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# Topic: Optimal control

 Optimal control - Wikipedia, the free encyclopedia Optimal control theory is a mathematical field that is concerned with control policies that can be deduced using optimization algorithms. Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. Another optimal control problem would be to minimize the fuel consumption, given that the car must complete the course in a given time. en.wikipedia.org /wiki/Optimal_control   (642 words)

 A brief history of feedback control - Chapter 1 Feedback control is the basic mechanism by which systems, whether mechanical, electrical, or biological, maintain their equilibrium or homeostasis. Feedback control may be defined as the use of difference signals, determined by comparing the actual values of system variables to their desired values, as a means of controlling a system. Various optimality principles were investigated, including the minimum-time principle in optics of P. de Fermat (1600's), the work of L. Euler in 1744, and Hamilton's result that a system moves in such a way as to minimize the time integral of the difference between the kinetic and potential energies. www.theorem.net /theorem/lewis1.html   (8851 words)

 Encyclopedia: Optimal control Pontryagins minimum principle is used in optimal control theory to find the best possible control for taking a dynamic system from one state to another. It is very common, when designing proper control systems, to model reality as a linear system, such as A linear system is a model of a system based on some kind of linear operator. The optimal control problem defined with the previous functional is usually called the state regulator problem and its solution the linear quadratic regulator (LQR) which is no more than a feedback matrix gain of the form For the square matrix section, see square matrix. www.nationmaster.com /encyclopedia/Optimal-control   (812 words)

 Optimal Control Of Thermally Convected Fluid Flows - Ito, Ravindran (ResearchIndex) We examine the optimal control of stationary thermally convected fluid flows from the theoretical and numerical point of view. We use thermal convection as control mechanism, that is, control is effected through the temperature on part of the boundary. Existence of optimal control is given and a first order necessary conditions of optimality from which optimal solutions can be obtained is established. citeseer.ist.psu.edu /ito98optimal.html   (492 words)

 Herschel A. Rabitz: Publications by Year Optimal control of population transfer in an optically dense medium, N. Wang and H. Rabitz, J. Optimal Hamiltonian identification: The synthesis of quantum optimal control and quantum inversion, J.M. Geremia and H. Rabitz, J. Optimally controlling the internal dynamics of a randomly orientated ensemble of molecules, G. Turinici and H. Rabitz, Phys. www.princeton.edu /~hrabitz/pubrecent.html   (12263 words)

 Optimal control -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: 2007-10-07) Optimal control theory is a mathematical field that is concerned with control policies that can be deduced using (The act of rendering optimal) optimization algorithms. The control which minimizes a certain (additional info and facts about cost functional) cost functional is called the optimal control. On a more general framework, given a (additional info and facts about dynamic system) dynamic system with input u(t), output y(t) and state x(t), one can define what is called a cost functional, which is a measure that the control designer should be able to minimize. www.absoluteastronomy.com /encyclopedia/o/op/optimal_control.htm   (622 words)

 Optimal Control Optimal control in this case will be the following: through the first half of the trajectory rocket will accelerate toward point B, and during the second half it will slow down. In out case, control that is close to optimal (discontinuous) is not an extremum: there always exists a control that is closer to the optimal and extremum is never achieved in the class of continuous functions. Consider optimal control for a simplified aerodynamic model, which accounts for a drag force (aerodynamic force vector is collinear to the velocity). www.geocities.com /levinkirill/SpaceModel/eng/OptimalControl.html   (2060 words)

 Optimal control   (Site not responding. Last check: 2007-10-07) Optimal control theory is a mathematical field that is with control policies that can be deduced optimization algorithms. This is a very good textbook for subjects on optimal controls with management science applications. This is a fantastic book on optimal control especially for readers who do not have to learn the math as they go. www.freeglossary.com /Optimal_control   (345 words)

 Computer Science Colloquium   (Site not responding. Last check: 2007-10-07) We present space-time multigrid methods that solve optimal control systems in one shot in the whole space-time cylinder which are robust with respect to changes of the values of the optimization parameters. Towards real-time optimal control of evolving reaction diffusion systems, the combination of the space-time multigrid approach with receding horizon techniques is proposed. The ability of the space-time multigrid approach in solving optimal control problems is demonstrated by applications to the control of an explosive phenomenon, control of chemical turbulence, and control of caridiac arrhythmias. www.cs.technion.ac.il /~colloq/20040610_14_30_Borzi.html   (169 words)

 Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations   (Site not responding. Last check: 2007-10-07) We investigate the optimal control of neuronal spiking activity for neurons receiving a class of random synaptic inputs, characterized by a positive parameter {alpha}. Optimal control signals and optimal variances are found exactly for the diffusion process approximating an integrate and fire model. The optimal variance obtained in the current paper sets the lowest possible bound in controlling the stochasticity of neuronal activity. www.osti.gov /energycitations/product.biblio.jsp?osti_id=20472968   (277 words)

