Learning-based Nonlinear Model Predictive Control

© 2017 This paper presents stabilizing Model Predictive Controllers (MPC) in which prediction models are inferred from experimental data of the inputs and outputs of the plant. Using a nonparametric machine learning technique called LACKI, the estimated (possibly nonlinear) model function together with an estimation of Holder constant is provided. Based on these, a number of predictive controllers with stability guaranteed by design are proposed. Firstly, the case when the prediction model is estimated offline is considered and robust stability and recursive feasibility is ensured by using tightened constraints in the optimisation problem. This controller has been extended to the more interesting and complex case: the online learning of the model, where the new data collected from feedback is added to enhance the prediction model. An on-line learning MPC based on a double sequence of predictions is proposed.Spanish MINECO Grant PRX15-00300 and projects DPI2013-48243-C2-2-R and DPI2016-76493-C3-1-R. UK Engineering and Physical Research Council, grant no.EP/J012300/1

Recent Advances in Transition-Metal-Catalyzed/Mediated Transformations of Vinylidenecyclopropanes

ConspectusVinylidenecyclopropanes (VDCPs), having an allene moiety connected to a highly strained cyclopropyl group, have attracted a substantial amount of attention since they are fascinating building blocks for organic synthesis. During recent years, the reactions of VDCPs in the presence of a Lewis acid or a Brønsted acid and those induced by heat or light have experienced significant advancements due to the unique structural and electronic properties of VDCPs. Transition-metal-catalyzed reactions of VDCPs were not intensely investigated until the last 5 years. Recently, significant progress has been made in transition-metal-catalyzed transformations of VDCPs, and they have emerged as a new direction for the chemistry of strained small rings, especially when new types of functionalized vinylidenecyclopropanes (FVDCPs) are used as substrates. To date, many interesting transformations have been explored using these novel VDCPs under the catalysis of transition metals, such as gold, palladium, or rhodium, and various novel and useful heterocyclic or polycyclic compounds have been generated. These new findings have enriched the chemistry of strained small carbocycles.This Account will describe the transition-metal-catalyzed transformations of VDCPs recently developed in our laboratory and by other groups. The chemistry of Au-catalyzed VDCPs has been enriched and extensively developed by our group. In this respect, a new process for generating gold carbenes from VDCPs has been disclosed. The reactivity of these new gold carbenoid species was fully investigated, and many novel reaction modes based on these new gold carbenoid species were explored, including oxidation reactions, intramolecular cyclopropanations, C­(sp³)–H bond functionalizations, and C–O bond cleavage reactions. Rh-catalyzed reactions of VDCPs are another key field of transition-metal-catalyzed reactions of VDCPs. In particular, rhodium-catalyzed cycloadditions, Pauson–Khand reactions, and C–H bond activations of FVDCPs have been explored in detail by our group. A new trimethylenemethane rhodium (TMM–Rh) complex generated from VDCPs was discovered and utilized as an electrophilic Rh−π-allyl precursor. Moreover, some unprecedented highly regio- and enantioselective asymmetric allylic substitutions via this novel TMM–Rh complex were developed with different kinds of nucleophiles. This Account will also summarize the recent advances in palladium-, copper-, and iron-catalyzed cycloisomerization reactions of VDCPs reported by our group and others. These reactions always afford the desired products with excellent chemo-, regio-, diastereo-, and enantioselectivities, which will make them highly valuable for the synthesis of key scaffolds in natural products and pharmaceutical molecules in the future

Direct Conversion of Sugars and Ethyl Levulinate into γ‑Valerolactone with Superparamagnetic Acid–Base Bifunctional ZrFeO_<i>x</i> Nanocatalysts

Acid–base bifunctional superparamagnetic FeZrO_<i>x</i> nanoparticles were synthesized via a two-step process of solvothermal treatment and hydrolysis–condensation, and were further employed to catalyze the conversion of ethyl levulinate (EL) to γ-valerolactone (GVL) using ethanol as both H-donor and solvent. ZrFeO(1:3)-300 nanoparticles (12.7 nm) with Fe₃O₄ core covered by ZrO₂ layer (0.65 nm thickness) having well-distributed acid–base sites (0.39 vs 0.28 mmol/g), moderate surface area (181 m²/g), pore size (9.8 nm), and strong magnetism (35.4 Am² kg^–1) exhibited superior catalytic performance, giving a high GVL yield of 87.2% at 230 °C in 3 h. The combination of the nanoparticles with solid acid HY2.6 promoted the direct transformation of sugars to produce GVL in moderate yield (around 45%). Moreover, the nanocatalyst was easily recovered by a magnet for six cycles with an average GVL yield of 83.9% from EL

Fitted creep curves of backfill materials with different moisture contents [33].

