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- Linear-quadratic-Gaussian_control abstract "In control theory, the linear-quadratic-Gaussian (LQG) control problem is one of the most fundamental optimal control problems. It concerns uncertain linear systems disturbed by additive white Gaussian noise, having incomplete state information (i.e. not all the state variables are measured and available for feedback) and undergoing control subject to quadratic costs. Moreover the solution is unique and constitutes a linear dynamic feedback control law that is easily computed and implemented. Finally the LQG controller is also fundamental to the optimal control of perturbed non-linear systems.The LQG controller is simply the combination of a Kalman filter i.e. a linear-quadratic estimator (LQE) with a linear-quadratic regulator (LQR). The separation principle guarantees that these can be designed and computed independently. LQG control applies to both linear time-invariant systems as well as linear time-varying systems. The application to linear time-invariant systems is well known. The application to linear time-varying systems enables the design of linear feedback controllers for non-linear uncertain systems.The LQG controller itself is a dynamic system like the system it controls. Both systems have the same state dimension. Therefore implementing the LQG controller may be problematic if the dimension of the system state is large. The reduced-order LQG problem (fixed-order LQG problem) overcomes this by fixing a-priori the number of states of the LQG controller. This problem is more difficult to solve because it is no longer separable. Also the solution is no longer unique. Despite these facts numerical algorithms are available to solve the associated optimal projection equations which constitute necessary and sufficient conditions for a locally optimal reduced-order LQG controller.Finally, a word of caution. LQG optimality does not automatically ensure good robustness properties. The robust stability of the closed loop system must be checked separately after the LQG controller has been designed. To promote robustness some of the system parameters may be assumed stochastic instead of deterministic. The associated more difficult control problem leads to a similar optimal controller of which only the controller parameters are different.".
- Linear-quadratic-Gaussian_control wikiPageID "5347179".
- Linear-quadratic-Gaussian_control wikiPageLength "12578".
- Linear-quadratic-Gaussian_control wikiPageOutDegree "24".
- Linear-quadratic-Gaussian_control wikiPageRevisionID "682759956".
- Linear-quadratic-Gaussian_control wikiPageWikiLink Additive_white_Gaussian_noise.
- Linear-quadratic-Gaussian_control wikiPageWikiLink Algebraic_Riccati_equation.
- Linear-quadratic-Gaussian_control wikiPageWikiLink Category:Control_theory.
- Linear-quadratic-Gaussian_control wikiPageWikiLink Category:Optimal_control.
- Linear-quadratic-Gaussian_control wikiPageWikiLink Category:Stochastic_control.
- Linear-quadratic-Gaussian_control wikiPageWikiLink Continuous-time.
- Linear-quadratic-Gaussian_control wikiPageWikiLink Control_theory.
- Linear-quadratic-Gaussian_control wikiPageWikiLink Cost_functional.
- Linear-quadratic-Gaussian_control wikiPageWikiLink Discrete-time.
- Linear-quadratic-Gaussian_control wikiPageWikiLink Discrete_time_and_continuous_time.
- Linear-quadratic-Gaussian_control wikiPageWikiLink Expected_value.
- Linear-quadratic-Gaussian_control wikiPageWikiLink Kalman_filter.
- Linear-quadratic-Gaussian_control wikiPageWikiLink LTI_system_theory.
- Linear-quadratic-Gaussian_control wikiPageWikiLink LTI_systems.
- Linear-quadratic-Gaussian_control wikiPageWikiLink Linear-quadratic_regulator.
- Linear-quadratic-Gaussian_control wikiPageWikiLink Linear_system.
- Linear-quadratic-Gaussian_control wikiPageWikiLink Mathematical_optimization.
- Linear-quadratic-Gaussian_control wikiPageWikiLink Optimal_control.
- Linear-quadratic-Gaussian_control wikiPageWikiLink Optimal_projection_equations.
- Linear-quadratic-Gaussian_control wikiPageWikiLink Separation_principle.
