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Ross–Fahroo Pseudospectral Method
Introduced by I. Michael Ross and F. Fahroo, the Ross–Fahroo pseudospectral methods are a broad collection of pseudospectral methods for optimal control.N. Bedrossian, M. Karpenko, and S. Bhatt, "Overclock My Satellite: Sophisticated Algorithms Boost Satellite Performance on the Cheap", ''IEEE Spectrum'', November 2012. I. M. Ross and F. Fahroo, A Pseudospectral Transformation of the Covectors of Optimal Control Systems, Proceedings of the First IFAC Symposium on System Structure and Control, Prague, Czech Republic, 29–31 August 2001. I. M. Ross and F. Fahroo, Legendre Pseudospectral Approximations of Optimal Control Problems, ''Lecture Notes in Control and Information Sciences'', Vol. 295, Springer-Verlag, 2003. I. M. Ross and F. Fahroo, Discrete Verification of Necessary Conditions for Switched Nonlinear Optimal Control Systems, Proceedings of the American Control Conference, Invited Paper, June 2004, Boston, MA. Examples of the Ross–Fahroo pseudospectral methods are th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fariba Fahroo
Fariba Fahroo is an American Persian mathematician, a program manager at the Air Force Office of Scientific Research, and a former program manager at the Defense Sciences Office. Along with I. M. Ross, she has published papers in pseudospectral optimal control theory.F. Fahroo and I. M. Ross, “A Second Look at Approximating Differential Inclusions,” Journal of Guidance, Control, and Dynamics, Vol.24, No.1, January–February 2001. F. Fahroo and I. M. Ross, “Costate Estimation by a Legendre Pseudospectral Method,” Journal of Guidance, Control, and Dynamics, Vol.24, No.2, March–April 2001, pp. 270–277F. Fahroo and I. M. Ross, “Direct Trajectory Optimization by a Chebyshev Pseudospectral Method,” Journal of Guidance, Control, and Dynamics, Vol. 25, No. 1, 2002, pp. 160–166F. Fahroo and I. M. Ross, “Pseudospectral Methods for Infinite-Horizon Optimal Control Problems,” Journal of Guidance, Control, and Dynamics, Vol. 31, No. 4, pp. 927–936, 2008. F. Fahroo and I. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Algebraic Equation
In electrical engineering, a differential-algebraic system of equations (DAEs) is a system of equations that either contains differential equations and algebraic equations, or is equivalent to such a system. In mathematics these are examples of ``differential algebraic varieties'' and correspond to ideals in differential polynomial rings (see the article on differential algebra for the algebraic setup. We can write these differential equations for a dependent vector of variables ''x'' in one independent variable ''t'', as ::F(\dot x(t),\, x(t),\,t)=0 When considering these symbols as functions of a real variable (as is the case in applications in electrical engineering or control theory) we look at x: ,bto\R^n as a vector of dependent variables x(t)=(x_1(t),\dots,x_n(t)) and the system has as many equations, which we consider as functions F=(F_1,\dots,F_n):\R^\to\R^n. They are distinct from ordinary differential equation (ODE) in that a DAE is not completely solvable for the deri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimal Control
Optimal control theory is a branch of mathematical optimization 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 calc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ross' π Lemma
Ross' lemma, named after I. Michael Ross, is a result in computational optimal control. Based on generating Carathéodory- solutions for feedback control, Ross' -lemma states that there is fundamental time constant within which a control solution must be computed for controllability and stability. This time constant, known as Ross' time constant, is proportional to the inverse of the Lipschitz constant of the vector field that governs the dynamics of a nonlinear control system. Theoretical implications The proportionality factor in the definition of Ross' time constant is dependent upon the magnitude of the disturbance on the plant and the specifications for feedback control. When there are no disturbances, Ross' -lemma shows that the open-loop optimal solution is the same as the closed-loop one. In the presence of disturbances, the proportionality factor can be written in terms of the Lambert W-function. Practical applications In practical applications, Ross' time constant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 modern Tunisia), in 814 BC. In most accounts, she was the queen of the Phoenician city-state of Tyre (today 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 was active around 300 BC, or about five centuries after the date given for the foundation of Carthage. Details about Dido's character, life, and role in the founding of Carthage are best known from the account given in Virgil's epic poem, the ''Aeneid,'' written around 20 BC, which tells the legendary story of the Trojan hero Aeneas. Dido is described as a clever and enterprising woman who flees her ruthless and autocratic brother, Pygmalion, after discovering ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
DIDO (software)
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] |
International Space Station
The International Space Station (ISS) is the largest modular space station currently in low Earth orbit. It is a multinational collaborative project involving five participating space agencies: NASA (United States), Roscosmos (Russia), JAXA (Japan), ESA (Europe), and CSA (Canada). The ownership and use of the space station is established by intergovernmental treaties and agreements. The station serves as a microgravity and space environment research laboratory in which scientific research is conducted in astrobiology, astronomy, meteorology, physics, and other fields. The ISS is suited for testing the spacecraft systems and equipment required for possible future long-duration missions to the Moon and Mars. The ISS programme evolved from the Space Station ''Freedom'', a 1984 American proposal to construct a permanently crewed Earth-orbiting station, and the contemporaneous Soviet/Russian '' Mir-2'' proposal from 1976 with similar aims. The ISS is the ninth space station to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bellman Pseudospectral Method
The Bellman pseudospectral method is a pseudospectral method for optimal control based on Bellman's principle of optimality. It is part of the larger theory of pseudospectral optimal control, a term coined by Ross. The method is named after Richard E. Bellman. It was introduced by Ross et al.I. M. Ross, Q. Gong and P. Sekhavat, The Bellman pseudospectral method, AIAA/AAS Astrodynamics Specialist Conference and Exhibit, Honolulu, Hawaii, AIAA-2008-6448, August 18–21, 2008. first as a means to solve multiscale optimal control problems, and later expanded to obtain suboptimal solutions for general optimal control problems. Theoretical foundations The multiscale version of the Bellman pseudospectral method is based on the spectral convergence property of the Ross–Fahroo pseudospectral methods. That is, because the Ross–Fahroo pseudospectral method converges at an exponentially fast rate, pointwise convergence to a solution is obtained at very low number of nodes even when the so ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Inclusion
In mathematics, differential inclusions are a generalization of the concept of ordinary differential equation of the form :\frac(t)\in F(t,x(t)), where ''F'' is a multivalued map, i.e. ''F''(''t'', ''x'') is a ''set'' rather than a single point in \R^d. Differential inclusions arise in many situations including differential variational inequalities, projected dynamical systems, Moreau's sweeping process, linear and nonlinear complementarity dynamical systems, discontinuous ordinary differential equations, switching dynamical systems, and fuzzy set arithmetic. For example, the basic rule for Coulomb friction is that the friction force has magnitude ''μN'' in the direction opposite to the direction of slip, where ''N'' is the normal force and ''μ'' is a constant (the friction coefficient). However, if the slip is zero, the friction force can be ''any'' force in the correct plane with magnitude smaller than or equal to ''μN''. Thus, writing the friction force as a function o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly. Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory of d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudospectral Optimal Control
Pseudospectral optimal control is a joint theoretical-computational method for solving optimal control problems. It combines pseudospectral (PS) theory with optimal control theory to produce 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 method, the Bellman pseudos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
