Constrained LQR Using Online Decomposition Techniques

This paper presents an algorithm to solve the infinite horizon constrained linear quadratic regulator (CLQR) problem using operator splitting methods. First, the CLQR problem is reformulated as a (finite-time) model predictive control (MPC) problem without terminal constraints. Second, the MPC problem is decomposed into smaller subproblems of fixed dimension independent of the horizon length. Third, using the fast alternating minimization algorithm to solve the subproblems, the horizon length is estimated online, by adding or removing subproblems based on a periodic check on the state of the last subproblem to determine whether it belongs to a given control invariant set. We show that the estimated horizon length is bounded and that the control sequence computed using the proposed algorithm is an optimal solution of the CLQR problem. Compared to state-of-the-art algorithms proposed to solve the CLQR problem, our design solves at each iteration only unconstrained least-squares problems and simple gradient calculations. Furthermore, our technique allows the horizon length to decrease online (a useful feature if the initial guess on the horizon is too conservative). Numerical results on a planar system show the potential of our algorithm.Comment: This technical report is an extended version of the paper titled "Constrained LQR Using Online Decomposition Techniques" submitted to the 2016 Conference on Decision and Contro

The NW sector of the Sicily Channel: geometry and evolution of inverted structural lineaments

The 3-D trend of anticline axial planes, fault planes and surfaces has been reconstructed in the offshore area between the Egadi Islands and the Sciacca High from the interpretation of multichannel seismic reflection profiles and well data (available from the VIDEPI project database). In particular, isopach maps generated for the five seismic units of age between Cretaceous and Quaternary allowed highlighting the space-time migration of the tectonic processes. The western portion of the studied area covers the submerged prolongation of the inner sector of the Sicilian-Maghrebian chain, limited in the NW and in the SE by two tectonic lineaments running along the western and eastern margins of the Adventure Bank: the Maghrebian Thrust Front and Adventure Thrust Front, respectively (see Argnani et al., 1986). The eastern portion is characterized by transpressive zones orientated NNE-SSW identifying the Separation Belt that partly corresponds to the foreland area which contains the Gela Nappe Thrust. Age constraints indicate that contraction related to the Sicilian-Maghrebian fold and thrust belt migrated progressively towards the southeast. The emplacement of the western front is attributable to the Middle-Upper Miocene while that of the eastern front is Plio-Pleistocene. Within this tectonic framework, two tectonic basins were identified on the basis of the different trend, age and evolution. The Adventure foredeep exhibits the maximum thickness of 500 m in correspondence of the Adventure Plateau. Here, the younger Gela foredeep displays minor depth showing a thickness increase towards the Gela Nappe and the Pantelleria graben. Positive inversion structures form by the Plio-Pleistocene compressional reactivation of preexisting structures limiting the Saccense and Trapanese domains were recognized the offshore sector between Mazara and Sciacca. Moreover, a correlation between the Campobello di Mazara-Castelvetrano alignment as proposed by Barreca et al., 2013, Ferranti et al., this meeting, and the tectonic units recognized in their offshore prolongation has been recognized. Therefore, we propose that in this area contractional tectonics is still active (see also Pepe et al., this meeting), and occurs on high-angle, NW-dipping crustal ramps (Monaco et al., 1996)

Architecture and Pliocene to Recent evolution of the offshore prolongation of the Granitola - Castelvetrano Thrust System (Sicily Channel)

