Robust model predictive control: robust control invariant sets and efficient implementation

Robust model predictive control (RMPC) is widely used in industry. However, the online computational burden of this algorithm restricts its development and application to systems with relatively slow dynamics. We investigate this problem in this thesis with the overall aim of reducing the online computational burden and improving the online efficiency. In RMPC schemes, robust control invariant (RCI) sets are vitally important in dealing with constraints and providing stability. They can be used as terminal (invariant) sets in RMPC schemes to reduce the online computational burden and ensure stability simultaneously. To this end, we present a novel algorithm for the computation of full-complexity polytopic RCI sets, and the corresponding feedback control law, for linear discrete-time systems subject to output and initial state constraints, performance bounds, and bounded additive disturbances. Two types of uncertainty, structured norm-bounded and polytopic uncertainty, are considered. These algorithms are then extended to deal with systems subject to asymmetric initial state and output constraints. Furthermore, the concept of RCI sets can be extended to invariant tubes, which are fundamental elements in tube based RMPC scheme. The online computational burden of tube based RMPC schemes is largely reduced to the same level as model predictive control for nominal systems. However, it is important that the constraint tightening that is needed is not excessive, otherwise the performance of the MPC design may deteriorate, and there may even not exist a feasible control law. Here, the algorithms we proposed for RCI set approximations are extended and applied to the problem of reducing the constraint tightening in tube based RMPC schemes. In order to ameliorate the computational complexity of the online RMPC algorithms, we propose an online-offline RMPC method, where a causal state feedback structure on the controller is considered. In order to improve the efficiency of the online computation, we calculate the state feedback gain offline using a semi-definite program (SDP). Then we propose a novel method to compute the control perturbation component online. The online optimization problem is derived using Farkas' Theorem, and then approximated by a quadratic program (QP) to reduce the online computational burden. A further approximation is made to derive a simplified online optimization problem, which results in a large reduction in the number of variables. Numerical examples are provided that demonstrate the advantages of all our proposed algorithms over current schemes.Open Acces

Merging of a CO WD and a He-rich white dwarf to produce a type Ia supernovae

Context: Although type Ia supernovae (SNe Ia) play a key role in astrophysics, the companions of the exploding carbon-oxygen white dwarfs (CO WDs) are still not completely identified. It has been suggested recently that a He-rich WD (a He WD or a hybrid HeCO WD) merges with a CO WD may produce an SN Ia. This theory was based on the double-detonation model, in which the shock compression in the CO core caused by the surface explosion of the He-rich shell might lead to the explosion of the whole CO WD. However, so far, very few binary population synthesis (BPS) studies have been made on the merger scenario of a CO WD and a He-rich WD in the context of SNe Ia. Aims: We aim to systematically study the Galactic birthrates and delay-time distributions of SNe Ia based on the merger scenario of a CO WD and a He-rich WD. Methods: We performed a series of Monte Carlo BPS simulations to investigate the properties of SNe Ia from the merging of a CO WD and a He-rich WD based on the Hurley rapid binary evolution code. We also considered the influence of different metallicities on the final results. Results: From our simulations, we found that no more than 15% of all SNe Ia stem from the merger scenario of a CO WD and a He-rich WD, and their delay times range from ~110 Myr to the Hubble time. This scenario mainly contributes to SN Ia explosions with intermediate and long delay times. The present work indicates that the merger scenario of a CO WD and a He-rich WD can roughly reproduce the birthrates of SN 1991bg-like events, and cover the range of their delay times. We also found that SN Ia birthrates from this scenario would be higher for the cases with low metallicities.Comment: 8 pages, 8 figures, accepted for publication in A&

A super-Eddington wind scenario for the progenitors of type Ia supernovae: binary population synthesis calculations

