@article{51208,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>Approximation of subdifferentials is one of the main tasks when computing descent directions for nonsmooth optimization problems. In this article, we propose a bisection method for weakly lower semismooth functions which is able to compute new subgradients that improve a given approximation in case a direction with insufficient descent was computed. Combined with a recently proposed deterministic gradient sampling approach, this yields a deterministic and provably convergent way to approximate subdifferentials for computing descent directions.</jats:p>}},
  author       = {{Gebken, Bennet}},
  issn         = {{0926-6003}},
  journal      = {{Computational Optimization and Applications}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Control and Optimization}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{A note on the convergence of deterministic gradient sampling in nonsmooth optimization}}},
  doi          = {{10.1007/s10589-024-00552-0}},
  year         = {{2024}},
}

@article{52726,
  abstract     = {{Heteroclinic structures organize global features of dynamical systems. We analyse whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more units. We find that while commonly analysed model equations such as network dynamics on undirected hypergraphs may be useful to describe local dynamics such as cluster synchronization, they give rise to obstructions that allow to design of heteroclinic structures in phase space. By contrast, directed hypergraphs break the homogeneity and lead to vector fields that support heteroclinic structures.}},
  author       = {{Bick, Christian and von der Gracht, Sören}},
  issn         = {{2051-1329}},
  journal      = {{Journal of Complex Networks}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Control and Optimization, Management Science and Operations Research, Computer Networks and Communications}},
  number       = {{2}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Heteroclinic dynamics in network dynamical systems with higher-order interactions}}},
  doi          = {{10.1093/comnet/cnae009}},
  volume       = {{12}},
  year         = {{2024}},
}

@article{53317,
  author       = {{Tao, Youshan and Winkler, Michael}},
  issn         = {{2163-2480}},
  journal      = {{Evolution Equations and Control Theory}},
  keywords     = {{Applied Mathematics, Control and Optimization, Modeling and Simulation}},
  number       = {{6}},
  pages        = {{1676--1687}},
  publisher    = {{American Institute of Mathematical Sciences (AIMS)}},
  title        = {{{Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities}}},
  doi          = {{10.3934/eect.2023031}},
  volume       = {{12}},
  year         = {{2023}},
}

@article{30861,
  abstract     = {{<jats:title>Abstract</jats:title><jats:p>We consider the problem of maximization of metabolite production in bacterial cells formulated as a dynamical optimal control problem (DOCP). According to Pontryagin’s maximum principle, optimal solutions are concatenations of singular and bang arcs and exhibit the chattering or <jats:italic>Fuller</jats:italic> phenomenon, which is problematic for applications. To avoid chattering, we introduce a reduced model which is still biologically relevant and retains the important structural features of the original problem. Using a combination of analytical and numerical methods, we show that the singular arc is dominant in the studied DOCPs and exhibits the <jats:italic>turnpike</jats:italic> property. This property is further used in order to design simple and realistic suboptimal control strategies.</jats:p>}},
  author       = {{Caillau, Jean-Baptiste and Djema, Walid and Gouzé, Jean-Luc and Maslovskaya, Sofya and Pomet, Jean-Baptiste}},
  issn         = {{0022-3239}},
  journal      = {{Journal of Optimization Theory and Applications}},
  keywords     = {{Applied Mathematics, Management Science and Operations Research, Control and Optimization}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Turnpike Property in Optimal Microbial Metabolite Production}}},
  doi          = {{10.1007/s10957-022-02023-0}},
  year         = {{2022}},
}

@article{35206,
  author       = {{Bonnard, Bernard and Rouot, Jérémy and Wembe Moafo, Boris Edgar}},
  issn         = {{2156-8472}},
  journal      = {{Mathematical Control and Related Fields}},
  keywords     = {{Applied Mathematics, Control and Optimization, General Medicine}},
  pages        = {{0--0}},
  publisher    = {{American Institute of Mathematical Sciences (AIMS)}},
  title        = {{{Accessibility properties of abnormal geodesics in optimal control illustrated by two case studies}}},
  doi          = {{10.3934/mcrf.2022052}},
  year         = {{2022}},
}

@article{47961,
  abstract     = {{<jats:p>Due to failures or even the absence of an electricity grid, microgrid systems are becoming popular solutions for electrifying African rural communities. However, they are heavily stressed and complex to control due to their intermittency and demand growth. Demand side management (DSM) serves as an option to increase the level of flexibility on the demand side by scheduling users’ consumption patterns profiles in response to supply. This paper proposes a demand-side management strategy based on load shifting and peak clipping. The proposed approach was modelled in a MATLAB/Simulink R2021a environment and was optimized using the artificial neural network (ANN) algorithm. Simulations were carried out to test the model’s efficacy in a stand-alone PV-battery microgrid in East Africa. The proposed algorithm reduces the peak demand, smoothing the load profile to the desired level, and improves the system’s peak to average ratio (PAR). The presence of deferrable loads has been considered to bring more flexible demand-side management. Results promise decreases in peak demand and peak to average ratio of about 31.2% and 7.5% through peak clipping. In addition, load shifting promises more flexibility to customers.</jats:p>}},
  author       = {{Philipo, Godiana Hagile and Kakande, Josephine Nakato and Krauter, Stefan}},
  issn         = {{1996-1073}},
  journal      = {{Energies}},
  keywords     = {{Energy (miscellaneous), Energy Engineering and Power Technology, Renewable Energy, Sustainability and the Environment, Electrical and Electronic Engineering, Control and Optimization, Engineering (miscellaneous), Building and Construction}},
  number       = {{14}},
  publisher    = {{MDPI AG}},
  title        = {{{Neural Network-Based Demand-Side Management in a Stand-Alone Solar PV-Battery Microgrid Using Load-Shifting and Peak-Clipping}}},
  doi          = {{10.3390/en15145215}},
  volume       = {{15}},
  year         = {{2022}},
}

@article{33866,
  abstract     = {{<jats:p>Helhmoltz–Kirchhoff equations of motions of vortices of an incompressible fluid in the plane define a dynamics with singularities and this leads to a Zermelo navigation problem describing the ship travel in such a field where the control is the heading angle. Considering one vortex, we define a time minimization problem which can be analyzed with the technics of geometric optimal control combined with numerical simulations, the geometric frame being the extension of Randers metrics in the punctured plane, with rotational symmetry. Candidates as minimizers are parameterized thanks to the Pontryagin Maximum Principle as extremal solutions of a Hamiltonian vector field. We analyze the time minimal solution to transfer the ship between two points where during the transfer the ship can be either in a strong current region in the vicinity of the vortex or in a weak current region. The analysis is based on a micro-local classification of the extremals using mainly the integrability properties of the dynamics due to the rotational symmetry. The discussion is complex and related to the existence of an isolated extremal (Reeb) circle due to the vortex singularity. The explicit computation of cut points where the extremal curves cease to be optimal is given and the spheres are described in the case where at the initial point the current is weak.</jats:p>}},
  author       = {{Bonnard, Bernard and Cots, Olivier and Wembe Moafo, Boris Edgar}},
  issn         = {{1292-8119}},
  journal      = {{ESAIM: Control, Optimisation and Calculus of Variations}},
  keywords     = {{Computational Mathematics, Control and Optimization, Control and Systems Engineering}},
  publisher    = {{EDP Sciences}},
  title        = {{{A Zermelo navigation problem with a vortex singularity}}},
  doi          = {{10.1051/cocv/2020058}},
  volume       = {{27}},
  year         = {{2020}},
}