Lyapunov stabilization of discrete-time feedforward dynamics

The paper discusses stabilization of nonlinear discrete-time dynamics in feedforward form. First it is shown how to define a Lyapunov function for the uncontrolled dynamics via the construction of a suitable cross-term. Then, stabilization is achieved in terms of u-average passivity. Several constructive cases are analyzed

Discrete port-controlled Hamiltonian dynamics and average passivation

The paper discusses the modeling and control of port-controlled Hamiltonian dynamics in a pure discrete-time domain. The main result stands in a novel differential-difference representation of discrete port-controlled Hamiltonian systems using the discrete gradient. In these terms, a passive output map is exhibited as well as a passivity based damping controller underlying the natural involvement of discrete-time average passivity

Perceptual and conceptual distortions of implicit hand maps

Recent studies have revealed that human position sense relies on a massively distorted representation of hand size and shape. By comparing the judged location of landmarks on an occluded hand, Longo and Haggard (2010) constructed implicit perceptual maps of represented hand structure, showing large underestimation of finger length and overestimation of hand width. Here, we investigated the contribution of two potential sources of distortions to such effects: perceptual distortions reflecting spatial warping of the representation of bodily tissue itself, perhaps reflecting distortions of somatotopic cortical maps, and conceptual distortions reflecting mistaken beliefs about the locations of different landmarks within the body. In Experiment 1 we compared distorted hand maps to a task in which participants explicitly judged the location of their knuckles in a hand silhouette. The results revealed the conceptual distortions are responsible for at least part of the underestimation of finger length, but cannot explain overestimation of hand width. Experiment 2 compared distortions of the participant’s own hand based on position sense with a prosthetic hand based on visual memory. Underestimation of finger length was found for both hands, providing further evidence that it reflects a conceptual distortion. In contrast, overestimation of hand width was specific to representation of the participant’s own hand, confirming it reflects a perceptual distortion. Together, these results suggest that distorted body representations do not reflect a single underlying cause. Rather, both perceptual and conceptual distortions contribute to the overall configuration of the hand representation

Energy-Balance PBC of nonlinear dynamics under sampling and delays

The paper provides a new class of passivity-based controllers (PBCs) for stabilizing sampled-data input-delayed dynamics at a desired equilibrium via energy-balancing (EB) and reduction. Given a nonlinear dynamics under piecewise constant and retarded input, we first exhibit a new dynamics (the reduced dynamics) that is free of delays and equivalent to the original one. Accordingly, we design the digital controller assigning a suitable energetic behaviour to the reduced delay-free model with a stable target equilibrium. Then, it is proved that such a controller solves the EB-PBC problem on the original retarded system. The results are illustrated over a simple mechanical system

A new connection protocol for multi-consensus of discrete-time systems

In this paper, a new connection protocol for consensus of multi-agent discrete-time systems under a general communication graph is proposed. In particular, the coupling is realized based on the outputs making each agent passive in the u-average sense so guaranteeing convergence to the agreement steady-state, with no need of mitigating the coupling gain, as typically done in concerned literature. The proposed connection rule is shown to apply for network dynamics under aperiodic sampling when the sampling sequence is known to all agents

Stabilization of the Acrobot via sampled-data passivity-based control

The paper deals with the sampled-data asymptotic stabilization of the Acrobot at its upward equilibrium. The proposed controller results from the action of an Input-Hamiltonian-Matching (IHM) strategy that shapes the closed-loop energy combined with a Damping Injection (DI) feedback designed on the sampled-data equivalent model. Simulations show the effectiveness of the proposed controller

Virtual Holonomic Constraints for Euler-Lagrange systems under sampling

In this paper, we consider the problem of imposing Virtual Holonomic Constraints to mechanical systems in Euler-Lagrangian form under sampling. An exact solution based on multi-rate sampling of order two over each input channel is described. The results are applied to orbital stabilization of the pendubot with illustrative simulations

A new distributed protocol for consensus of discrete-time systems

In this paper, a new distributed protocol is proposed to force consensus in a discrete-time network of scalar agents with an arbitrarily assignable convergence rate. Several simulations validate the performances and the improvements with respect to more standard protocols

A gradient descent algorithm built on approximate discrete gradients

We propose an optimization method obtained by the approximation of a novel discretization approach for gradient dynamics recently proposed by the authors. It is shown that the proposed algorithm ensures convergence for all amplitudes of the step size, contrarily to classical implementations

Discrete-time energy-balance passivity-based control

In this paper, new results for passivation and stabilization of discrete-time nonlinear systems via energy balancing are established. When specified on sampled-data systems, the approach is constructive for computing stabilizing digital controllers that assign, at all sampling instants, a target energy profile while stabilizing a target equilibrium. The class of mechanical systems is discussed as an example. Simulations are reported highlighting, for position regulation of a 2R robot, the effect of approximate solutions with respect to standard emulation