Neuro-based Canonical Transformation of Port Controlled Hamiltonian Systems
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Neuro-based Canonical Transformation of Port Controlled Hamiltonian Systems Aminuddin Qureshi, Sami El Ferik*, and Frank L. Lewis 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 closedform 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). Keywords: Canonical transformation, L2 disturbance attenuation, neural networks, port controlled Hamiltonian systems.
1.
INTRODUCTION
Port Controlled Hamiltonian (PCH) models are known for their ability to represent a wide range of dynamical systems including the important class of Euler-Lagrange (EL) form, as well as those found in several electrical, electromechanical and chemical applications. Indeed PCH models explicitly consider the energy-relevant properties of the Hamiltonian systems, incorporate the ideas of networking and port based modeling, and are best suited for energy shaping and Passivity Based Control (PBC) techniques. Several approaches have been proposed to design a controller for PCH systems. In particular, model-based control synthesis, [1], include canonical transformation, control by interconnection, energy balancing, interconnection and damping assignment passivity-based (IDAPBC) (see [1] and refrences there-in). Application of the PCH framework is intensifying in different fields (see for instance, [1–4]). Of interest to this work, canonical transformations are frequently used to facilitate the systems’ analysis and controller design. The theory of canonical transformation of PCH systems has been established in [5] and [6]. Tracking control problem of PCH systems is managed by transforming the original system’s dynamics from state-space
to tracking error-space and then stabilizing the system in the error-space. Evaluation of the closed-form expression for the state feedback to perform the desired canonical transformation needs the solution of a set of partial differential equations (PDEs) satisfying certain conditions. Solving the PDEs is not easy, in general. With increased order and nonlinearities of the systems, solving such PDEs can become too difficult to design the controller and t
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