passivitybased

Passivity-based control is a design approach in control theory that leverages the passivity property of physical systems to ensure stability and performance. Passivity relates input power and stored or dissipated energy through energy-like inequalities. By exploiting these energy properties, engineers aim to shape closed-loop behavior without relying solely on exact dynamical models.

A common mathematical framework for passivity-based methods is the port-Hamiltonian representation. In this view, a system is described by an energy function that represents stored energy, an interconnection structure that is skew-symmetric, and a damping mechanism that dissipates energy. The plant is viewed as an interconnection of energy storage, dissipative elements, and power ports through which inputs and outputs exchange energy. The control objective is achieved by designing how energy flows into the system, often by modifying the energy function or the interconnection and damping terms.

Key design techniques include energy shaping, where the desired energy landscape is imposed to create a stable equilibrium, and damping injection, which adds dissipation to dissipate perturbations. A notable method is Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC), which seeks to realize a target energy and damping structure in the closed loop by solving matching conditions. Controlled Lagrangian and other energy-based approaches are related variations.

Applications span robotics, mechanical systems, electrical circuits, underwater and aerial vehicles, and renewable-energy systems. Benefits include systematic stability guarantees and robustness to certain model uncertainties, though solving the required matching equations can be challenging and may demand full state feedback or observers. The approach traces its roots to the port-Hamiltonian formalism developed in the 1990s by van der Schaft, Maschke, Ortega, and coworkers.