Using Linear Quadratic Gaussian Optimal Control for Lateral Motion of Aircraft
The purpose of this paper is to provide a practical
example to the Linear Quadratic Gaussian (LQG) controller. This
method includes a description and some discussion of the discrete
Kalman state estimator. One aspect of this optimality is that the
estimator incorporates all information that can be provided to it. It
processes all available measurements, regardless of their precision, to
estimate the current value of the variables of interest, with use of
knowledge of the system and measurement device dynamics, the
statistical description of the system noises, measurement errors, and
uncertainty in the dynamics models.
Since the time of its introduction, the Kalman filter has been the
subject of extensive research and application, particularly in the area
of autonomous or assisted navigation. For example, to determine the
velocity of an aircraft or sideslip angle, one could use a Doppler
radar, the velocity indications of an inertial navigation system, or the
relative wind information in the air data system. Rather than ignore
any of these outputs, a Kalman filter could be built to combine all of
this data and knowledge of the various systems- dynamics to
generate an overall best estimate of velocity and sideslip angle.
[1] H. W. Sorenson., "Least-Squares estimation: from Gauss to Kalman",
IEEE Spectrum, Vol. 7, pp. 63-68, July 1970.
[2] A. Gelb, "Applied Optimal Estimation", MIT Press, Cambridge, MA.
1974.
[3] P. S. Maybeck, "Applied Optimal EstimationÔÇöKalman Filter Design
and Implementation", notes for a continuing education course offered by
the Air Force Institute of Technology, Wright-Patterson AFB, Ohio,
semiannually since December 1974.
[4] R. Lewis, "Optimal Estimation with an Introduction to Stochastic
Control Theory", John Wiley & Sons, Inc. 1986.
[5] A.C. Harvey, "Structural Time Series Models and the Kalman Filter",
Cambridge University Press, Cambridge, 1989.
[6] A.L. Gonzalez Blazquez, "Mathematical modelling for analysis of nonlinear
aircraft dynamics", Computers and structures, Vol. 37, No 2, pp.
193 -197, July 1990.
[7] R. Azuma and G. Bishop, "Improving Static and Dynamic Registration
in an Optical See-Through HMD", SIGGRAPH 94 Conference
Proceedings, Annual Conference Series, pp. 197-204, ACM
SIGGRAPH, Addison Wesley, July 1994.
[8] J. Simon and K. Jeffery, "A New Extension of the Kalman Filter to
nonlinear Systems" In The Proceedings of AeroSense: The 11th
International Symposium on Aerospace/Defense Sensing,Simulation and
Controls, Multi Sensor Fusion, Tracking and Resource Management II,
SPIE, 1997.
[9] A. Maddi, "Modélisation et contr├┤le du vol latéral d-un avion",
Magister Thesis, Electronics Department, University of Blida, Algeia,
1997.
[10] M. Grewal and A. Andrews, "Kalman Filtering Theory and Practice
Using MATLAB", (Second ed.), New York, NY USA: John Wiley &
Sons, Inc., 2001.
[11] P.C. Murphy and V. Klein, "Estimation of Aircraft Unsteady
Aerodynamic Parameters From Dynamic Wind Tunnel Testing" , AIAA
2001- 4016, August 2001
[12] G. Bishop, G. Welch, "An Introduction to the Kalman Filter", University
of North Carolina at Chapel Hill, Department of Computer Science,
SIGGRAPH 2001.
[13] D. Simon, "Optimal state estimation: Kalman, H-infinity, and nonlinear
approaches", John Wiley & Sons, 2006.
[1] H. W. Sorenson., "Least-Squares estimation: from Gauss to Kalman",
IEEE Spectrum, Vol. 7, pp. 63-68, July 1970.
[2] A. Gelb, "Applied Optimal Estimation", MIT Press, Cambridge, MA.
1974.
[3] P. S. Maybeck, "Applied Optimal EstimationÔÇöKalman Filter Design
and Implementation", notes for a continuing education course offered by
the Air Force Institute of Technology, Wright-Patterson AFB, Ohio,
semiannually since December 1974.
[4] R. Lewis, "Optimal Estimation with an Introduction to Stochastic
Control Theory", John Wiley & Sons, Inc. 1986.
[5] A.C. Harvey, "Structural Time Series Models and the Kalman Filter",
Cambridge University Press, Cambridge, 1989.
[6] A.L. Gonzalez Blazquez, "Mathematical modelling for analysis of nonlinear
aircraft dynamics", Computers and structures, Vol. 37, No 2, pp.
193 -197, July 1990.
[7] R. Azuma and G. Bishop, "Improving Static and Dynamic Registration
in an Optical See-Through HMD", SIGGRAPH 94 Conference
Proceedings, Annual Conference Series, pp. 197-204, ACM
SIGGRAPH, Addison Wesley, July 1994.
[8] J. Simon and K. Jeffery, "A New Extension of the Kalman Filter to
nonlinear Systems" In The Proceedings of AeroSense: The 11th
International Symposium on Aerospace/Defense Sensing,Simulation and
Controls, Multi Sensor Fusion, Tracking and Resource Management II,
SPIE, 1997.
[9] A. Maddi, "Modélisation et contr├┤le du vol latéral d-un avion",
Magister Thesis, Electronics Department, University of Blida, Algeia,
1997.
[10] M. Grewal and A. Andrews, "Kalman Filtering Theory and Practice
Using MATLAB", (Second ed.), New York, NY USA: John Wiley &
Sons, Inc., 2001.
[11] P.C. Murphy and V. Klein, "Estimation of Aircraft Unsteady
Aerodynamic Parameters From Dynamic Wind Tunnel Testing" , AIAA
2001- 4016, August 2001
[12] G. Bishop, G. Welch, "An Introduction to the Kalman Filter", University
of North Carolina at Chapel Hill, Department of Computer Science,
SIGGRAPH 2001.
[13] D. Simon, "Optimal state estimation: Kalman, H-infinity, and nonlinear
approaches", John Wiley & Sons, 2006.
@article{"International Journal of Electrical, Electronic and Communication Sciences:61590", author = "A. Maddi and A. Guessoum and D. Berkani", title = "Using Linear Quadratic Gaussian Optimal Control for Lateral Motion of Aircraft", abstract = "The purpose of this paper is to provide a practical
example to the Linear Quadratic Gaussian (LQG) controller. This
method includes a description and some discussion of the discrete
Kalman state estimator. One aspect of this optimality is that the
estimator incorporates all information that can be provided to it. It
processes all available measurements, regardless of their precision, to
estimate the current value of the variables of interest, with use of
knowledge of the system and measurement device dynamics, the
statistical description of the system noises, measurement errors, and
uncertainty in the dynamics models.
Since the time of its introduction, the Kalman filter has been the
subject of extensive research and application, particularly in the area
of autonomous or assisted navigation. For example, to determine the
velocity of an aircraft or sideslip angle, one could use a Doppler
radar, the velocity indications of an inertial navigation system, or the
relative wind information in the air data system. Rather than ignore
any of these outputs, a Kalman filter could be built to combine all of
this data and knowledge of the various systems- dynamics to
generate an overall best estimate of velocity and sideslip angle.", keywords = "Aircraft motion, Kalman filter, LQG control, Lateral
stability, State estimator.", volume = "3", number = "1", pages = "106-5", }