Multitask learning and nonlinear optimal control of the COVID-19 outbreak: A geometric programming approach

We propose a multitask learning approach to learn the parameters of a compartmental discrete-time epidemic model from various data sources and use it to design optimal control strategies of human-mobility restrictions that both curb the epidemic and minimize the economic costs associated with implementing non-pharmaceutical interventions. We develop an extension of the SEIR epidemic model that captures the effects of changes in human mobility on the spread of the disease. The parameters of the model are learned using a multitask learning approach that leverages both data on the number of deaths across a set of regions, and cellphone data on individuals’ mobility patterns specific to each region. Using this model, we propose a nonlinear optimal control problem aiming to find the optimal mobility-based intervention strategy that curbs the spread of the epidemic while obeying a budget on the economic cost incurred. We also show that the solution to this nonlinear optimal control problem can be efficiently found, in polynomial time, using tools from geometric programming. Furthermore, in the absence of a straightforward mapping from human mobility data to economic costs, we propose a practical method by which a budget on economic losses incurred may be chosen to eliminate excess deaths due to over-utilization of hospital resources. Our results are demonstrated with numerical simulations using real data from the COVID-19 pandemic in the Philadelphia metropolitan area.     

切换系统多面体区域的生存性判别

本文研究了切换系统关于多面体区域的生存性判别问题.考虑多面体由有限点集凸包来表示,利用非光滑分析理论,得到一个切换系统生存性的充分条件.该条件只需检验在极点处是否满足特定条件,而不需要对每个边界点进行验证.其优点在于将生存性的判别转化为向量内积与切锥的计算.这种生存性判别方法简便易行.最后通过实例阐述了算法的有效性.     

MPI-CUDA parallelization of a finite-strip program for geometric nonlinear analysis: A hybrid approach

A finite-strip geometric nonlinear analysis is presented for elastic problems involving folded-plate structures. Compared with the standard finite-element method, its main advantages are in data preparation, program complexity, and execution time. The finite-strip method, which satisfies the von Karman plate equations in the nonlinear elastic range, leads to the coupling of all harmonics. However, coupling of series terms dramatically increases computation time in existing finite-strip sequential programs when a large number of series terms is used. The research reported in this paper combines various parallelization techniques and architectures (computing clusters and graphic processing units) with suitable programming models (MPI and CUDA) to speed up lengthy computations. In addition, a metric expressing the computational weight of input sets is presented. This metric allows computational complexity comparison of different inputs.     

Application of optimal control theory to analysis of cancer chemotherapy regimens

Cancer chemotherapy with application of one drug is studied. The negative and inhibiting effect of the tumor on normal cells is taken into account. Under certain assumptions, we determine the optimal regimen that minimizes the tumor burden at the end of a fixed period of therapy while maintaining the normal cell population above a prescribed level.     

PREPRO: a computer program for encoding regional exploration data for use in characteristic analysis

The preprocessor (PREPRO) computer program offers the exploration geologist a variety of options for encoding regional exploration data into ternary form for use in characteristic analysis. PREPRO's options include variable-input formats, cursor input, ordering among a set of input variables, and selectable ternary transformations. Moreover, the program provides for the display of results which, in turn, makes possible review, reselection, and retransformation of variables. Most important, the performance of the listed steps in an interactive computing environment results in rapid and efficient preprocessing of the data.     

Optimal input design for model discrimination using Pontryagin’s maximum principle: Application to kinetic model structures

The paper presents a methodology for an optimal input design for model discrimination. To allow analytical solutions, the method, using Pontryagin’s maximum principle, is developed for non-linear single-state systems that are affine in their joint input. The method is demonstrated on a fed-batch reactor case study with first-order and Monod kinetics.     

Stability analysis for a second-order continuous finite-time control system subject to a disturbance

In this paper, using finite-time control method, we consider the disturbance analysis of a second-order system with unknown but bounded disturbance. We show that the states of the second-order system will be stabilized to a region containing the origin. The radius of this region is determined by the control parameters and can be rendered as small as desired. The rigorous stability analysis is also given. Compared with the conventional PD control law, the finite-time control law yields a better disturbance rejection performance. Numerical simulation results show the effectiveness of the method.     

仿射非线性控制系统生存性的判别

讨论了仿射非线性控制系统关于由不等式表示的区域生存性判别问题．基于非光滑分析理论, 给出了在一点处检验生存性条件是否成立的方法, 该方法将生存性条件的检验转化为判别凸不等式组的相容性(是否有解),然后利用投影方法对凸不等式组的相容性进行判别．     

Contraction theory for nonlinear stability analysis and learning-based control: A tutorial overview

Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results in a necessary and sufficient characterization of incremental exponential stability of multiple solution trajectories with respect to each other. By using a squared differential length as a Lyapunov-like function, its nonlinear stability analysis boils down to finding a suitable contraction metric that satisfies a stability condition expressed as a linear matrix inequality, indicating that many parallels can be drawn between well-known linear systems theory and contraction theory for nonlinear systems. Furthermore, contraction theory takes advantage of a superior robustness property of exponential stability used in conjunction with the comparison lemma. This yields much-needed safety and stability guarantees for neural network-based control and estimation schemes, without resorting to a more involved method of using uniform asymptotic stability for input-to-state stability. Such distinctive features permit systematic construction of a contraction metric via convex optimization, thereby obtaining an explicit exponential bound on the distance between a time-varying target trajectory and solution trajectories perturbed externally due to disturbances and learning errors. The objective of this paper is therefore to present a tutorial overview of contraction theory and its advantages in nonlinear stability analysis of deterministic and stochastic systems, with an emphasis on deriving formal robustness and stability guarantees for various learning-based and data-driven automatic control methods. In particular, we provide a detailed review of techniques for finding contraction metrics and associated control and estimation laws using deep neural networks.     

An optimal control methodology for plant growth—Case study of a water supply problem of sunflower

An optimal control methodology is proposed for plant growth. This methodology is demonstrated by solving a water supply problem for optimal sunflower fruit filling. The functional–structural sunflower growth is described by a dynamical system given soil water conditions. Numerical solutions are obtained through an iterative optimization procedure, in which the gradients of the objective function, i.e. the sunflower fruit weight, are calculated efficiently either with adjoint modeling or by differentiation algorithms. Further improvements in sunflower yield have been found compared to those obtained using genetic algorithms in our previous studies. The optimal water supplies adapt to the fruit filling. For instance, during the mid-season growth, the supply frequency condenses and the supply amplitude peaks. By contrast, much less supplies are needed during the early and ending growth stages. The supply frequency is a determining factor, whereas the sunflower growth is less sensitive to the time and amount of one specific irrigation. These optimization results agree with common qualitative agronomic practices. Moreover they provide more precise quantitative control for sunflower growth.     

Application of grey system theory to phosphorite sinter process: From modeling to control

The sintering process of phosphorite ore occurs with a large amount of return caused by untimely process control. The control task of phosphorite ore sintering is to regulate the parameters of the process to obtain a high quality sinter. The parameter clearly responsible for sinter quality is the temperature in the wind box. Therefore, in order to solve the control task, it is necessary to predict the highest temperature of the charge (also known as the burn through point (BTP)). In this paper, the theory of grey systems is used as a predictive model, which makes it possible to obtain an adequate model that uses a small number of initial samples of real temperature data. Based on the grey model GMC(1,n) a new optimal model is presented, which is constructed by using optimization algorithm. Optimal model predicts the BTP, and to establish an optimal regulation, a control synthesis is carried out through an optimization of the prediction according to the “particle swarm” algorithm.     

An optimal hierarchical control scheme for smart generation units: An application to combined steam and electricity generation

Optimal management of thermal and energy grids with fluctuating demand and prices requires to orchestrate the generation units (GU) among all their operating modes. A hierarchical approach is proposed to control coupled energy nonlinear systems. The high level hybrid optimization defines the unit commitment, with the optimal transition strategy, and best production profiles. The low level dynamic model predictive control (MPC), receiving the set-points from the upper layer, safely governs the systems considering process constraints. To enhance the overall efficiency of the system, a method to optimal start-up the GU is here presented: a linear parameter-varying MPC computes the optimal trajectory in closed-loop by iteratively linearizing the system along the previous optimal solution. The introduction of an intermediate equilibrium state as additional decision variable permits the reduction of the optimization horizon, while a terminal cost term steers the system to the target set-point. Simulation results show the effectiveness of the proposed approach.     

Optimal maintenance model for a multistate deteriorating system: a geometric process approach

A monotone process model is introduced for a deteriorating system with k+1 states (k working states and one failure state). We prove that the model is equivalent to a geometric process model for a two-state system, in the sense that both systems have the same long-run average cost per unit time and the same optimal maintenance policy. Finally, an optimal maintenance policy for the deteriorating system is determined analytically.     

A nonparametric approach to design robust controllers for uncertain systems: Application to an air flow heating system

This paper presents an approach to design robust fixed structure controllers for uncertain systems using a finite set of measurements in the frequency domain. In traditional control system design, usually, based on measurements, a model of the plant, which is only an approximation of the physical system, is first built, and then control approaches are used to design a controller based on the identified model. Errors associated with the identification process as well as the inevitable uncertainties associated with plant parameter variations, external disturbances, measurement noise, etc. are expected to all contribute to the degradation of the performance of such a scheme. In this paper, we propose a nonparametric method that uses frequency-domain data to directly design a robust controller, for a class of uncertainties, without the need for model identification. The proposed technique, which is based on interval analysis, allows us to take into account the plant uncertainties during the controller synthesis itself. The technique relies on computing the controller parameters for which the set of all possible frequency responses of the closed-loop system are included in the envelope of a desired frequency response. Such an inclusion problem can be solved using interval techniques. The main advantages of the proposed approach are: (1) the control design does not require any mathematical model, (2) the controller is robust with respect to plant uncertainties, and (3) the controller structure can be chosen a priori, which allows us to select low-order controllers. To illustrate the proposed method and demonstrate its efficacy, an application to an air flow heating system is presented.     

