Abstract
The model-based controllers generally suffer from the lack of precise dynamic models. Making reliable analytical models can be evaded by soft modeling techniques, while the consequences of modeling imprecisions are tackled by either robust or adaptive techniques. In robotics, the prevailing adaptive techniques are based on Lyapunov’s “direct method” that normally uses special error metrics and adaptation rules containing fragments of the Lyapunov function. The soft models and controllers need massive parallelism and suffer from the curse of dimensionality. A different adaptive approach based on Banach’s fixed point theorem and using special abstract rotations was recently suggested. Similar rotations were suggested to develop particular neural network-like soft models, too. Presently, via integrating these approaches, a uniform adaptive controlling and modeling methodology is suggested with especial emphasis on the effects of the measurement noises. Its applicability is investigated via simulations for a two degree of freedom mechanical system in which one of the generalized coordinates is under control, while the other one belongs to a coupled parasite dynamical system. The results are promising for allowing the development of relatively coarse soft models and a simple adaptive rule that can be implemented in embedded systems.
Highlights
The results are promising for allowing the development of relatively coarse soft models and a simple adaptive rule that can be implemented in embedded systems
In which q1 denotes the rotational angle of the wheel, q2 is the radial distance of the mass point along the spoke, measured from the rotational axle, r is the zero force position of the spring connected the axle with the mass point, k is the spring constant, d denotes the viscous damping coefficient of the mass point as it moves along the spoke, m is its inertia, and Θ corresponds to the inertia momentum of the wheel, Q1 denotes the driving torque
The figures contain simulation results obtained when the exact dynamic model was in use to support comparative analysis
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. To tackle the problem of the curse of dimensionality, to evade the need for massive parallelism and sophisticated data synchronization in the learning and operating phases of the traditional structures, in [86], a novel soft computing structure was suggested that is more or less akin to a coarse resolution grid or a fuzzy model in which very approximate and simple rules are applied for control purposes. It broke with the Lyapunov functionbased design that generally was present in the switching controllers and in the “Linear.
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