Dynamic complexity of optimal paths and discount factors for strongly concave problems

We study the relationship between the dynamical complexity of optimal paths and the discount factor in general infinite-horizon discrete-time concave problems. Given a dynamic systemx _t+1=h(x _t ), defined on the state space, we find two discount factors 0 < ^{* **} < 1 having the following properties. For any fixed discount factor 0 < < ^*, the dynamic system is the solution to some concave problem. For any discount factor ^** < < 1, the dynamic system is not the solution to any strongly concave problem. We prove that the upper bound ^** is a decreasing function of the topological entropy of the dynamic system. Different upper bounds are also discussed.This research was partially supported by MURST, National Group on Nonlinear dynamics in Economics and Social Sciences. The author would like to thank two anonymous referees for helpful comments and suggestions.     

Cord-slope form of Taylor's expansion in univariate global optimization

Interval arithmetic and Taylor's formula can be used to bound the slope of the cord of a univariate function at a given point. This leads in turn to bounding the values of the function itself. Computing such bounds for the function, its first and second derviatives, allows the determination of intervals in which this function cannot have a global minimum. Exploiting this information together with a simple branching rule yields an efficient algorithm for global minimization of univariate functions. Computational experience is reported.The first and second authors have been supported by FCAR (Fonds pour la Formation de Chercheurs et l'Aide à la Recherche) Grant 92EQ1048 and AFOSR Grant 90-0008 to Rutgers University. The first author has also been supported by NSERC (Natural Sciences and Engineering Research Council of Canada) Grant to HEC and NSERC Grant GP0105574. The second author has been supported by NSERC Grant GP0036426, FCAR Grant 90NC0305, and a NSF Visiting Professorship for Women in Science at Princeton University. Work of the third author was done in part while he was a graduate student at the Department of Mathematics, Rutgers University, New Brunswick, New Jersey, USA and during a visit to GERAD, June–August 1991.     

Design and optimal tuning of nonlinear PI compensators

In this paper, linear time-invariant single-input single-output (SISO) systems that are stabilizable by linear proportional and integral (PI) compensators are considered. For such systems, a five-parameter nonlinear PI compensator is proposed. The parameters of the proposed compensator are tuned by solving an optimization problem. The optimization problem always has a solution.Additionally, a general nonlinear PI compensator is proposed and is approximated by easy-to-compute compensators, for instance, a six-parameter nonlinear PI compensator. The parameters of the approximate compensators are tuned to satisfy an optimality condition. The superiority of the proposed nonlinear PI compensators over linear PI compensators is discussed and is demonstrated for two feedback systems.     

由偏微支配的系统的最优控制理论中的奇异摄动方法*

本文介绍了由偏微分方程支配的系统的最优控制理论中有关应用奇异摄动方法时出现的各种问题。考虑了渐近分析来自状态方程。或来自性能指标函数,也考虑了状态方程是定义在摄动域内的情形。     

Quantum Fourier Transform-Based Arithmetic Logic Unit on a Quantum Processor

This study proposes and construct a primitive quantum arithmetic logic unit (qALU) based on the quantum Fourier transform (QFT). The qALU is capable of performing arithmetic ADD (addition) and logic NAND gate operations. It designs a scalable quantum circuit and presents the circuits for driving ADD and NAND operations on two-input and four-input quantum channels, respectively. By comparing the required number of quantum gates for serial and parallel architectures in executing arithmetic addition, it evaluates the performance. It also execute the proposed quantum Fourier transform-based qALU design on real quantum processor hardware provided by IBM. The results demonstrate that the proposed circuit can perform arithmetic and logic operations with a high success rate. Furthermore, it discusses in detail the potential implementations of the qALU circuit in the field of computer science, highlighting the possibility of constructing a soft-core processor on a quantum processing unit.     

Generalized convexity and concavity of the optimal value function in nonlinear programming

In this paper we consider generalized convexity and concavity properties of the optimal value functionf ^* for the general parametric optimization problemP(_ε) of the form min _x f(x, ε) s.t.x∈R(ε). Many results on convexity and concavity characterizations off ^* were presented by the authors in a previous paper. Such properties off ^* and the solution set mapS ^* form an important part of the theoretical basis for sensitivity, stability and parametric analysis in mathematical optimization. We give sufficient conditions for several types of generalized convexity and concavity off ^*, in terms of respective generalized convexity and concavity assumptions onf and convexity and concavity assumptions on the feasible region point-to-set mapR. Specializations of these results to the parametric inequality-equality constrained nonlinear programming problem are provided. Research supported by Grant ECS-8619859, National Science Foundation and Contract N00014-86-K-0052, Office of Naval Research.     

热源塔热泵系统夏季工况优化运行实验研究

由于热源塔在冬夏季工况下的换热能力存在较大差异,按冬季工况设计的热源塔热泵系统,在夏季工况下运行时存在换热能力过剩的问题,影响系统性能。为解决上述问题,本文构建了热源塔热泵系统,实验研究了其冬夏季工况的性能差异。在此基础上,对夏季工况下的优化运行进行了实验研究,结果表明,通过调节空气和溶液流量,将热源塔的逼近度和冷幅分别控制在3.5℃和4.3℃,可使得系统性能系数由3.6提升至3.9,并对其节能机理进行了分析。     

THE BÄCKLUND TRANSFORMATION AND NONLINEAR SUPERPOSITION FORMULA OF SOLUTIONS FOR THE LIOUVILLE’S EQUATION IN HIGHER DIMENSIONS

In this paper, we show that Backlund transformation derived by Leibbrandt et al. for the Liouville’s equation in three spatial dimensions, ▽²a=expa, ▽²=-∂_x²+∂_y²+∂_z² can be decomposed into several Backlund transformations for the same equation in two spatial dimensions, moreover, the superposition formula which is derived from this transformation is actually invalid, thus the discussions based on that formula is incorrect as well. We also considered some results about the Liouville’s equation in N spatial dimensions.     

Optimal control theory of an age-structured coronavirus disease model and the dynamical analysis of the underlying ordinary differential equation model having constant parameters

This paper addresses the dynamics of COVID-19 using the approach of age-structured modeling. A particular case of the model is presented by taking into account age-free parameters. The sub-model consisting of ordinary differential equations (ODEs) is investigated for possible equilibria, and qualitative aspects of the model are rigorously presented. In order to control the spread of the disease, we considered two age- and time-dependent non-pharmaceutical control measures in the age-structured model, and an optimal control problem using a general maximum principle of Pontryagin type is achieved. Finally, sample simulations are plotted which support our theoretical work.     

Robust inverse optimal control for flexible structures

An inverse optimal control problem is formulated to develop robust control laws for purely oscillatory systems. The optimal control solution requires output feedback with specified constraints, leading to robustness with respect to unmodeled modes and a large class of parameter variations. The robustness properties are proved directly from known properties of control laws resulting from quadratic performance indices. The control laws are useful for poorly damped flexible structures.This research was supported by the Office of Naval Research, Contract No. N00014-77-C-0247.