The role of the equilibrium in potential energy-shaping stabilization of mechanical systems

You might know Rodolfo from Control Engineering. In this column he describes the role of equilibrium in potential energy-shaping stabilization of mechanical systems. Although this article is more mathematical than you’re probably used to, you will probably find it quite applicabl

Stabilization of Underactuated Systems of Degree One via Neural Interconnection and Damping Assignment Passivity Based Control

In this work, we show the potential of the universal approximation property of neural networks in the design of interconnection and damping assignment passivity-based controllers (IDA-PBC) for stabilizing nonlinear underactuated mechanical systems of degree one. Towards this end, we reformulate the IDA-PBC design methodology as a neural supervised learning problem that approximates the solution of the partial differential matching equations, which fulfills the equilibrium assignment and stability conditions. The output of the neural learning process has clear physical and control-theoretic interpretations in terms of energy, passivity and Lyapunov stability. The proposed approach is numerically evaluated in two well-known underactuated systems: the inverted pendulum on a cart and inertial wheel pendulum, whose analytic IDA-PBC solutions are non-trivial to obtain

Virtual contractivity-based control of fully-actuated mechanical systems in the port-Hamiltonian framework

We present a trajectory tracking control design method for a class of mechanical systems in the port-Hamiltonian framework. The proposed solution is based on the virtual contractivity-based control (v-CBC) method, which employs the notions of virtual systems and of contractivity. This approach leads to a family of asymptotic tracking controllers that are not limited to those that preserve the pH structure of the closed-loop system nor require an intermediate change of coordinates. Nevertheless, structure preservation and other properties (e.g., passivity) are possible under sufficient conditions. The performance of the proposed v-CBC scheme is experimentally evaluated on a planar robot of two degrees of freedom (DoF)

Total Energy Shaping with Neural Interconnection and Damping Assignment - Passivity Based Control

In this work we exploit the universal approximation property of Neural Networks (NNs) to design interconnection and damping assignment (IDA) passivity-based control (PBC) schemes for fully-actuated mechanical systems in the port-Hamiltonian (pH) framework. To that end, we transform the IDA-PBC method into a supervised learning problem that solves the partial differential matching equations, and fulfills equilibrium assignment and Lyapunov stability conditions. A main consequence of this, is that the output of the learning algorithm has a clear control-theoretic interpretation in terms of passivity and Lyapunov stability. The proposed control design methodology is validated for mechanical systems of one and two degrees-of-freedom via numerical simulations.Comment: Accepted in 4th Annual Learning for Dynamics and Control (L4DC) Conferenc