H2/H filtering theory and an aerospace application

Robust filtering for uncertain nonlinearly parameterized plants

“…Equation (11 (9), there is a such that (73) holds. By the projection lemma, this, together with (72) [which is equivalent to (9)], is sufficient for the existence of satisfying (12). Furthermore, for , (73) automatically holds true for , and thus, together with (72), implies (14) as well.…”

“…Finally, the equivalence between (12) and (13) follows from the congruence transformation diag applied to (12) He was with the Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, from June 1989 to July 1994, as a member of technical staff. Since August 1994 to July 1998, he was with the Electrical and Computer Engineering Department, University of Wisconsin, Madison.…”

Robust filtering for uncertain nonlinearly parameterized plants

“…Equation (11 (9), there is a such that (73) holds. By the projection lemma, this, together with (72) [which is equivalent to (9)], is sufficient for the existence of satisfying (12). Furthermore, for , (73) automatically holds true for , and thus, together with (72), implies (14) as well.…”

“…Finally, the equivalence between (12) and (13) follows from the congruence transformation diag applied to (12) He was with the Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, from June 1989 to July 1994, as a member of technical staff. Since August 1994 to July 1998, he was with the Electrical and Computer Engineering Department, University of Wisconsin, Madison.…”

Robust ℋ︁∞sliding mode control for nonlinear stochastic systems with multiple data packet losses

“…The nominal system matrix A is taken from the model of an F‐404 aircraft engine system in 36. Note that this example is actually a special case of the physical models studied in 2, 36–38. Moreover, in order to make the model more realistic and more close to the real‐world engineering practices, we add the stochastic noises, the data packet loss and the external disturbances caused by the complex and time‐varying working conditions in the system.…”

Continuous‐time Kalman filtering on the orthogonal group O(n)

“…Although various estimation and filtering methods, such as methods and mixed methods , have been developed, the Kalman filter has long been the cornerstone of stochastic linear state estimation. Various extended Kalman filter (EKFs), including the additive EKF and multiplicative EKF, have successfully been used for attitude estimation using a quaternion parameterization of attitude .…”

Robust filtering for uncertain nonlinearly parameterized plants

“…Equation (11 (9), there is a such that (73) holds. By the projection lemma, this, together with (72) [which is equivalent to (9)], is sufficient for the existence of satisfying (12). Furthermore, for , (73) automatically holds true for , and thus, together with (72), implies (14) as well.…”

“…Finally, the equivalence between (12) and (13) follows from the congruence transformation diag applied to (12) He was with the Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, from June 1989 to July 1994, as a member of technical staff. Since August 1994 to July 1998, he was with the Electrical and Computer Engineering Department, University of Wisconsin, Madison.…”

Robust ℋ︁∞sliding mode control for nonlinear stochastic systems with multiple data packet losses

“…The nominal system matrix A is taken from the model of an F‐404 aircraft engine system in 36. Note that this example is actually a special case of the physical models studied in 2, 36–38. Moreover, in order to make the model more realistic and more close to the real‐world engineering practices, we add the stochastic noises, the data packet loss and the external disturbances caused by the complex and time‐varying working conditions in the system.…”

Continuous‐time Kalman filtering on the orthogonal group O(n)

“…Although various estimation and filtering methods, such as methods and mixed methods , have been developed, the Kalman filter has long been the cornerstone of stochastic linear state estimation. Various extended Kalman filter (EKFs), including the additive EKF and multiplicative EKF, have successfully been used for attitude estimation using a quaternion parameterization of attitude .…”

Robust filtering for uncertain nonlinearly parameterized plants

“…Equation (11 (9), there is a such that (73) holds. By the projection lemma, this, together with (72) [which is equivalent to (9)], is sufficient for the existence of satisfying (12). Furthermore, for , (73) automatically holds true for , and thus, together with (72), implies (14) as well.…”

“…Finally, the equivalence between (12) and (13) follows from the congruence transformation diag applied to (12) He was with the Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, from June 1989 to July 1994, as a member of technical staff. Since August 1994 to July 1998, he was with the Electrical and Computer Engineering Department, University of Wisconsin, Madison.…”

Robust ℋ︁∞sliding mode control for nonlinear stochastic systems with multiple data packet losses

“…The nominal system matrix A is taken from the model of an F‐404 aircraft engine system in 36. Note that this example is actually a special case of the physical models studied in 2, 36–38. Moreover, in order to make the model more realistic and more close to the real‐world engineering practices, we add the stochastic noises, the data packet loss and the external disturbances caused by the complex and time‐varying working conditions in the system.…”

Continuous‐time Kalman filtering on the orthogonal group O(n)

“…Although various estimation and filtering methods, such as methods and mixed methods , have been developed, the Kalman filter has long been the cornerstone of stochastic linear state estimation. Various extended Kalman filter (EKFs), including the additive EKF and multiplicative EKF, have successfully been used for attitude estimation using a quaternion parameterization of attitude .…”