Constructive solid analysis: a hierarchical, geometry-based meshless analysis procedure for integrated design and analysis

In this paper, we propose an analysis methodology that is procedurally analogous to Constructive Solid Geometry (CSG) integrating design and analysis, and thereby enabling efficient optimal design. The procedure, due to its analogous nature to CSG, is termed Constructive Solid Analysis (CSA). The analysis methodology is partitioned, hierarchical and is based on constructing the boundary value problem for a compound geometry through operations on the field quantities defined on the primitives. Although the CSA procedure will allow any basis for approximating the fields, Non-Uniform Rational B-Splines (NURBS), currently popular in the geometric modeling literature, are used to represent the geometry of the primitives as well as the analysis fields. The use of the same basis to represent geometry and analysis fields enables ‘representational’ integration, and further, the developed methodology may be classified as a partition of unity meshless analysis scheme. A more general null-space solution scheme and a somewhat restrictive range-space solution scheme are outlined to solve the discretized equations resulting from the use of NURBS. Several representative problems from the field of linear elasticity are solved to demonstrate the validity of the procedure and to evaluate its computational cost relative to the finite element method. The optimal orientation of an elliptical hole to applied tractions is determined to demonstrate the power of the proposed methodology for shape optimal design.     

A model-based supervisory energy management strategy for a 12 V vehicle electrical system

This paper describes the development, implementation, and experimental verification of a supervisory energy management strategy for the vehicle electrical system of a passenger car. The control strategy commands the alternator duty cycle such that vehicle fuel economy is optimized whilst the instantaneous load current demand is met and constraints on the system voltage and battery state of charge are satisfied.The work is based on a control-oriented model of the vehicle electrical system, experimentally validated against vehicle data. Then, a constrained global optimal control problem is formulated for the energy management of the electrical system, and analytically solved using the Pontryagin׳s Minimum Principle (PMP). The optimal solution obtained is evaluated for a range of different driving cycles and electrical load current profiles, leading to the formulation of an adaptive supervisory control strategy that is implemented and tested in vehicle.     

Application of a neuro-fuzzy system to control a mobile vehicle

We describe a fuzzy control based on a neural network, which is obtained by merging the advantages of a neural network, a competitive algorithm, and fuzzy control. This adaptive fuzzy control system can deal with data sampled by a neural network. From such training data, it can produce more reasonable fuzzy rules by a competitive (clustering) algorithm, and finally control the object by the optimized fuzzy rules. This is not a simple combination of the three methods, but a merger into one control system. Some experiments and future considerations are also given.This work was presented in part at the 8th International Symposium on Artificial Life and Robotics, Oita, Japan, January 24–26, 2003     

Koopman operator dynamical models: Learning,analysis and control

The Koopman operator allows for handling nonlinear systems through a globally linear representation. In general, the operator is infinite-dimensional – necessitating finite approximations – for which there is no overarching framework. Although there are principled ways of learning such finite approximations, they are in many instances overlooked in favor of, often ill-posed and unstructured methods. Also, Koopman operator theory has long-standing connections to known system-theoretic and dynamical system notions that are not universally recognized. Given the former and latter realities, this work aims to bridge the gap between various concepts regarding both theory and tractable realizations. Firstly, we review data-driven representations (both unstructured and structured) for Koopman operator dynamical models, categorizing various existing methodologies and highlighting their differences. Furthermore, we provide concise insight into the paradigm’s relation to system-theoretic notions and analyze the prospect of using the paradigm for modeling control systems. Additionally, we outline the current challenges and comment on future perspectives.     

Stochastic model predictive control for remanufacturing system management

Uncertainties in the quality, quantity, and operational time of used products pose a challenge to the management of remanufacturing systems. In addition, it becomes a necessity to optimize the operation of the remanufacturing system to balance the quality of products, remanufacturing efficiency, and service level. In this study, a stochastic discrete-time dynamical model is proposed to represent a remanufacturing system, where the relationship between the market satisfaction, inventory status, and operational actions is explicitly modeled. This includes production and inventory planning, resource allocation and acquisition. To handle uncertainties, a stochastic model predictive control approach is proposed to plan the actions that optimize the remanufacturing efficiency. Our results in the simulation examples show that: (a) without supplies, the remanufacturing system has better stability and robustness than a conventional manufacturing system with the same initial stocks; and (b) with insufficient initial stocks, the remanufacturing system demands fewer and more gradual supplies, thereby keeping the system stable. Finally, a sensitivity analysis is conducted for testing the performance of the remanufacturing system. By changing the operational action capacity, different state equilibria are discovered, which correspond to distinct system response characteristics. The study reveals notable managerial insights and effects of product commonality, demand patterns, and operational actions scheduling on the efficiency of the remanufacturing system.