High-resolution, seismic profiles were recorded in the offshore of Mazara - Punta Granitola with the purpose of reconstructing the architecture and Pliocene to Recent evolution of the south-west prolongation of the Granitola- Castelvetrano Thrust System, identified as an active structure possibly related to destructive historical earthquakes (Barreca et al., 2014; Ferranti et al., this meeting). A number of seismic units were identified. The oldest one is interpreted as representative of the Lower Pliocene pelagic deposits known in the region as Trubi. Lower-middle Pleistocene calcarenites are widespread along the continental shelf (CS) between Mazara del Vallo while their top rapidly deepens moving southeast-ward Capo Granitola. In this area, lower-middle Pleistocene calcarenites are unconformably overlain by the late Pleistocene- Holocene deposits. These latter are thin or absent NW of Punta Granitola along the CS, at water depth less than ~30 m, suggesting that this sector experienced uplift during the Quaternary. Small scale, NW- and SE-displacing reverse faults are observed along the CS where they cut the lower-middle Pleistocene calcarenites and offset the seafloor. South-eastwards, south-east-verging, reverse faults affect lower-middle Pleistocene calcarenites as well as the late Pleistocene-Holocene layers, suggesting that fault displacement acted during the post-LGM. Growth folding of Upper Pleistocene-Holocene deposits and thrust faults, predominantly dipping to the NW, affecting Pliocene rocks are observed in the immediate offshore Capo Granitola. The integration of the new data with those obtained from multi-channel profiles suggests that the active folds and thrusts are the uppermost expression of steep crustal ramps (Monaco et al., 1996; Lavecchia et al., 2007; Meccariello et al., this meeting) which upthrust the Saccense platform at depth

Plio-Quaternary tectonic evolution offshore the Capo Vaticano Promontory

We reconstruct the Plio-Quaternary tectono-stratigraphic evolution in the offshore Capo Vaticano (W Calabria, Italy) by integrating data obtained from single- and multi-channel reflection seismic profiles and a reprocessed version of the CROP M2A/III line. NW-trending, high-angle normal faults, dipping ~70° to the south-west formed along the continental slope connecting the south-west continental shelf of the Capo Vaticano Promontory to the Gioia Tauro Basin (Pepe et al., 2014). Faults generally have small displacements up to 40 m and are sealed by Pleistocene deposits. West of the Capo Vaticano promontory and in the Gioia Basin, a SE-dipping, normal fault system, more than 32 km long, is recognized. Faults affect lower (?) Pleistocene and are sealed by probably post-0.7 Ma deposits. These faults are here tentatively interpreted as the antithetic faults of major, Late Pliocene to Quaternary, NW-dipping, normal faults, which form the currently active tectonic belt along the Calabrian Arc (e.g. Monaco and Tortorici, 2000; Faccenna et al., 2011). In the Santa Eufemia Gulf, reverse faults affecting Plio-Quaternary and older sedimentary successions are observed. Faults also offset the seafloor thus indicating their recent activity. A normal fault system has been also inferred on the basis of the present day depth variations of the edges of submerged depositional terraces and associated abrasion platforms, along which a vertical displacement of ~21 m during the Late Pleistocene-Holocene has been inferred. The information derived in offshore the Capo Vaticano Promontory represents an important step towards an accurate 3-D kinematic description of the tectono-stratigraphic evolution of the western (Tyrrhenian) side of the Calabrian Arc orogenic wedge during the Plio-Quaternary

Ampiezza e tassi dei movimenti verticali a Capo Vaticano (Calabria occidentale,Italia) negli ultimi 20 mila anni determinati sulla base di cunei progradanti epiattaforme di abrasione.