 An a priori Estimate for Discrete Approximations in Nonlinear Optimal Control An a priori Estimate for Discrete Approximations in Nonlinear Optimal Control: SIAM Journal on Control and Optimization Vol. We examine the convergence of an approximate discretization applied to the first-order optimality conditions for a nonlinear optimal control problem with convex control constraints. Under an assumption of the coercivity type we prove the existence of an optimal control for the original problem such that its $L^\infty$ distance from the approximating sequence is proportional to the error. epubs.siam.org /sam-bin/dbq/article/26948   (128 words)

 Title page for ETD etd-02042002-152330 The continuous time model of the problem is proposed, analyzed and we came up with an optimal control law for the pursuer is obtained so that the evader is driven to the desired destination position in the x-y grid following the local shortest path in the Euler Lagrange sense. In this and we show that the optimal control policy is in the form of a feedback control law that enables the pursuer to achieve the same objective using the shortest path. Finally, the case with active evader is considered, the optimal control law for this case is obtained through the application of dynamic programming technique. scholar.lib.vt.edu /theses/available/etd-02042002-152330   (311 words)

 Nonlinearly constrained optimal control problems involving piecewise smooth controls   (Site not responding. Last check: 2007-10-07) In this paper, we consider a class of optimal control problems involving inequality continuous-state constraints in which the control is piecewise smooth. The requirement for this type of control is more stringent than that for the control considered in standard optimal control problems in which the controls are usually taken as bounded measurable functions. In this paper, we shall show that this class of optimal control problems can easily be transformed into an equivalent class of combined optimal parameter selection and optimal control problems. anziamj.austms.org.au /V32/part2/Teo.html   (174 words)

 Desensitized Optimal Control   (Site not responding. Last check: 2007-10-07) The DOC approach enables engineers to find an optimal trade-off between the performance of a trajectory in the nominal unperturbed case, and the sensitivity of mission-critical quantities in the neighborhood of the nominal solution. It is always possible to convert a constant parameter that appears in a problem formulation into a state by introducing a trivial differential equation (state rate of parameter is zero) and appropriate initial conditions (initial value of the new state is equal to the nominal value of the constant parameter). If a control is perturbed at one instant, the control would have the ability to jump back to its preferred optimal value the very next instant. www.ama-inc.com /engineering/ENG_DesensitizedOptimization.shtml   (812 words)

 - July 1988 -Optimal Control Theory and Economic Analysis 3 - Suresh P Sethi Gerald L Thompson   (Site not responding. Last check: 2007-10-07) Optimal Control and Differential Games Collection of Papers Proceedings of the Steklov Institute of Mathematics Vol 185 Issue 2 of 4. Optimal Control of Random Sequences in Problems With Constraints Mathematics and Its Applications Kluwer Academic Publishers Vol 410. Optimal Control Theory Applications to Management Science and Economics Second Edition. www.reviewofbooks.net /272121optimal_control_theory_economic_analysis_3.html   (75 words)

 Sampled-Data and Discrete-Time $H_2$ Optimal Control Given a linear time-invariant continuous-time system, the problem of minimizing the $H_2$ performance over all sampled-data controllers with a fixed sampling period can be reduced to a pure discrete-time $H_2$ optimal control problem. We also show that the $H_2$ performance of a continuous-time controller can always be recovered asymptotically by choosing the sampling period sufficiently small. Finally, we show that the optimal sampled-data $H_2$ performance converges to the continuous-time optimal $H_2$ performance as the sampling period converges to zero. epubs.siam.org /sam-bin/dbq/article/24199   (185 words)

 Optimal Control of Distributed Proceses using Reduced Order Models These problems are usually solved by the Control Vector Parameterization (CVP) approach, which transforms the original dynamic optimization method into an outer nonlinear programming problem, which requires the solution of an inner initial value problem (IVP). The solution of this IVP (set of partial and ordinary differential equations) for each function evaluation is usually very demanding in terms of computation time, thus efficient numerical techniques are necessary in order to reduce the overall computational effort of the CVP optimizations. In this work, the use of low order models, obtained by GalĂ«rking projection on a set of proper orthogonal functions, is presented as a very efficient alternative for the rapid solution of this class of problems. www.optimization-online.org /DB_HTML/2001/01/256.html   (173 words)

 Control Systems and Optimisations - Cambridge University Press   (Site not responding. Last check: 2007-10-07) This book addresses the theory of optimal control to solve practical problems in the face of uncertainty. 'The author stated the goal at the beginning of the book as 'to aid readers in utilizing the theory of optimal control to solve practical problems in the face of uncertainty.' It appears this goal has been achieved. Applied Linear Optimal Control: Examples and Algorithms should be a good addition to the optimal control community. www.cambridge.org /uk/browse/default.asp?subjectid=177   (221 words)

