Bo Zhang, Jeffrey Uhlmann
In this paper we significantly extend previous work on methods for ensuring that control system behavior is invariant with respect to units chosen for critical state variables when intermediate operations require solutions to underdetermined or overdetermined systems of equations. For example, least-squares methods are intrinsically sensitive to whether lengths are defined in units of, e.g., centimeters or meters. Prior work has argued that many practical control systems have such unrecognized unit dependencies and are thus vulnerable to exhibiting unexpected behaviors in some situations. Here we extend the underlying theory of unit-consistent generalized inverses (UC inverse) to the more common practical situation in which some state variables have unit dependencies while others require consistency with respect to rigid rotations. We also extend the theory of UC inverse by formally proving that their consistency guarantees are preserved under Kronecker (tensor) products, which is a critical property for using and analyzing complex control systems defined as compositions of simpler subsystems.
Control Systems, Generalized Matrix Inverse, Inverse Problems, Kronecker product, Linear Estimation, Linear Systems, Moore-Penrose Pseudoinverse, System Design, UC Generalized Inverse, Unit Consistency
Cite this paper
Bo Zhang, Jeffrey Uhlmann. (2020) Examining a Mixed Inverse Approach for Stable Control of a Rover. International Journal of Control Systems and Robotics, 5, 1-7