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Towards A Constructive Framework For Stabilization And Control Of Nonlinear Systems: The Passivity And Immersion (P&I) Approach
  • Shadab Nayyer Syed ,
  • Sushama Wagh ,
  • Navdeep Singh
Shadab Nayyer Syed
VJTI Mumbai India

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Sushama Wagh
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Navdeep Singh
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Abstract

The varied and complex dynamics of systems encountered in the real world challenge the formulation of a systematic strategy for designing a stabilizing feedback law. Thus far, the control strategies formulated to handle this problem are specific to the systems with a suitable structure rather than a general approach. In view of this, the paper attempts to sketch the outline of a proposed theory which provides a stepping stone to be general enough. Keeping it central to the development of the stabilizing feedback law, it is applicable wherever possible for a general class of systems in standard structured and unstructured forms discussed in the literature. The foundation behind this generalized theory of controller design utilizes the idea of an invariant target manifold giving rise to a non-degenerate two form, through which the definition of certain passive outputs and storage functions leads to a generation arises of control law for stabilizing the system. Because the above ideas connect with the immersion design policy and passivity theory of controller design, the developed methodology is labeled as the “Passivity and Immersion based approach” (P&I). The rigorously solved examples demonstrate how the diversified design paradigms can be unified in the proposed P&I methodology. Additionally, the target dynamics are set to achieve the parameter-independent implicit manifolds, passive output, and associated storage function in order to mitigate the impacts of the parametric changes in the system