Carthage)
Dido ( ; , ), also known as Elissa ( , ), was the legendary founder and first queen of the Phoenician city-state of Carthage (located in Tunisia), in 814 BC. In most accounts, she was the queen of the Phoenician city-state of Tyre (located in Lebanon) who fled tyranny to found her own city in northwest Africa. Known only through ancient Greek and Roman sources, all of which were written well after Carthage's founding, her historicity remains uncertain. The oldest references to Dido are attributed to Timaeus, who lived in Taormina in Sicily, and died around 260 BC, which is about five centuries after the date given for the foundation of Carthage. Timaeus told the legends surrounding the founding of Carthage by Dido in his Sicilian ''History''. By his account, Dido founded Carthage in 814 BC, around the same time as the foundation of Rome, and he alluded to the growing conflict between the two cities in his own day. Details about Dido's character, life, and role in the foun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
DIDO (optimal Control)
DIDO ( ) is a MATLAB optimal control toolbox for solving general-purpose optimal control problems.Ross, I. M. ''A Primer on Pontryagin's Principle in Optimal Control'', Second Edition, Collegiate Publishers, San Francisco, 2015.Eren, H., "Optimal Control and the Software," ''Measurements, Instrumentation, and Sensors Handbook'', Second Edition, CRC Press, 2014, pp.92-1-16. It is widely used in academia, industry, and NASA. Hailed as a breakthrough software, DIDO is based on the pseudospectral optimal control theory of Ross and Fahroo. The latest enhancements to DIDO are described in Ross. Usage DIDO utilizes trademarked expressions and objects that facilitate a user to quickly formulate and solve optimal control problems.A. M. Hawkins, ''Constrained Trajectory Optimization of a Soft Lunar Landing From a Parking Orbit,'' S.M. Thesis, Dept. of Aeronautics and Astronautics, Massachusetts Institute of Technology, 2005. http://dspace.mit.edu/handle/1721.1/32431 Rapidity in formulation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
