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

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

Approximate transverse feedback linearization under digital control

Thanks to a suitable redesign of the maps involved in the continuous-time solution, a digital design procedure preserving transverse feedback linearization up to a prefixed order of approximation in the sampling period is described. Simulated examples illustrate the results

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

Passivity Techniques and Hamiltonian Structures in Discrete Time

The object of this paper is to show the impact of representing discrete-time dynamics as two coupled difference/differential equations in establishing passivity properties and describing port-Hamiltonian structures as well as the related energy-based control strategies

Quaternion-Based Attitude Stabilization via Discrete-Time IDA-PBC

In this letter, we propose a new sampled-data controller for stabilization of the attitude dynamics at a desired constant configuration. The design is based on discrete-time interconnection and damping assignment (IDA) passivity-based control (PBC) and the recently proposed Hamiltonian representation of discrete-time nonlinear dynamics. Approximate solutions are provided with simulations illustrating performances

Steering and Formation Control of Unicycles Under Single-Rate Sampling

In this paper, we propose a new digital feedback law for controlling unicycles in a sampled-data scenario. More in detail, two open problems are solved. First, assuming piecewise constant control and sampled-data measures of the state, we consider the problem of driving one unicycle toward a desired position in the plane with a target fixed orientation. Then, we tackle the problem of forcing a network of unicycles to a desired formation with the same orientation when assuming asynchronous sampled-data communication and piecewise constant controls. The design relies upon discrete-time passivity-based arguments yielding the first feedback law (within the digital literature) that employs single-rate sampling while keeping into account the effects of digital devices. The results are finally illustrated through simulations aimed at showing the benefits of the proposed controller to recover the same performances under the continuous-time control law, whose performances are unavoidably lost when implemented in practice

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

Sampled-data steering of unicycles via PBC

In this paper, on the basis of a recently proposed discrete-time port-Hamiltonian representation of sampled-data dynamics, we propose a new time-varying digital feedback for steering mobile robots. The quality of the proposed passivity-based control is validated and compared through simulations with the existing literature and the continuous-time implementation using the unicycle as a case study

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