Stability analysis of a stochastic port-Hamiltonian car-following model

Port-Hamiltonian systems are pertinent representations of many non-linear physical systems. In this article, we formulate and analyse a general class of stochastic car-following models having a systematic port-Hamiltonian structure. The model class is a generalisation of classical car-following approaches, including the Optimal Velocity model by Bando et al. (1995), the Full Velocity Difference model by Jiang et al. (2001), and recent stochastic following models based on the Ornstein-Uhlenbeck process. In contrast to traditional models for which the interaction is totally asymmetric (i.e., depending only on the speed and distance to the predecessor), the port-Hamiltonian car-following model also depends on the distance to the follower. We determine the exact stability condition of the finite system with $N$ vehicles and periodic boundaries. The stable system is ergodic with a unique Gaussian invariant measure. Other model properties are studied using numerical simulation. It turns out that the Hamiltonian component improves the flow stability, reducing the total energy in the system. Furthermore, it prevents the problematic formation of stop-and-go waves with periodic dynamics, even in the presence of stochastic perturbations.Comment: 23 pages, 4 figure

Mini-Workshop: Recent Developments on Approximation Methods for Controlled Evolution Equations

This mini-workshop brought together mathematicians engaged in partial differential equations, functional analysis, numerical analysis and systems theory in order to address a number of current problems in the approximation of controlled evolution equations

A Statistical Theory of Designed Quantum Transport Across Disordered Networks

We explain how centrosymmetry, together with a dominant doublet in the local density of states, can guarantee interference-assisted, strongly enhanced, strictly coherent quantum excitation transport between two predefined sites of a random network of two-level systems. Starting from a generalisation of the chaos assisted tunnelling mechanism, we formulate a random matrix theoretical framework for the analytical prediction of the transfer time distribution, of lower bounds of the transfer efficiency, and of the scaling behaviour of characteristic statistical properties with the size of the network.Comment: 23 pages, 8 figure

Mini-Workshop: Mathematics of Dissipation – Dynamics, Data and Control (hybrid meeting)

Dissipation of energy --- as well as its sibling the increase of entropy --- are fundamental facts inherent to any physical system. The concept of dissipativity has been extended to a more general system theoretic setting via port-Hamiltonian systems and this framework is a driver of innovations in many of areas of science and technology. The particular strength of the approach lies in the modularity of modeling, the strong geometric, analytic and algebraic properties and the very good approximation properties

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

Stability of port-Hamiltonian systems with mixed time delays subject to input saturation

In this paper, we investigate the stability of port-Hamiltonian systems with mixed time-varying delays as well as input saturation. Three types of time delays, including state delay, input delay, and output delay, are all assumed to be bounded. By introducing the output feedback control law and utilizing serval Lyapunov–Krasovskii functionals, we present three delay-dependent stability criteria in terms of the linear matrix inequality. Meanwhile, we use Wirtinger’s inequality, constraint conditions, and Lyapunov–Krasovskii functionals of triple and quadruple integral form to obtain less conservative results. Some numerical examples demonstrate and support our results

Switching Quantum Dynamics for Fast Stabilization

Control strategies for dissipative preparation of target quantum states, both pure and mixed, and subspaces are obtained by switching between a set of available semigroup generators. We show that the class of problems of interest can be recast, from a control--theoretic perspective, into a switched-stabilization problem for linear dynamics. This is attained by a suitable affine transformation of the coherence-vector representation. In particular, we propose and compare stabilizing time-based and state-based switching rules for entangled state preparation, showing that the latter not only ensure faster convergence with respect to non-switching methods, but can designed so that they retain robustness with respect to initialization, as long as the target is a pure state or a subspace.Comment: 15 pages, 4 figure

Robust Adaptive Control and L

This paper deals with the robust stabilizability and L2 disturbance attenuation for a class of time-delay Hamiltonian control systems with uncertainties and external disturbances. Firstly, the robust stability of the given systems is studied, and delay-dependent criteria are established based on the dissipative structural properties of the Hamiltonian systems and the Lyapunov-Krasovskii (L-K) functional approach. Secondly, the problem of L2 disturbance attenuation is considered for the Hamiltonian systems subject to external disturbances. An adaptive control law is designed corresponding to the time-varying delay pattern involved in the systems. It is shown that the closed-loop systems under the feedback control law can guarantee the γ-dissipative inequalities be satisfied. Finally, two numerical examples are provided to illustrate the theoretical developments