 Citations: Optimal control of a somersaulting platform diver - Murthy, Keerthi (ResearchIndex)   (Site not responding. Last check: 2007-10-07) They formulated a time optimal control problem using state and control constraints and a numerical approach to compute the solution. The somersault is similar to a dive in that the creature must apply forces to the ground to generate the needed angular momentum for the ballistic part of the maneuver and the control techniques for the divers build on the control ideas developed for the somersaulting robots. They formulated a time optimal control problem using state and control constraints and used a numerical approach to compute the solution. citeseer.ist.psu.edu /context/27792/0   (325 words)

 Optimal Control Applied to Cell-Cycle-Specific Cancer Chemotherapy Optimal Control Applied to Cell-Cycle-Specific Cancer Chemotherapy: SIAM Journal on Applied Mathematics Vol. Next we show that an optimal control exists for this problem, and then we characterize our optimal control in terms of the solutions to the optimality system, which is the state system coupled with the adjoint system. optimal control, cancer, chemotherapy, cell cycle, bone marrow epubs.siam.org /sam-bin/dbq/article/33850   (197 words)

 Book: Optimal Control and Estimation   (Site not responding. Last check: 2007-10-07) The first two chapters introduce optimal control and review the mathematics of control and estimation. Chapter 3 addresses optimal control of systems that may be nonlinear and time-varying, but whose inputs and parameters are known without error. The power of stochastic optimal control becomes apparent, as interpreted by notions drawn from classical control applied to multi-input/multi-output systems.... www.princeton.edu /~stengel/OptConEst.html   (479 words)

 Fast Solution of Optimal Control Problems in the Selective Cooling of Steel - Tr, Unger (ResearchIndex) This leads to a nonlinear parabolic control problem with state constraint in a 2D domain. A method of instantaneous control is applied to set up a fast solution technique. A mathematical description of the problem leads to a boundary control problem for a linearized 2D heat equation where 2 IR 2 is the... citeseer.ist.psu.edu /tr99fast.html   (488 words)

 [No title]   (Site not responding. Last check: 2007-10-07) Macki and A. Strauss, Introduction to Optimal Control Theory, Springer-Verlang, 1982. Joshi, H. R., 2002, Optimal Control of an HIV Immunology Model, Optimal Control Appl. Lenhart, M. Liang, and V. Protopopescu, 1999, Optimal Control of the Effects of Boundary Habitat Hostility, Math. www.math.utk.edu /~lenhart/docs/references3   (568 words)

 [No title] Note that the Optimal Control problems consist in minimizing, in the sense of a least square method, a cost function for which the constraints are given by a PDE. We were then interested in two approaches meant to designing efficient algorithms well-adapted to distributed memory machines: Furthermore, the approach was extended to the parabolic case: the optimal control problem of the heat equation. A. Bounaïm, On the Optimal Control Problem of the Heat Equation: New Formulation of the Problem Using a Non-Overlapping Domain Decomposition Technique, Preprint, January 2002. www.ifi.uio.no /~aichab/phd_work.html   (764 words)

 Textbook: Dynamic Programming and Optimal Control The leading and most up-to-date textbook on the far-ranging algorithmic methododogy of Dynamic Programming, which can be used for optimal control, Markovian decision problems, planning and sequential decision making under uncertainty, and discrete/combinatorial optimization. Stochastic Optimal Control: The Discrete-Time Case (Athena Scientific, 1996), which deals with the mathematical foundations of the subject, It is a valuable reference for control theorists, mathematicians, and all those who use systems and control theory in their work. www.athenasc.com /dpbook.html   (645 words)

 Applied Linear Optimal Control - Cambridge University Press   (Site not responding. Last check: 2007-10-07) This book is one of the first to aid readers in utilizing the theory of optimal control to solve practical problems in the face of uncertainty. Topics covered include random inputs and random errors in measurement, uncertainty in inputs from the environment, and uncertainty in the parameters of the dynamic model. With hundreds of problems and worked examples, together with a CD-ROM containing MATLAB codes of the OPTEST, this is a comprehensive text on dynamic control, providing an excellent theoretical and practical tool for graduate students and researchers in all engineering disciplines, as well as in applied mathematics and computer science. www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0521012317   (306 words)

 49: Calculus of variations and optimal control; optimization In many cases, optimal functions or curves can be expressed as solutions to differential equations. However, the spaces on which the analysis are done may represent configurations of some physical system, say, so that this field also applies to optimization problems in economics or control theory for example. See also 65K (for numerical optimization), 90C (for applications of optimization to operations research, mathematical programming, etc.), 93 (for control theory in general), and 34H05 for differential equations in control problems. www.math.niu.edu /~rusin/known-math/index/49-XX.html   (432 words)

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