- Linear-quadratic-Gaussian_control wikiPageWikiLink Stochastic_control.
- Linear-quadratic-Gaussian_control wikiPageWikiLink Time-variant_system.
- Linear-quadratic-Gaussian_control wikiPageWikiLink Witsenhausens_counterexample.
- Linear-quadratic-Gaussian_control wikiPageWikiLinkText "LQG (Linear-Quadratic-Gaussian) problem".
- Linear-quadratic-Gaussian_control wikiPageWikiLinkText "LQG Control".
- Linear-quadratic-Gaussian_control wikiPageWikiLinkText "LQG".
- Linear-quadratic-Gaussian_control wikiPageWikiLinkText "Linear-Quadratic-Gaussian (LQG) control problem".
- Linear-quadratic-Gaussian_control wikiPageWikiLinkText "Linear-Quadratic-Gaussian control problem".
- Linear-quadratic-Gaussian_control wikiPageWikiLinkText "Linear-quadratic-Gaussian control".
- Linear-quadratic-Gaussian_control wikiPageWikiLinkText "conventional discrete-time full-order LQG problem".
- Linear-quadratic-Gaussian_control wikiPageWikiLinkText "conventional full-order LQG control problem".
- Linear-quadratic-Gaussian_control wikiPageWikiLinkText "conventional full-order LQG controller".
- Linear-quadratic-Gaussian_control wikiPageWikiLinkText "linear-quadratic-Gaussian control".
- Linear-quadratic-Gaussian_control wikiPageWikiLinkText "linear-quadratic-Gaussian control#Mathematical description of the problem and solution".
- Linear-quadratic-Gaussian_control wikiPageWikiLinkText "matrix Riccati equation".
- Linear-quadratic-Gaussian_control hasPhotoCollection Linear-quadratic-Gaussian_control.
- Linear-quadratic-Gaussian_control wikiPageUsesTemplate Template:Reflist.
- Linear-quadratic-Gaussian_control subject Category:Control_theory.
- Linear-quadratic-Gaussian_control subject Category:Optimal_control.
- Linear-quadratic-Gaussian_control subject Category:Stochastic_control.
- Linear-quadratic-Gaussian_control type Process.
- Linear-quadratic-Gaussian_control comment "In control theory, the linear-quadratic-Gaussian (LQG) control problem is one of the most fundamental optimal control problems. It concerns uncertain linear systems disturbed by additive white Gaussian noise, having incomplete state information (i.e. not all the state variables are measured and available for feedback) and undergoing control subject to quadratic costs. Moreover the solution is unique and constitutes a linear dynamic feedback control law that is easily computed and implemented.".
- Linear-quadratic-Gaussian_control label "Linear-quadratic-Gaussian control".
- Linear-quadratic-Gaussian_control sameAs متحكم_خطي_تربيعي_غاوسي.
- Linear-quadratic-Gaussian_control sameAs LQG-Regler.
- Linear-quadratic-Gaussian_control sameAs Control_lineal_cuadrático_gaussiano.
- Linear-quadratic-Gaussian_control sameAs Commande_LQG.
- Linear-quadratic-Gaussian_control sameAs Controllo_lineare_quadratico_gaussiano.
- Linear-quadratic-Gaussian_control sameAs Regulator_liniowo-kwadratowy-Gaussa.
- Linear-quadratic-Gaussian_control sameAs m.0dgq9n.
- Linear-quadratic-Gaussian_control sameAs Линейно-квадратичное_гауссовское_управление.
- Linear-quadratic-Gaussian_control sameAs Q1798304.
- Linear-quadratic-Gaussian_control sameAs Q1798304.
- Linear-quadratic-Gaussian_control wasDerivedFrom Linear-quadratic-Gaussian_control?oldid=682759956.
- Linear-quadratic-Gaussian_control isPrimaryTopicOf Linear-quadratic-Gaussian_control.