Fitted creep curves of backfill materials with different moisture contents [33].</p

Creep curves of fractional element with different <i>α</i> values.

Creep curves of fractional element with different α values.</p

Main elements of cemented fillers [33].

Filling mining technology is an important representative technology to realize green and low-carbon mining. The backfill materials have distinct rheological characteristics under the long-term action of formation loads and groundwater seepage. In order to study the creep characteristics of backfill materials under different moisture contents and reveal their aging-mechanical properties, based on the Riemann-Liouville fractional calculus and damage mechanics theory, the fractional element and damage variables are introduced to improve the traditional Bingham model, and the fractional Bingham creep damage model is proposed. Based on the experimental data of gangue cemented backfill under different moisture content, the parameters of the creep model are obtained by using user-defined function fitting and the least square method. The results show that the improved Bingham fractional creep damage model can describe the whole creep process of backfill materials under different moisture contents, and the rationality of the model is verified. Compared with the traditional Bingham model, the fitting degree of the Bingham fractional creep damage model is higher, which solves the problem that the traditional Bingham model cannot describe the nonlinear creep stage. Model parameter α and ξ increase with the increase of axial stress and moisture content. Under the same moisture content, η gradually increases with the increase of axial stress. This work has a certain reference significance for studying the mechanical properties and creep constitutive model of backfill materials containing water.</div

Classical creep curve.

Filling mining technology is an important representative technology to realize green and low-carbon mining. The backfill materials have distinct rheological characteristics under the long-term action of formation loads and groundwater seepage. In order to study the creep characteristics of backfill materials under different moisture contents and reveal their aging-mechanical properties, based on the Riemann-Liouville fractional calculus and damage mechanics theory, the fractional element and damage variables are introduced to improve the traditional Bingham model, and the fractional Bingham creep damage model is proposed. Based on the experimental data of gangue cemented backfill under different moisture content, the parameters of the creep model are obtained by using user-defined function fitting and the least square method. The results show that the improved Bingham fractional creep damage model can describe the whole creep process of backfill materials under different moisture contents, and the rationality of the model is verified. Compared with the traditional Bingham model, the fitting degree of the Bingham fractional creep damage model is higher, which solves the problem that the traditional Bingham model cannot describe the nonlinear creep stage. Model parameter α and ξ increase with the increase of axial stress and moisture content. Under the same moisture content, η gradually increases with the increase of axial stress. This work has a certain reference significance for studying the mechanical properties and creep constitutive model of backfill materials containing water.</div

Creep curves of backfill materials with different moisture contents [33].

Creep curves of backfill materials with different moisture contents [33].</p

Inversion results of creep parameters.

Filling mining technology is an important representative technology to realize green and low-carbon mining. The backfill materials have distinct rheological characteristics under the long-term action of formation loads and groundwater seepage. In order to study the creep characteristics of backfill materials under different moisture contents and reveal their aging-mechanical properties, based on the Riemann-Liouville fractional calculus and damage mechanics theory, the fractional element and damage variables are introduced to improve the traditional Bingham model, and the fractional Bingham creep damage model is proposed. Based on the experimental data of gangue cemented backfill under different moisture content, the parameters of the creep model are obtained by using user-defined function fitting and the least square method. The results show that the improved Bingham fractional creep damage model can describe the whole creep process of backfill materials under different moisture contents, and the rationality of the model is verified. Compared with the traditional Bingham model, the fitting degree of the Bingham fractional creep damage model is higher, which solves the problem that the traditional Bingham model cannot describe the nonlinear creep stage. Model parameter α and ξ increase with the increase of axial stress and moisture content. Under the same moisture content, η gradually increases with the increase of axial stress. This work has a certain reference significance for studying the mechanical properties and creep constitutive model of backfill materials containing water.</div

Fitted curves of parameters <i>ξ</i>, <i>α</i>, <i>η</i> and moisture content.

Fitted curves of parameters ξ, α, η and moisture content.</p