Advances in Statistical Control, Algebraic Systems Theory, and Dynamic Systems Characteristics, 2008
How should we interpret the motto: The zeros of a linear system become the poles of its inverse s... more How should we interpret the motto: The zeros of a linear system become the poles of its inverse system? Rudolf Kalman first introduced the idea of the set of poles of a system as a module over an appropriate polynomial ring. Through the lens of the motto above, this historical survey discusses the work of Mike Sain and his coauthors on the module-theoretic approach to zeros of a linear system and the application of these ideas to inverse systems and system design.
We study gliding and rolling, and we develop inverse systems for estimation of internal and conta... more We study gliding and rolling, and we develop inverse systems for estimation of internal and contact forces of constraint. A primitive approximation of biped locomotion serves as a motivation for this work. A class of constraints is formulated in this state space. Rolling and gliding are common in contact sports, in interaction of humans and robots with their environment where one surface makes contact with another surface, and at skeletal joints in living systems. This formulation of constraints is important for control purposes. The estimation of applied and constraint forces and torques at the joints of natural and robotic systems is a challenge. Direct and indirect measurement methods involving a combination of kinematic data and computation are discussed. The basic methodology is developed for one single rigid body for simplicity, brevity, and precision. Computer simulations are presented to demonstrate the feasibility and effectiveness of the approaches presented. The methodology can be applied to a multilink model of bipedal systems where natural and/or artificial connectors and actuators are modeled. Estimation of the forces is accomplished by the inverse of the nonlinear plant designed by using a robust high gain feedback system. The inverse is shown to be stable, and bounds on the tracking error are developed. Lyapunov stability methods are used to establish global stability of the inverse system.
1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes, 1981
Under broad assumptions, it is known [1] that there is, in general, no "separation principle... more Under broad assumptions, it is known [1] that there is, in general, no "separation principle" to guarantee optimality of a division between control law design and filtering of plant uncertainty. It is possible, however, to develop parameterizations of nominal responses and to examine their capabilities in the feedback situation. In an earlier study, the authors presented a coordinate-free approach [34]
Proceedings of the 27th IEEE Conference on Decision and Control, 2000
ABSTRACT The model-matching equation ( T z)= P ( z ) M ( z ) induces constraints on the multivari... more ABSTRACT The model-matching equation ( T z)= P ( z ) M ( z ) induces constraints on the multivariate zero structures of P ( z ) and M ( z ), and the nature of the constraint is best explained by extending the usual notion of zero. In particular, the extended Γ-zero module of P ( z ) must contain as a submodule the module Z Γ of matching Γ-zeros, which depends only on T ( z ) and M ( z ), and the extended Ω-zero module of M ( z ) must contain as a factor module the module Z Ω of matching Ω-zeros, which depends only on T ( z ) and P ( z ). Essential solutions, in which the constraint is by module isomorphism, are possible if and only if the nullity of P ( z ) does not exceed the nullity of T ( z ), on the one hand, or the conullity of M ( z ) does not exceed the conullity of T ( z ), on the other
... The staff of the Consorzio Geneva Ricerche, particularly Ms. Piera Ponta and Ms. Camilla Marc... more ... The staff of the Consorzio Geneva Ricerche, particularly Ms. Piera Ponta and Ms. Camilla Marconi, worked diligently over many months and ... AT ALOUANI, AH NOUREDDINE, RA SMOAK 65 i Instrumental Variables Estimators for State Space Models of Time Series M. AOKI 73 ...
This paper presents and characterizes a new module Z' of zeros in solutions P(z) to the linea... more This paper presents and characterizes a new module Z' of zeros in solutions P(z) to the linear transfer function equation T(z) = P(z) M(z). Unlike the module Z of [1], Z' is finitely generated and torsion, and is thus of classical, finite-dimensional, state-space type. It is, however, a more elaborate module than Z in terms of its submodules and factors. In addition, Z of [1] is established as an essential submodule of the extended, ¿-zeros of P(z).