Ampiezza e tassi dei movimenti tettonici verticali sono stati quantificati nel settore offshore di Capo Vaticano (Calabria occidentale), nell’intervallo Pleistocene superiore – Olocene, sulla base delle profondità del ciglio dei cunei progradanti infralitorali e delle piattaforme di abrasione formatesi durante l’ultimo massimo glaciale (LGM). I cunei progradanti sono stati riconosciuti in profili sismici a riflessione ad alta risoluzione Sparker. I dati sismici sono stati acquisiti lungo la piattaforma e la scarpata continentale superiore, durante le crociere oceanografiche Marisk 2010 e 2012 organizzate dall’IAMC del CNR di Napoli, il DISTEM dell’Università di Palermo e il Dip. di Scienze della Terra dell’Università di Napoli. La deformazione tettonica verticale del promontorio di Capo Vaticano e del suo prolungamento offshore è caratterizzata da una marcata asimmetria, con profondità dei cigli dei cunei infralitorali che si approfondisce progressivamente procedendo verso NE. La rimozione della componente non tettonica dei movimenti verticali, ottenuta utilizzando dati sulle variazioni glacio-eustatiche del tardo Quaternario [Lambeck et al., 2011], indica nell’area in esame ~11 (± 5) m di sollevamento e di ~25 (± 5) m di subsidenza, nell’intervallo post-LGM, muovendoci da sud-ovest verso nord-est, su una distanza di ~22 km. Il valore medio del tasso di sollevamento e di subsidenza (considerando la componente sia regionale sia locale) per gli ultimi 20.350 (± 1,35) anni sono pari a 0,52 (± 0,28) mm/anno e di 1,23 (± 0,32) mm/anno, rispettivamente. I valori dell’ampiezza e il pattern dei movimenti verticali ottenuti attraverso l’analisi dei cunei progradanti infralitorali sono comparabili, sebbene a tassi parzialmente differenti, sia con quelli determinati attraverso marker geomorfologici tardo Olocenici [Spampinato et al., 2012] che con i tassi di sollevamento a lungo termine calcolati sulla base delle posizioni dei terrazzi marini formatisi a 80 a 215 mila anni [Cucci & Tertulliani, 2010]. L’integrazione dei nuovi dati con quelli disponibili in letteratura indica che il basculamento del promontorio di Capo Vaticano è episodico ed è avvenuto principalmente tra 215 e 125 mila anni e nel post-LGM

Seismotectonics of the active thrust front in southwestern Sicily: hints on the Belice and Selinunte seismogenic sources

We present a seismotectonic model of the active thrust front in western Sicily, which includes the area hit by the 1968 Belice earthquake sequence. The ~40 km long South-WEstern Sicilian Thrust (SWEST) is formed by two aligned albeit non-parallel fault arrays, the Granitola-Castelevetrano Thrust System (GCTS) in the west and the Partanna- Poggioreale Thrust System (PPTS) in the east. The ~NE-SW trending, NW-dipping GCTS straddles from the Pelagian coastline to Castelvetrano, is ~18 km long and composed of two segments, with the northern, ~12 km long one showing geodetic and geologic evidence of active deformation (Barreca et al., 2014). The segment is marked by a sharp gradient in Differential SAR interferometry (DinSAR and STAMPs) and GPS velocity fields. Geologic evidence include an up to 60 m high, and up to 15° steep scarp, which is the fore-limb of a broad fold involving Lower Pleistocene shore calcarenites, and cm-scale reverse displacement of an ancient road dated as early Bronze-Hellenistic age. Inversion of fault slip-lineation data from structures displacing the archaeological remains yields a ~N110°E shortening axis, consistent with the geodetic shortening direction estimated from GPS differential velocities. The ~ENE-WSW trending PPTS stretches from Partanna to the macro-seismic area of the 1968 earthquake sequence and is composed of two ~10 km long segments limited by relay ramps. Although geologic and geodetic evidence of deformation are less clear than for the GCTS, we nonetheless observe a gradient in interferometry data for the western segment, and evidence of slow deformation (creep?) in historical to recent (last ~400 yr?) man-made structures. Integration of geologic, geodetic and seismology data suggests the active folds and thrusts are the uppermost expression of steep (45°) crustal ramps (Monaco et al., 1996) which upthrust the Saccense platform at depth. Based on macroseismic and seismological evidence (Monaco et al., 1996), we contend that the PPTS was partly activated during the 1968 sequence, and that rupture stopped at the junction with the GCTS. The current geodetic strain accumulation on the GCTS, on the other hand, suggests that the fault array has been significantly loaded, and that its last important co-seismic event could have been caused the 4th–5th century A.D. destruction of Selinunte (Bottari et al., 2009)

Risk Model Development and Validation for Prediction of Coronary Artery Aneurysms in Kawasaki Disease in a North American Population.

