837 research outputs found
Model-free tracking control of complex dynamical trajectories with machine learning
Nonlinear tracking control enabling a dynamical system to track a desired
trajectory is fundamental to robotics, serving a wide range of civil and
defense applications. In control engineering, designing tracking control
requires complete knowledge of the system model and equations. We develop a
model-free, machine-learning framework to control a two-arm robotic manipulator
using only partially observed states, where the controller is realized by
reservoir computing. Stochastic input is exploited for training, which consists
of the observed partial state vector as the first and its immediate future as
the second component so that the neural machine regards the latter as the
future state of the former. In the testing (deployment) phase, the
immediate-future component is replaced by the desired observational vector from
the reference trajectory. We demonstrate the effectiveness of the control
framework using a variety of periodic and chaotic signals, and establish its
robustness against measurement noise, disturbances, and uncertainties.Comment: 16 pages, 8 figure
An Approach of Tracking Control for Chaotic Systems
Combining the ergodicity of chaos and the Jacobian matrix, we design a general tracking controller for continuous and discrete chaotic systems. The control scheme has the ability to track a bounded reference signal. We prove its globally asymptotic stability and extend it to generalized projective synchronization. Numerical simulations verify the effectiveness of the proposed scheme
Advanced Mathematics and Computational Applications in Control Systems Engineering
Control system engineering is a multidisciplinary discipline that applies automatic control theory to design systems with desired behaviors in control environments. Automatic control theory has played a vital role in the advancement of engineering and science. It has become an essential and integral part of modern industrial and manufacturing processes. Today, the requirements for control precision have increased, and real systems have become more complex. In control engineering and all other engineering disciplines, the impact of advanced mathematical and computational methods is rapidly increasing. Advanced mathematical methods are needed because real-world control systems need to comply with several conditions related to product quality and safety constraints that have to be taken into account in the problem formulation. Conversely, the increment in mathematical complexity has an impact on the computational aspects related to numerical simulation and practical implementation of the algorithms, where a balance must also be maintained between implementation costs and the performance of the control system. This book is a comprehensive set of articles reflecting recent advances in developing and applying advanced mathematics and computational applications in control system engineering
Unified linear time-invariant model predictive control for strong nonlinear chaotic systems
It is well known that an alone linear controller is difficult to control a chaotic system, because intensive nonlinearities exist in such system. Meanwhile, depending closely on a precise mathematical modeling of the system and high computational complexity, model predictive control has its inherent drawback in controlling nonlinear systems. In this paper, a unified linear time-invariant model predictive control for intensive nonlinear chaotic systems is presented. The presented model predictive control algorithm is based on an extended state observer, and the precise mathematical modeling is not required. Through this method, not only the required coefficient matrix of impulse response can be derived analytically, but also the future output prediction is explicitly calculated by only using the current output sample. Therefore, the computational complexity can be reduced sufficiently. The merits of this method include, the Diophantine equation needing no calculation, and independence of precise mathematical modeling. According to the variation of the cost function, the order of the controller can be reduced, and the system stability is enhanced. Finally, numerical simulations of three kinds of chaotic systems confirm the effectiveness of the proposed method
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