Advances in Statistical Control, Algebraic Systems Theory, and Dynamic Systems Characteristics, 2008
How should we interpret the motto: The zeros of a linear system become the poles of its inverse s... more How should we interpret the motto: The zeros of a linear system become the poles of its inverse system? Rudolf Kalman first introduced the idea of the set of poles of a system as a module over an appropriate polynomial ring. Through the lens of the motto above, this historical survey discusses the work of Mike Sain and his coauthors on the module-theoretic approach to zeros of a linear system and the application of these ideas to inverse systems and system design.
We study gliding and rolling, and we develop inverse systems for estimation of internal and conta... more We study gliding and rolling, and we develop inverse systems for estimation of internal and contact forces of constraint. A primitive approximation of biped locomotion serves as a motivation for this work. A class of constraints is formulated in this state space. Rolling and gliding are common in contact sports, in interaction of humans and robots with their environment where one surface makes contact with another surface, and at skeletal joints in living systems. This formulation of constraints is important for control purposes. The estimation of applied and constraint forces and torques at the joints of natural and robotic systems is a challenge. Direct and indirect measurement methods involving a combination of kinematic data and computation are discussed. The basic methodology is developed for one single rigid body for simplicity, brevity, and precision. Computer simulations are presented to demonstrate the feasibility and effectiveness of the approaches presented. The methodology can be applied to a multilink model of bipedal systems where natural and/or artificial connectors and actuators are modeled. Estimation of the forces is accomplished by the inverse of the nonlinear plant designed by using a robust high gain feedback system. The inverse is shown to be stable, and bounds on the tracking error are developed. Lyapunov stability methods are used to establish global stability of the inverse system.
1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes, 1981
Under broad assumptions, it is known [1] that there is, in general, no "separation principle... more Under broad assumptions, it is known [1] that there is, in general, no "separation principle" to guarantee optimality of a division between control law design and filtering of plant uncertainty. It is possible, however, to develop parameterizations of nominal responses and to examine their capabilities in the feedback situation. In an earlier study, the authors presented a coordinate-free approach [34]
Proceedings of the 27th IEEE Conference on Decision and Control, 2000
ABSTRACT The model-matching equation ( T z)= P ( z ) M ( z ) induces constraints on the multivari... more ABSTRACT The model-matching equation ( T z)= P ( z ) M ( z ) induces constraints on the multivariate zero structures of P ( z ) and M ( z ), and the nature of the constraint is best explained by extending the usual notion of zero. In particular, the extended Γ-zero module of P ( z ) must contain as a submodule the module Z Γ of matching Γ-zeros, which depends only on T ( z ) and M ( z ), and the extended Ω-zero module of M ( z ) must contain as a factor module the module Z Ω of matching Ω-zeros, which depends only on T ( z ) and P ( z ). Essential solutions, in which the constraint is by module isomorphism, are possible if and only if the nullity of P ( z ) does not exceed the nullity of T ( z ), on the one hand, or the conullity of M ( z ) does not exceed the conullity of T ( z ), on the other
... The staff of the Consorzio Geneva Ricerche, particularly Ms. Piera Ponta and Ms. Camilla Marc... more ... The staff of the Consorzio Geneva Ricerche, particularly Ms. Piera Ponta and Ms. Camilla Marconi, worked diligently over many months and ... AT ALOUANI, AH NOUREDDINE, RA SMOAK 65 i Instrumental Variables Estimators for State Space Models of Time Series M. AOKI 73 ...
This paper presents and characterizes a new module Z' of zeros in solutions P(z) to the linea... more This paper presents and characterizes a new module Z' of zeros in solutions P(z) to the linear transfer function equation T(z) = P(z) M(z). Unlike the module Z of [1], Z' is finitely generated and torsion, and is thus of classical, finite-dimensional, state-space type. It is, however, a more elaborate module than Z in terms of its submodules and factors. In addition, Z of [1] is established as an essential submodule of the extended, ¿-zeros of P(z).
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Papers by Bostwick Wyman