Hybrid decentralized maximum entropy control for large-scale dynamical systems

Significant research efforts have been devoted to large-scale dynamical systems, with the aim of understanding their complicated behaviors and managing their responses in real-time. One pivotal technological obstacle in this process is the existence of uncertainty. Although many of these large-scale dynamical systems function well in the design stage, they may easily fail when operating in realistic environment, where environmental uncertainties modulate system dynamics and complicate real-time predication and management tasks. This dissertation aims to develop systematic methodologies to evaluate the performance of large-scale dynamical systems under uncertainty, as a step toward real-time decision support. Two uncertainty evaluation approaches are pursued: the analytical approach and the effective simulation approach. The analytical approach abstracts the dynamics of original stochastic systems, and develops tractable analysis (e.g., jump-linear analysis) for the approximated systems. Despite the potential bias introduced in the approximation process, the analytical approach provides rich insights valuable for evaluating and managing the performance of large-scale dynamical systems under uncertainty. When a system’s complexity and scale are beyond tractable analysis, the effective simulation approach becomes very useful. The effective simulation approach aims to use a few smartly selected simulations to quickly evaluate a complex system’s statistical performance. This approach was originally developed to evaluate a single uncertain variable. This dissertation extends the approach to be scalable and effective for evaluating large-scale systems under a large-number of uncertain variables. While a large portion of this dissertation focuses on the development of generic methods and theoretical analysis that are applicable to broad large-scale dynamical systems, many results are illustrated through a representative large-scale system application on strategic air traffic management application, which is concerned with designing robust management plans subject to a wide range of weather possibilities at 2-15 hours look-ahead time.

Extreme UltraViolet (EUV) lithography is a new technology for production of integrated circuits. In EUV lithographic machines, optical elements are heated by absorption of exposure energy. Heating induces thermoelastic deformations of optical elements and consequently, it creates wavefront aberrations. These Thermally Induced Wavefront Aberrations (TIWA) can significantly degrade the resolution of EUV lithographic machines. One of the ways to correct TIWA and consequently, to improve the resolution of EUV lithographic machines, is to use the Adaptive Optics (AO) technique and predictive control algorithms. However, the predictive control of TIWA is a challenging problem, mainly because the dynamical behavior of TIWA is described by thermoelastic Partial Differential Equations (PDEs). By discretizing the thermoelastic equations using the finite difference or finite element methods, large-scale state-space models can be obtained. A striking feature of these state-space models is that they have sparse (multi) banded matrices. Consequently, these state-space models can be interpreted as large-scale networks of local subsystems. All this implies that the problem of correcting TIWA can be placed in a much more general context of identifying, estimating and controlling large-scale interconnected (distributed) systems. However, currently used estimation and control algorithms are not computationally feasible for large-scale systems. For this reason, this thesis focuses on the development of computationally efficient identification, estimation and control algorithms for large-scale interconnected systems. In this thesis, we prove that the inverses of (finite-time) Gramians of large-scale interconnected systems, obtained by discretizing PDEs, belong to a class of off-diagonally decaying matrices. Consequently, these inverses can be approximated by sparse (multi) banded matrices with O(N) complexity, where N is the number of local subsystems. To compute the approximate inverses, the Chebyshev approximation method and the Newton iteration are used. On the basis of these theoretical results, we develop novel estimation and identification algorithms for large-scale interconnected systems. The computational and memory complexity of these methods scale with O(N). This is the main advantage over the traditional estimation and identification methods, which complexity is O(N^3). Furthermore, in this thesis we develop and experimentally verify AO control algorithms for predictive correction of TIWA. The experimental results give a good first indication for a possible implementation of the developed predictive control algorithms in EUV lithographic machines. Finally, we develop and experimentally test an iterative learning control algorithm for high performance correction of wavefront aberrations.

