Neuro-based Canonical Transformation of Port Controlled Hamiltonian Systems

Abstract

In the literature of control theory, tracking control of port controlled Hamiltonian systems is generally achieved using canonical transformation. Closed form evaluation of state-feedback for the canonical transformation requires the solution of certain partial differential equations which becomes very difficult for nonlinear systems. This paper presents the application of neural networks for the canonical transformation of port controlled Hamiltonian systems. Instead of solving the partial differential equations, neural networks are used to approximate the closed-form state-feedback required for canonical transformation. Ultimate boundedness of the tracking and neural network weight errors is guaranteed. The proposed approach is structure preserving. The application of neural networks is direct and off-line processing of neural networks is not needed. Efficacy of the proposed approach is demonstrated with the examples of a mass-spring system, a two-link robot arm and an Autonomous Underwater Vehicle (AUV).

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Correspondence to Sami El Ferik.

Additional information

Recommended by Editor Kyoung Kwan Ahn.

The authors would like to acknowledge the support provided by King Fahd University of Petroleum and Minerals (KFUPM) for funding this work through project, no.IN141048.

Aminuddin Qureshi obtained his degrees of B.Sc. in Electrical Engineering from UET Peshawar-Pakistan, an M.Sc. in Systems Engineering from PIEAS-Pakistan and Ph.D. in Systems Engineering from KFUPM-Saudi Arabia, in 2001, 2003, and 2014, respectively. He has worked on several R&D projects in the areas of signal processing and control. Currently, he is involved in the diagnostics and prognostics of industrial structures, systems and components. His areas of interest are signal processing, artificial intelligence applied to control systems and diagnostics and prognostics.

Sami El Ferik is an Associate Professor in Control and Instrumentation, Department of Systems Engineering, at KFUPM. He obtained his B.Sc degree in Electrical Engineering from Laval University, Quebec, Canada, and both of his M.S. and Ph.D. in Electrical and Computer Engineering from Ecole Polytechnique, University of Montreal, Montreal, Canada. He worked with Pratt and Whitney Canada as a Staff Control Analyst at the Research and Development Center of Systems, Controls, and Accessories. His research interests are in sensing, monitoring, and control with strong multidisciplinary research and applications. His research contributions are in control of drug administration, process control and control loop performance monitoring, control of systems with delays, modeling and control of stochastic systems, analysis of network stability, condition monitoring and condition-based maintenance.

Frank L. Lewis, National Academy of Inventors, Fellow IEEE, Fellow IFAC, PE Texas, U.K. Chartered Engineer, is a UTA Distinguished Scholar Professor, UTA Distinguished Teaching Professor, and Moncrief-O’Donnell Chair at the University of Texas at Arlington Research Institute. He obtained his Bachelor’s Degree in Physics/EE and the MSEE at Rice University, an M.S. degree in Aeronautical Engineering from the University of West Florida, and a Ph.D. degree at Ga. Tech. He is the author of seven U.S. patents, numerous journal papers, and 14 books.

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Qureshi, A., El Ferik, S. & Lewis, F.L. Neuro-based Canonical Transformation of Port Controlled Hamiltonian Systems. Int. J. Control Autom. Syst. (2020). https://doi.org/10.1007/s12555-019-0029-1

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Keywords

  • Canonical transformation
  • L2 disturbance attenuation
  • neural networks
  • port controlled Hamiltonian systems