Energy is one of the fundamental concepts in science and engineering practice, where it is common to view dynamical systems as energy-transformation devices. This perspective is particularly useful in studying complex nonlinear systems by decomposing them into simpler subsystems which, upon interconnection, add up their energies to determine the full systems behavior. The action of a controller may be also understood in energy terms as another dynamical system -- typically implemented in a computer -- interconnected with the process to modify its behavior. The control problem can then be recast as finding a dynamical system and an interconnection pattern such that the overall energy function takes the desired form. This energy shaping approach is the essence of passivity based control (PBC), a controller design technique that is increasingly dominant in control applications.
Since the introduction of this controller design methodology 25 years ago many theoretical extensions and practical applications have been reported in the literature. The theoretical developments include some variations and shortcuts that are useful when dealing with particular classes of systems, and the incorporation of additional features to handle control scenarios other than just stabilization. On the application side the method has provided solutions to a wide variety of physical problems. The purpose of this seminar is to review the fundamental theory, main new results and practical applications of this control system design approach as well as to discuss the current open problems and future directions.
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