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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 wikiPageRevisionID "558908609".
- Linear-quadratic-Gaussian_control hasPhotoCollection Linear-quadratic-Gaussian_control.
- 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 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 "Commande LQG".
- Linear-quadratic-Gaussian_control label "Control lineal cuadrático gaussiano".
- Linear-quadratic-Gaussian_control label "Controllo lineare quadratico gaussiano".
- Linear-quadratic-Gaussian_control label "LQG-Regler".
- Linear-quadratic-Gaussian_control label "Linear-quadratic-Gaussian control".
- Linear-quadratic-Gaussian_control label "Regulator liniowo-kwadratowy-Gaussa".
- Linear-quadratic-Gaussian_control label "Линейно-квадратичное гауссовское управление".
- Linear-quadratic-Gaussian_control label "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 Q1798304.
- Linear-quadratic-Gaussian_control sameAs Q1798304.
- Linear-quadratic-Gaussian_control wasDerivedFrom Linear-quadratic-Gaussian_control?oldid=558908609.
- Linear-quadratic-Gaussian_control isPrimaryTopicOf Linear-quadratic-Gaussian_control.