20 research outputs found
Consensus-based control for a network of diffusion PDEs with boundary local interaction
In this paper the problem of driving the state of a network of identical
agents, modeled by boundary-controlled heat equations, towards a common
steady-state profile is addressed. Decentralized consensus protocols are
proposed to address two distinct problems. The first problem is that of
steering the states of all agents towards the same constant steady-state
profile which corresponds to the spatial average of the agents initial
condition. A linear local interaction rule addressing this requirement is
given. The second problem deals with the case where the controlled boundaries
of the agents dynamics are corrupted by additive persistent disturbances. To
achieve synchronization between agents, while completely rejecting the effect
of the boundary disturbances, a nonlinear sliding-mode based consensus protocol
is proposed. Performance of the proposed local interaction rules are analyzed
by applying a Lyapunov-based approach. Simulation results are presented to
support the effectiveness of the proposed algorithms
A network dynamics approach to chemical reaction networks
A crisp survey is given of chemical reaction networks from the perspective of
general nonlinear network dynamics, in particular of consensus dynamics. It is
shown how by starting from the complex-balanced assumption the reaction
dynamics governed by mass action kinetics can be rewritten into a form which
allows for a very simple derivation of a number of key results in chemical
reaction network theory, and which directly relates to the thermodynamics of
the system. Central in this formulation is the definition of a balanced
Laplacian matrix on the graph of chemical complexes together with a resulting
fundamental inequality. This directly leads to the characterization of the set
of equilibria and their stability. Both the form of the dynamics and the
deduced dynamical behavior are very similar to consensus dynamics. The
assumption of complex-balancedness is revisited from the point of view of
Kirchhoff's Matrix Tree theorem, providing a new perspective. Finally, using
the classical idea of extending the graph of chemical complexes by an extra
'zero' complex, a complete steady-state stability analysis of mass action
kinetics reaction networks with constant inflows and mass action outflows is
given.Comment: 18 page
Modeling of physical network systems
Conservation laws and balance equations for physical network systems typically can be described with the aid of the incidence matrix of a directed graph, and an associated symmetric Laplacian matrix. Some basic examples are discussed, and the extension to k-complexes is indicated. Physical distribution networks often involve a non-symmetric Laplacian matrix. It is shown how, in case the connected components of the graph are strongly connected, such systems can be converted into a form with balanced Laplacian matrix by constructive use of Kirchhoffs Matrix Tree theorem, giving rise to a port-Hamiltonian description. Application to the dual case of asymmetric consensus algorithms is given. Finally it is shown how the minimal storage function for physical network systems with controlled flows can be explicitly computed. (C) 2015 Elsevier B.V. All rights reserved
AirPhyNet: Harnessing Physics-Guided Neural Networks for Air Quality Prediction
Air quality prediction and modelling plays a pivotal role in public health
and environment management, for individuals and authorities to make informed
decisions. Although traditional data-driven models have shown promise in this
domain, their long-term prediction accuracy can be limited, especially in
scenarios with sparse or incomplete data and they often rely on black-box deep
learning structures that lack solid physical foundation leading to reduced
transparency and interpretability in predictions. To address these limitations,
this paper presents a novel approach named Physics guided Neural Network for
Air Quality Prediction (AirPhyNet). Specifically, we leverage two
well-established physics principles of air particle movement (diffusion and
advection) by representing them as differential equation networks. Then, we
utilize a graph structure to integrate physics knowledge into a neural network
architecture and exploit latent representations to capture spatio-temporal
relationships within the air quality data. Experiments on two real-world
benchmark datasets demonstrate that AirPhyNet outperforms state-of-the-art
models for different testing scenarios including different lead time (24h, 48h,
72h), sparse data and sudden change prediction, achieving reduction in
prediction errors up to 10%. Moreover, a case study further validates that our
model captures underlying physical processes of particle movement and generates
accurate predictions with real physical meaning.Comment: Accepted by the 12th International Conference on Learning
Representations (ICLR 2024