Rodolfo Reyes‐Báez

Rodolfo Reyes-Báez, Alejandro Donaire, Arjan van der Schaft et al.

In this work we propose a family of trajectory tracking controllers for marine craft in the port-Hamiltonian (pH) framework using virtual differential passivity based control (v-dPBC). Two pH models of marine craft are considered, one in a body frame and another in an inertial frame. The structure and workless forces of pH models are exploited to design two virtual control systems which are related to the original marine craft's pH models. These virtual systems are rendered differentially passive with an imposed steady-state trajectory, both by means of a control scheme. Finally, the original marine craft pH models in closed-loop with above controllers solve the trajectory tracking problem. The performance of the closedloop system is evaluated on numerical simulations.

Rodolfo Reyes-Báez, Arjan van der Schaft, Bayu Jayawardhana

In this paper, we propose a novel trajectory tracking controller for fully-actuated mechanical port-Hamiltonian (pH) systems, which is based on recent advances in contraction-based control theory. Our proposed controller renders a desired sliding manifold (where the reference trajectory lies) attractive by making the corresponding error system partially contracting. Finally, we present numerical simulation results where a SCARA robot is commanded by our proposed tracking control law.

Rodolfo Reyes-Baez, Arjan van der Schaft, Bayu Jayawardhana

In this paper we present three distributed control laws for the coordination of networked Euler-Lagrange (EL) systems. We first reformulate the passivity-based control design method in \cite{Arcak} by considering that each edge is associated with an \emph{artificial spring system} instead of the usual diffusive coupling among the communicating agents. With this configuration, the networked EL system possesses a "symmetric" feedback structure which together with the strict passivity of both agents' and edges' dynamics lead to a strictly passive network dynamics. Subsequently we present the networked version of two different passivity-based tracking controllers %local controllers that are particular cases of our method and the one in \cite{Arcak}. Numerical simulation is presented to show the performance of the proposed methods.

Santiago Sanchez-Escalonilla, Rodolfo Reyes-Baez, Bayu Jayawardhana

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.

Rodolfo Reyes-Báez, Arjan van der Schaft, Bayu Jayawardhana et al.

In this work we present a constructive method to design a family of virtual contraction based controllers that solve the standard trajectory tracking problem of flexible-joint robots (FJRs) in the port-Hamiltonian (pH) framework. The proposed design method, called virtual contraction based control (v-CBC), combines the concepts of virtual control systems and contraction analysis. It is shown that under potential energy matching conditions, the closed-loop virtual system is contractive and exponential convergence to a predefined trajectory is guaranteed. Moreover, the closed-loop virtual system exhibits properties such as structure preservation, differential passivity and the existence of (incrementally) passive maps.