The goal in type 1 diabetes (T1D) therapy is to maintain optimal glycemic control under any circumstance. Diabetes technology is in continuous development to achieve this goal. The most advanced Food and Drug Administration- and European Medicines Agency-approved devices are hybrid closed-loop (HCL) systems, which deliver insulin subcutaneously in response to glucose levels according to an automated algorithm. T1D is frequently encountered in the perioperative period. The latest international guidelines for the management of children with diabetes undergoing surgery include specific adjustments to the patient's insulin therapy, hourly blood glucose monitoring, and intravenous (IV) insulin infusion. However, these guidelines were published while the HCL systems were still marginal. We present a case of a 9-year-old boy with long-standing T1D, under HCL system therapy for the last 9 months, and needing surgery for an appendectomy. We agreed with the family, the surgical team, and the anesthesiologists to continue HCL insulin infusion, without further adjustments, hourly blood glucose checks or IV insulin, while monitoring closely. The HCL system was able to keep glycemia within range for the total duration of the overnight fast, the surgery, and the initial recovery, without any external intervention or correction bolus. This is, to the best of our knowledge, the first reported pediatric case to undergo major surgery using a HCL system, and the results were absolutely satisfactory for the patient, his family, and the medical team. We believe that technology is ripe enough to advocate for a “take your pump to surgery” message, minimizing the impact and our interventions. The medical team may discuss this possibility with the family and patients.

BackgroundPregnancy in the setting of type 1 diabetes (T1D) is associated with increased morbidity and mortality. There is strong evidence to suggest that the use of continuous glucose monitoring (CGM) is associated with better glycemic control and reduced adverse pregnancy outcomes. As hybrid closed-loop (HCL) systems are increasingly used among women with T1D, many prefer to continue off-label use of these systems during pregnancy. However, most of the available HCL systems’ glucose targets and algorithms are not designed to overcome the challenges that face insulin therapy during pregnancy. We are reporting on two females with T1D who used MiniMed 780G, an advanced HCL system, during their pregnancy with good outcomes. Cases presentationCase 1: A 23-year-old woman with T1D presented at 6 weeks gestation. She used MiniMed 780G before pregnancy and throughout her pregnancy. By assisting her HCL system with some techniques, such as earlier bolusing before meals and the use of fake carbs to correct high glucose, and providing frequent follow-up, she achieved pregnancy-specific HbA1C and CGM glycemic targets and had good perinatal outcomes. Case 2: A 26-year-old female with T1D presented at 10 weeks gestation. She had been using MiniMed 670G since before pregnancy, thereafter, she was shifted to MiniMed 780G at 23 weeks gestation. We offered her the same techniques to support her HCL, and she achieved pregnancy-specific time in range (psTIR) in the 3rd trimester with good perinatal outcomes. ConclusionWe could achieve most of the pregnancy-specific glycemic targets with good maternal, fetal, and neonatal outcomes using MiniMed 780G, assisted with some techniques to increase the efficiency of insulin therapy during pregnancy.

Time-reversal symmetry, Poincaré recurrence, irreversibility, and the entropic arrow of time: From mechanics to system thermodynamics

Control vector Lyapunov functions for large-scale impulsive dynamical systems

Distributed controller design for a class of sparse singular systems with privacy constraints

In this paper we develop thermodynamic models for discrete-time large-scale dynamical systems. Specifically, using compartmental dynamical system theory, we develop energy flow models possessing energy conservation, energy equipartition, temperature equipartition, and entropy nonconservation principles for discrete-time, large-scale dynamical systems. Furthermore, we introduce a new and dual notion to entropy, namely, ectropy, as a measure of the tendency of a dynamical system to do useful work and grow more organized, and show that conservation of energy in an isolated thermodynamic system necessarily leads to nonconservation of ectropy and entropy. In addition, using the system ectropy as a Lyapunov function candidate we show that our discrete-time, large-scale thermodynamic energy flow model has convergent trajectories to Lyapunov stable equilibria determined by the system initial subsystem energies.

It is important content that the studying connective stability among the stability studying of the large-scale interconnected systems. The many results recently have been given for the normal systems, the studying result of the singular large scale systems, however, is a little. The paper discussed the connective stability of a kind of nonlinear singular large-scale dynamical systems by means of singular Lyapunov equation and vector Lyapunov function. A stable domain of connective parameters is given in the paper which is simple in form. At last we give an example to show the usage of the method and its efficiency.

Mitigating reader-to-reader collisions is one of the principal challenges in a large-scale dynamic RFID system with a number of readers deployed in order to maximize the system performance (i.e., throughput, fairness and latency). In prior works, contention-based and activity scheduling medium access control (MAC) protocols are commonly used approaches to reduce such problems. Existing protocols typically perform worse in a large-scale RFID dynamic system and require more additional components or are based on unrealistic assumptions. So far, many research efforts have been made to improve the performance or the reliability of Carrier Sense Multiple Access (CSMA) techniques for Mobile Ad-Hoc Networks (MANETs) by using an adaptive Backoff schemes. In this paper, we look at these well known solutions that proved their efficiency in high congestion wireless networks. We evaluate the performance and characterize these solutions when they are used to reserve the wireless channel through broadcasting message for reader-to-tag communication. Based on the application requirements, we study their capacity to mitigate collisions, the channel access latency, the average number of successful requests sent per reader and the fairness index in the context of RFID networks.

Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems

In analysis and control of large-scale nonlinear dynamical systems, a distributed approach is often an attractive option due to its computational tractability and usually low communication requirements. Success of the distributed control design relies on the separability of the network into weakly interacting subsystems such that minimal information exchange between subsystems is sufficient to achieve satisfactory control performance. While distributed analysis and control design for dynamical network have been well studied, decomposition of nonlinear networks into weakly interacting subsystems has not received as much attention. In this article we propose a vector Lyapunov functions based approach to quantify the energy-flow in a dynamical network via a model of a comparison system. Introducing a notion of power and energy flow in a dynamical network, we use sum-of-squares programming tools to partition polynomial networks into weakly interacting subsystems. Examples are provided to illustrate the proposed method of decomposition.

Model order reduction (MOR) has emerged as a de-facto solution for simulation, control, and optimization of large-scale and complex dynamical systems from the past decades. This paper demonstrates two comprehensive MOR approaches to overcome the overall computational cost required to simulate the nonlinear, viscous Burger’s equation. The former scheme is the approximate proper orthogonal decomposition (APOD), which involves capturing the approximate snapshot ensemble of the states by performing multiple linearizations along the state-trajectory. The latter technique is based on the notion of nonlinear moment matching (NLMM), in which the reduced projection basis is generated by numerically solving the simplified, nonlinear, Sylvester equation. Both the reduction schemes are tested on the high-fidelity finite difference (FD) formulation of 1D and the 2D Burgers’ equation. The results show substantial computational savings in extracting the orthonormal projection basis required to generate the reduced manifold. Furthermore, a comparative study of both methods is presented with proper orthogonal decomposition (POD) for various test signals.

In this paper, we study fundamental performance limitations of distributed feedback control in large-scale networked dynamical systems. Specifically, we address the question of whether dynamic feedback controllers perform better than static (memoryless) ones when subject to locality constraints. We consider distributed linear consensus and vehicular formation control problems modeled over toric lattice networks. For the resulting spatially invariant systems, we study the large-scale asymptotics (in network size) of global performance metrics that quantify the level of network coherence. With static feedback from relative state measurements, such metrics are known to scale unfavorably in lattices of low spatial dimensions, preventing, for example, a one-dimensional string of vehicles to move like a rigid object. We show that the same limitations in general apply also to dynamic feedback control that is locally of first order. This means that the addition of one local state to the controller gives a similar asymptotic performance to the memoryless case. This holds unless the controller can access noiseless measurements of its local state with respect to an absolute reference frame, in which case the addition of controller memory may fundamentally improve performance. In simulations of platoons with 20–200 vehicles, we show that the performance limitations we derive manifest as unwanted accordionlike motions. Similar behaviors are to be expected in any network that is embeddable in a low-dimensional toric lattice, and the same fundamental limitations would apply. To derive our results, we present a general technical framework for the analysis of stability and performance of spatially invariant systems in the limit of large networks.

Vector Lyapunov theory has been developed to weaken the hypothesis of standard Lyapunov theory in order to enlarge the class of Lyapunov functions that can be used for analyzing system stability. In this paper, we provide generalizations to the recent extensions of vector Lyapunov theory for continuous-time systems to address stability and control design of impulsive dynamical systems via vector Lyapunov functions. Specifically, we provide a generalized comparison principle involving hybrid comparison dynamics that are dependent on comparison system states as well as the nonlinear impulsive dynamical system states. Furthermore, we develop stability results for impulsive dynamical systems that involve vector Lyapunov functions and hybrid comparison inequalities. Based on these results, we show that partial stability for state-dependent impulsive dynamical systems can be addressed via vector Lyapunov functions. Furthermore, we extend the novel notion of control vector Lyapunov functions to impulsive dynamical systems. Using control vector Lyapunov functions, we present a universal decentralized feedback stabilizer for a decentralized affine in the control nonlinear impulsive dynamical system. These results are then used to develop decentralized controllers for large-scale impulsive dynamical systems with robustness guarantees against full modeling uncertainty