Background Accurate prediction of coronary artery aneurysms ( CAAs ) in patients with Kawasaki disease remains challenging in North American cohorts. We sought to develop and validate a risk model for CAA prediction. Methods and Results A binary outcome of CAA was defined as left anterior descending or right coronary artery Z score ≥2.5 at 2 to 8 weeks after fever onset in a development cohort (n=903) and a validation cohort (n=185) of patients with Kawasaki disease. Associations of baseline clinical, laboratory, and echocardiographic variables with later CAA were assessed in the development cohort using logistic regression. Discrimination (c statistic) and calibration (Hosmer-Lemeshow) of the final model were evaluated. A practical risk score assigning points to each variable in the final model was created based on model coefficients from the development cohort. Predictors of CAAs at 2 to 8 weeks were baseline Z score of left anterior descending or right coronary artery ≥2.0, age <6 months, Asian race, and C-reactive protein ≥13 mg/ dL (c=0.82 in the development cohort, c=0.93 in the validation cohort). The CAA risk score assigned 2 points for baseline Z score of left anterior descending or right coronary artery ≥2.0 and 1 point for each of the other variables, with creation of low- (0-1), moderate- (2), and high- (3-5) risk groups. The odds of CAA s were 16-fold greater in the high- versus the low-risk groups in the development cohort (odds ratio, 16.4; 95% CI , 9.71-27.7 [ P<0.001]), and >40-fold greater in the validation cohort (odds ratio, 44.0; 95% CI, 10.8-180 [ P<0.001]). Conclusions Our risk model for CAA in Kawasaki disease consisting of baseline demographic, laboratory, and echocardiographic variables had excellent predictive utility and should undergo prospective testing

PRIN Project 2010-11 “Active and recent geodynamics of Calabrian Arc and accretionary complex in the Ionian Sea”: new constraints from geological, geodetic and seismological data

This contribution illustrates the preliminary results of our Research Unit in the PRIN Project 2010-11, which focuses on active and recent geodynamics of Calabrian Arc. The integration of the new geological, geodetic and seismological data supports the inferred recent plate boundary reorganization in the central-southern Mediterranean, where the regional GNNS velocity fields point to a deceleration or cessation of Calabrian Arc migration, and to extension along the axis of the Calabrian Arc, accommodated by normal faulting (e.g. Capo Vaticano and Messina Straits (Aloisi et al., 2012; Pepe et al., 2014; Spampinato et al., 2014). The study of the lateral borders of the Arc revealed that oblique strike-slip displacement has occurred during its southeastwards migration. Active dextral transtension is occurring along the NNW-striking Aeolian-Tindari Letojanni fault system, forming the southern boundary of the Arc. It joins to the north other two boundaries characterized by different tectonic regimes, a contractional belt in the southern Tyrrhenian sea, where a tectonic inversion has occurred since the middle Pleistocene, and the extensional one in northeastern Sicily and western Calabria (Palano et al., 2012; Barreca et al., 2014a). Along the northern boundary of the Arc, the so-called Pollino line (onshore) and Sibari Line (offshore), active deformation has been documented on folds growing above blind oblique thrust ramps extending offshore, controlling the present morphobathymetric pattern (Santoro et al., 2013). Although external to the Calabrian Arc, we also devoted attention to the front of the Maghrebian thrust belt in western Sicily where we presented the first evidence of historical co-seismic deformation on a thrust array running from the Belice area to the Sicily Channel (Barreca et al., 2014b). Morphotectonic analysis and fault numeric modeling of uplifted Pleistocene marine terraces and Holocene paleo-shorelines has documented that most of the uplift along the Calabrian Arc is related to regional processes and the residual to coseismic displacement on major faults, both transpressional and transtensional, at the borders, and extensional along the chain axis