Infinite horizon sparse optimal control

A class of infinite horizon optimal control problems involving $L^p$-type cost functionals with $0<p\leq 1$ is discussed. The existence of optimal controls is studied for both the convex case with $p=1$ and the nonconvex case with $0<p<1$, and the sparsity structure of the optimal controls promoted by the $L^p$-type penalties is analyzed. A dynamic programming approach is proposed to numerically approximate the corresponding sparse optimal controllers

Junction conditions for finite horizon optimal control problems on multi-domains with continuous and discontinuous solutions

This paper deals with junction conditions for Hamilton-Jacobi-Bellman (HJB) equations for finite horizon control problems on multi-domains. We consider two different cases where the final cost is continuous or lower semi-continuous. In the continuous case we extend the results of "Hamilton-Jacobi-Bellman equations on multi-domains" by the second and third authors in a more general framework with switching running costs and weaker controllability assumptions. The comparison principle has been established to guarantee the uniqueness and the stability results for the HJB system on such multi-domains. In the lower semi-continuous case, we characterize the value function as the unique lower semi-continuous viscosity solution of the HJB system, under a local controllability assumption

Singular perturbation of optimal control problems on multi-domains

International audienceThe goal of this paper is to study a singular perturbation problem in the framework of optimal control on multi-domains. We consider an optimal control problem in which the controlled system contains a fast and a slow variables. This problem is reformulated as an Hamilton-Jacobi-Bellman (HJB) equation. The main difficulty comes from the fact that the fast variable lives in a multi-domain. The geometric singularity of the multi-domains leads to the discontinuity of the Hamiltonian. Under a controllability assumption on the fast variables, the limit equation (as the velocity of the fast variable goes to infinity) is obtained via a PDE approache and by means of the tools of the control theory

Hamilton-Jacobi-Bellman Equations on Multi-Domains

International audienceA system of Hamilton Jacobi (HJ) equations on a partition of $\R^d$ is considered, and a uniqueness and existence result of viscosity solution is analyzed. While the notion of viscosity notion is by now well known, the question of uniqueness of solution, when the Hamiltonian is discontinuous, remains an important issue. A uniqueness result has been derived for a class of problems, where the behavior of the solution, in the region of discontinuity of the Hamiltonian, is assumed to be irrelevant and can be ignored (see reference [10]) . Here, we provide a new uniqueness result for a more general class of Hamilton-Jacobi equations

Sparse and switching infinite horizon optimal controls with mixed-norm penalizations

© 2020 EDP Sciences, SMAI. A class of infinite horizon optimal control problems involving mixed quasi-norms of Lp-type cost functionals for the controls is discussed. These functionals enhance sparsity and switching properties of the optimal controls. The existence of optimal controls and their structural properties are analyzed on the basis of first order optimality conditions. A dynamic programming approach is used for numerical realization

STATCOM Control for Power System Voltage Control Applications

A static compensator (STATCOM) is a device that can provide reactive support to a bus. It consists of voltage sourced converters connected to an energy storage device on one side and to the power system on the other. In this paper the conventional method of PI control is compared and contrasted with various feedback control strategies. A linear optimal control based on LQR control is shown to be superior in terms of response profile and control effort required. These methodologies are applied to an example power syste

Transmission conditions on interfaces for Hamilton-Jacobi-Bellman equations

International audienceWe establish a comparison principle for a Hamilton-Jacobi-Bellman equation, more appropriately a system, related to an infinite horizon problem in presence of an interface. Namely a low dimensional subset of the state variable space where discontinuities in controlled dynamics and costs take place. Since corresponding Hamiltonians, at least for the subsolution part, do not enjoy any semicontinuity property, the comparison argument is rather based on a separation principle of the controlled dynamics across the interface. For this, we essentially use the notion of "-partition and minimal "-partition for intervals of definition of an integral trajectory

State-constrained Optimal Control Problems of Impulsive Differential Equations

International audienceThe present paper studies an optimal control problem governed by measure driven differential systems and in presence of state constraints. The first result shows that using the graph completion of the measure, the optimal solutions can be obtained by solving a reparametrized control problem of absolutely continuous trajectories but with time-dependent state-constraints. The second result shows that it is possible to characterize the epigraph of the reparametrized value function by a Hamilton-Jacobi equation without assuming any controllability assumption

Metal-organic-framework derived Co-Pd bond is preferred over Fe-Pd for reductive upgrading of furfural to tetrahydrofurfuryl alcohol

Combined noble-transition metal catalysts have been used to produce a wide range of important non-petroleum-based chemicals from biomass-derived furfural (as a platform molecule) and have garnered colossal research interest due to the urgent demand for sustainable and clean fuels. Herein, we report the palladium-modified metal–organic-framework (MOF) assisted preparation of PdCo3O4 and PdFe3O4 nanoparticles encapsulated in a graphitic N-doped carbon (NC) matrix via facile in situ thermolysis. This provides a change in selectivity with superior catalytic activity for the reductive upgrading of biomass-derived furfural (FA). Under the optimized reaction conditions, the newly designed PdCo3O4@NC catalyst exhibited highly efficient catalytic performance in the hydrogenation of furfural, providing 100% furfural conversion with 95% yield of tetrahydrofurfuryl alcohol (THFAL). In contrast, the as-synthesized Pd–Fe3O4@NC afforded a THFAL yield of 70% after an 8 h reaction with four consecutive recycling tests. Based on different characterization data (XPS, H2-TPR) for nanohybrids, we can conclude that the presence of PdCo-Nx active sites, and the multiple synergistic effects between Co3O4 and Pd(II), Co3O4 and Pd0, as well as the presence of N in the carbonaceous matrix, are responsible for the superior catalytic activity and improved catalyst stability. Our strategy provides a facile design and synthesis process for a noble-transition metal alloy as a superior biomass refining, robust catalyst via noble metal modified MOFs as precursors

Targeting Platelet–Leukocyte Interactions: Identification of the Integrin Mac-1 Binding Site for the Platelet Counter Receptor Glycoprotein Ibα

The firm adhesion and transplatelet migration of leukocytes on vascular thrombus are dependent on the interaction of the leukocyte integrin Mac-1 (αMβ2, CD11b/CD18) and the platelet counter receptor glycoprotein (GP) Ibα. Previous studies have established a central role for the I domain, a stretch of ∼200 amino acids within the αM subunit, in the binding of GP Ibα. This study was undertaken to establish the molecular basis of GP Ibα recognition by αMβ2. The P201–K217 sequence, which spans an exposed loop and amphipathic α4 helix in the three-dimensional structure of the αMI domain, was identified as the binding site for GP Ibα. Mutant cell lines in which the αMI domain segments P201–G207 and R208–K217 were switched to the homologous, but non-GP Ibα binding, αL domain segments failed to support adhesion to GP Ibα. Mutation of amino acid residues within P201–K217, H210–A212, T213–I215, and R216–K217 resulted in the loss of the binding function of the recombinant αMI domains to GP Ibα. Synthetic peptides duplicating the P201–K217, but not scrambled versions, directly bound GP Ibα and inhibited αMβ2-dependent adhesion to GP Ibα and adherent platelets. Finally, grafting critical amino acids within the P201–K217 sequence onto αL, converted αLβ2 into a GP Ibα binding integrin. Thus, the P201–K217 sequence within the αMI domain is necessary and sufficient for GP Ibα binding. These observations provide a molecular target for disrupting leukocyte–platelet complexes that promote vascular inflammation in thrombosis, atherosclerosis, and angioplasty-related restenosis