Reduction and non-linear controllability of symmetric distributed systems

McMickell, M.B.

doi:10.1080/00207170310001633277

Cited by 20 publications

(4 citation statements)

References 18 publications

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“…Figure 5 shows the singular values and strong accessibility signature. As expected from symmetry arguments in [28], that can also be recognized in equation (3.12), the effect of removing 6 u is similar to removing 4 u . By comparing Figure 5 with Figure 3 observe that one mode is obtained that is not locally strong accessible in both cases.…”

Section: Large-scale System Examplessupporting

confidence: 57%

“…To demonstrate the high efficiency of our algorithm, and its applicability to largescale systems, the first two examples presented in this section are those with the highest state dimension appearing in [28]- [30]. For one of these examples it is very easy to extend the state dimension, as we will do.…”

Section: Large-scale System Examplesmentioning

confidence: 99%

“…For one of these examples it is very easy to extend the state dimension, as we will do. Furthermore we will extend the analysis performed in [28]- [30] by checking local strong accessibility for different combinations of control inputs.…”

Section: Large-scale System Examplesmentioning

confidence: 99%

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Sensitivity Matrices as Keys to Local Structural System Properties of Large-Scale Nonlinear Systems.

Lgv¹,

Stigter²,

Molenaar³

2021

Preprint

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Sensitivities are shown to play a key role in a very efficient algorithm, presented in this paper, to establish three fundamental structural system properties: local structural identifiability, local observability and local strong accessibility. Sensitivities have the advantageous property to be governed by linear dynamics, also if the system itself is nonlinear . By integrating their linear dynamics over a short time period, and by sampling the result, a sensitivity matrix is obtained. If this sensitivity matrix satisfies a rank condition, then the local structural system property under investigation holds. This rank condition will be referred to in this paper as the sensitivity rank condition (SERC). Applying a singular value decomposition (SVD) to the sensitivity matrix not only determines its rank but also pinpoints exactly the system components causing a possible failure to satisfy the local structural system property. The algorithm is very efficient because integration of linear systems over short time-periods and computation of an SVD are computationally cheap. Therefore, it allows for the handling of large-scale systems in the order of seconds, as opposed to conventional algorithms that mostly rely on Lie series expansions and a corresponding Lie algebraic rank condition (LARC). We extensively discuss the (dis)advantages of both algorithms and to which extent their results coincide. A series of examples is presented to illustrate these results.

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Section: Large-scale System Examplessupporting

confidence: 57%

Section: Large-scale System Examplesmentioning

confidence: 99%

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Sensitivity Matrices as Keys to Local Structural System Properties of Large-Scale Nonlinear Systems.

Lgv¹,

Stigter²,

Molenaar³

2021

Preprint

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“…We implemented this motion planning algorithm on a system of four MICAbot mobile robots. A detailed description of this experimental platform can be found in McMickell et al (2003). We first present a sketch of the model used and associated simulation results.…”

Section: Experimental Implementationmentioning

confidence: 99%

Motion Planning for Nonlinear Symmetric Distributed Robotic Formations

McMickell

2007

The International Journal of Robotics Research

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This paper develops a motion planning algorithm which exploits symmetries in distributed systems to reduce motion planning computation complexity. Symmetries allow for algebraic manipulations that are computationally costly, which normally must be carried out for each component in a distributed system, to be related among various symmetric components in a distributed system by a simple algebraic relationship. This leads to a large reduction in the complexity of the overall motion planning problem for a group of distributed mobile robotic agents. In particular, due to the manner in which a symmetric system is defined, the structure of the Chen-Fliess-Sussmann differential equations has a simple relationship among various symmetric components of a distributed system. Essentially, symmetries are defined in a manner which preserves the Lie algebraic structure of each component. In a system with distributed computational capability, the motion planning computations may be distributed throughout formation in such a way that the objectives of the formation are satisfied and collision avoidance is guaranteed. The algorithm maintains a rigid body formation at the beginning and end of the trajectory, as well as possibly specified intermediate points. Due to the generally nonholonomic nature of mobile robots, guaranteeing a rigid body formation during the intermediate motion is impossible. However, it is possible to bound the magnitude of the deviation from the rigid body formation at any point along the trajectory. Simulation and experimental results are provided to demonstrate the utility of the algorithm.

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Fractional-order system identification for health monitoring

Leyden

2018

Nonlinear Dyn

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Reduction and non-linear controllability of symmetric distributed systems

Cited by 20 publications

References 18 publications

Sensitivity Matrices as Keys to Local Structural System Properties of Large-Scale Nonlinear Systems.

Sensitivity Matrices as Keys to Local Structural System Properties of Large-Scale Nonlinear Systems.

Motion Planning for Nonlinear Symmetric Distributed Robotic Formations

Fractional-order system identification for health monitoring

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