Analysis and optimization of certain qualities of controllability and observability for linear dynamical systems

Sequential Co-Design of an Artifact and its Controller Via Control Proxy Functions

“…The natural frequency is considered as the basis for a CPF because previous work has shown that, in some cases, it can be used as an effective proxy for a system's ease of control [e.g., Peters et al (2008); Hale et al (1985); Khot and Abhyankar (1993)]. The controllability Grammian matrix, W c , will be considered as the basis for a CPF because it has been successfully used for the location of actuators [e.g., Muller and Weber (1972); Roh and Park (1997); Lim and Gawronski (1993)]. Furthermore, it has been shown that, for some problem formulations, there is a relationship between W c and the coupling vector Γ v ].…”

Optimization of measurement schedules and sensor designs for linear dynamic systems

“…Then the followingare equivalent. In this section, we discuss the problem considered by Johnson [2] and ~iiller and Weber [3]. The motivation for considering nonrandomized designs is that in many practical situations, it is not possible to employ randomized designs.…”

“…This is also true for the control version of the N~~ order integrator problem considered in Refs. [2,3]. The observability matrix is where IQI = h; ; clearly h; = k 1 and hf = 0.…”

Optimal Sensor Configuration and Fault-Tolerant Estimation of Vehicle States

“…There are some criteria to measure the degree of observability. For example, Muller and Weber [1] outlined three candidate measures including minimum eigenvalue of the observability Gramian to find the degree of observability for linear systems. Chamseddine et al in [2] introduced two other criteria: the trace of the observability Gramian and the robust spectral norm which is the minimum singular value of the observability Gramian.…”

“…Nakhaeinejad et al [4] suggested a similar approach not only for analysis of the faults, but also for defining a guideline for model-based sensor selection for induction motors. Among all of the abovementioned methods, the condition number is more common and is frequently used in the literature [1], [5], [6]. In this paper, all of the introduced observability and sensor configuration methods are chosen and applied to determine the best sensor configuration for estimation of vehicle states.…”