Passivity and Immersion (P&I) Approach for Constructive Stabilization and Control of Nonlinear Systems

This letter proposes a control algorithm as a stepping stone for the stabilization and control of structured and unstructured systems discussed in the literature. The foundation behind this proposed controller design theory utilizes an invariant target manifold giving rise to a non-degenerate form, through which the definition of certain passive outputs and storage functions provide the control law for stabilizing the system. The proposed control framework is developed by integrating the notions of immersion and passivity hence labeled as the “Passivity and Immersion (P&I) approach.” Immersing the system dynamics into the user-defined lower order target dynamics and using the concept of attractivity of the manifold based upon the passivity theory results in encompassing various design paradigms under a single roof of the P&I approach. The benchmark examples are solved to show the effectiveness of the proposed P&I approach in confirming how the various design paradigms can be unified.