The super-Eddington wind scenario has been proposed as an alternative way for producing type Ia supernovae (SNe Ia). The super-Eddington wind can naturally prevent the carbon--oxygen white dwarfs (CO WDs) with high mass-accretion rates from becoming red-giant-like stars. Furthermore, it works in low-metallicity environments, which may explain SNe Ia observed at high redshifts. In this article, we systematically investigated the most prominent single-degenerate WD+MS channel based on the super-Eddington wind scenario. We combined the Eggleton stellar evolution code with a rapid binary population synthesis (BPS) approach to predict SN Ia birthrates for the WD+MS channel by adopting the super-Eddington wind scenario and detailed mass-accumulation efficiencies of H-shell flashes on the WDs. Our BPS calculations found that the estimated SN Ia birthrates for the WD+MS channel are ~0.009-0.315*10^{-3}{yr}^{-1} if we adopt the Eddington accretion rate as the critical accretion rate, which are much lower than that of the observations (<10% of the observed SN Ia birthrates). This indicates that the WD+MS channel only contributes a small proportion of all SNe Ia. The birthrates in this simulation are lower than previous studies, the main reason of which is that new mass-accumulation efficiencies of H-shell flashes are adopted. We also found that the critical mass-accretion rate has a significant influence on the birthrates of SNe Ia. Meanwhile, the results of our BPS calculations are sensitive to the values of the common-envelope ejection efficiency.Comment: 14 pages, 9 figures, 1 table, accepted for publication in Astronomy and Astrophysic

Robust Adaptive Learning-based Path Tracking Control of Autonomous Vehicles under Uncertain Driving Environments

This paper investigates the path tracking control problem of autonomous vehicles subject to modelling uncertainties and external disturbances. The problem is approached by employing a 2-degree of freedom vehicle model, which is reformulated into a newly defined parametric form with the system uncertainties being lumped into an unknown parametric vector. On top of the parametric system representation, a novel robust adaptive learning control (RALC) approach is then developed, which estimates the system uncertainties through iterative learning while treating the external disturbances by adopting a robust term. It is shown that the proposed approach is able to improve the lateral tracking performance gradually through learning from previous control experiences, despite only partial knowledge of the vehicle dynamics being available. It is noteworthy that a novel technique targeting at the non-square input distribution matrix is employed so as to deal with the under-actuation property of the vehicle dynamics, which extends the adaptive learning control theory from square systems to non-square systems. Moreover, the convergence properties of the RALC algorithm are analysed under the framework of Lyapunov-like theory by virtue of the composite energy function and the λ-norm. The effectiveness of the proposed control scheme is verified by representative simulation examples and comparisons with existing methods

Blue straggler evolution caught in the act in the Large Magellanic Cloud globular cluster Hodge 11

High-resolution {\sl Hubble Space Telescope} imaging observations show that the radial distribution of the field-decontaminated sample of 162 'blue straggler' stars (BSs) in the $11.7^{+0.2}_{-0.1}$ Gyr-old Large Magellanic Cloud cluster Hodge 11 exhibits a clear bimodality. In combination with their distinct loci in color--magnitude space, this offers new evidence in support of theoretical expectations that suggest different BS formation channels as a function of stellar density. In the cluster's color--magnitude diagram, the BSs in the inner 15$"$ (roughly corresponding to the cluster's core radius) are located more closely to the theoretical sequence resulting from stellar collisions, while those in the periphery (at radii between 85$"$ and 100$"$) are preferentially found in the region expected to contain objects formed through binary mass transfer or coalescence. In addition, the objects' distribution in color--magntiude space provides us with the rare opportunity in an extragalactic environment to quantify the evolution of the cluster's collisionally induced BS population and the likely period that has elapsed since their formation epoch, which we estimate to have occurred $\sim$4--5 Gyr ago.Comment: 13 pages, 4 figure, accepted by Astrophysical Journal Letter

An innovative fracture plugging evaluation method for drill-in fluid loss control and formation damage prevention in deep fractured tight reservoirs

Lost circulation, resulting from the undesired loss of drilling fluid into formation fractures, stands as a significant technical obstacle in the exploration and production of oil, gas, and geothermal reservoirs. Effective mitigation of this challenge requires the development and application of robust experimental evaluation methods to assess the effectiveness of fracture plugging. The traditional approach to fracture plugging evaluation relies on a uniform evaluation index and experimental parameters for various lost circulation types. Unfortunately, this practice frequently results in inconsistent performance of loss control formulas during laboratory experiments and field tests. To address this issue, this paper introduces an innovative evaluation method that accounts for the specific characteristics of the three major lost circulation types. By adopting this approach, a more scientifically rigorous design and optimization of loss control formulas can be achieved, ensuring their effectiveness in managing lost circulation challenges. The development of the new method involves a systematic five-step establishment process: lost circulation type determination, evaluation index weight calculation, fitness degree analysis between laboratory experiment and field test, experimental parameters optimization, and quantitative scoring of loss control formula. Analytic hierarchy process is adopted to calculate the evaluation index weight. Quantitative scoring model is proposed to finally determine the integrated formula score for the quantitative evaluation and scientific optimization of loss control formula. To bridge the gap between laboratory and field applications, laboratory evaluation tests are developed to address different types of lost circulation scenarios. The experimental results demonstrate significant improvements achieved through the optimized formula. Specifically, the maximum plugging pressure increased from 5 MPa to 20.8 MPa, while the initial and cumulative loss volumes witnessed reductions of 30.3 ml and 121.2 ml, respectively. Moreover, the evaluation method proposed in this paper exhibits a fitting degree of over 90 % when compared to the actual control effect on drilling fluid loss. These findings substantiate the successful establishment of a connection between laboratory evaluations and field performance, providing valuable insights for future applications. Finally, a novel evaluation method for assessing the fracture plugging effect is established, accounting for various lost circulation types in deep fractured tight reservoirs. The reliability of this proposed evaluation method is validated by field test. Building upon this method, a high-score formula is designed and effectively deployed in a deep fractured tight reservoir in Tarim Basin, China. The successful application highlights the practical value and robustness of the developed evaluation method, offering promising prospects for future operations in similar reservoir settings

GluNet: A Deep Learning Framework For Accurate Glucose Forecasting

For people with Type 1 diabetes (T1D), forecasting of \red{blood glucose (BG)} can be used to effectively avoid hyperglycemia, hypoglycemia and associated complications. The latest continuous glucose monitoring (CGM) technology allows people to observe glucose in real-time. However, an accurate glucose forecast remains a challenge. In this work, we introduce GluNet, a framework that leverages on a personalized deep neural network to predict the probabilistic distribution of short-term (30-60 minutes) future CGM measurements for subjects with T1D based on their historical data including glucose measurements, meal information, insulin doses, and other factors. It adopts the latest deep learning techniques consisting of four components: data pre-processing, label transform/recover, multi-layers of dilated convolution neural network (CNN), and post-processing. The method is evaluated in−silico for both adult and adolescent subjects. The results show significant improvements over existing methods in the literature through a comprehensive comparison in terms of root mean square error (RMSE) (8.88 ± 0.77 mg/dL) with short time lag (0.83 ± 0.40 minutes) for prediction horizons (PH) = 30 mins (minutes), and RMSE (19.90 ± 3.17 mg/dL) with time lag (16.43 ± 4.07 mins) for PH = 60 mins for virtual adult subjects. In addition, GluNet is also tested on two clinical data sets. Results show that it achieves an RMSE (19.28 ± 2.76 mg/dL) with time lag (8.03 ± 4.07 mins) for PH = 30 mins and an RMSE (31.83 ± 3.49 mg/dL) with time lag (17.78 ± 8.00 mins) for PH = 60 mins. These are the best reported results for glucose forecasting when compared with other methods including the neural network for predicting glucose (NNPG), the support vector regression (SVR), the latent variable with exogenous input (LVX), and the auto regression with exogenous input (ARX) algorithm