A Synthesis of Thermodynamic Models Unifying Traditional and Work-Driven Operations with Heat and Mass Exchange

A novel trend in the theory of thermodynamic limits for energy convertors and traditional heat and mass exchangers is analyzed, where certain special controls called, the Carnot control variables, play a common role. In terms of these controls an expression for the lost work has the same form in irreversible energy convertors and in traditional processes of purely dissipative transport. For sequential-type equipment of a finite size, enhanced limits are obtained for the energy production or consumption. Formal models of simplest energy convertors and characteristics of endoreversible operations are particularly lucid in terms of the Carnot controls. Progress in the theory of energy generation problems is achieved; examples of applications are outlined. Efficiency decrease caused by dissipation and finite rate bounds are estimated for work released from an engine or work added to a heat pump. It is shown that a simplification in the analysis of energy limits in complex thermal operations is achieved when Carnot controls are applied. Extensions involve mass transfer problems and a finite-rate counterpart of classical available energy (exergy).     

Nonequilibrium Thermodynamics as an Extension of Classical Thermodynamics

This work analyses several new directions in nonequilibrium thermodynamics, focusing on their practical exploitation rather than on any detailed analysis of the underlying theory. Neglected are the practical aspects of thermodynamic slability of nonequilibrium systems and graphical analyses of practical processes on thermodynamic charts, as those frequently considered in earlier papers. The problems described in the text are presented mainly from the perspective of the work of the present author and associated researchers, without an attempt to give a comprehensive presentation of the work of other researchers. Amongst many new results a generalization of exergy for state changes occurring in a finite time seems to be most important.     

An asymptotically optimal policy for finite support models in the multiarmed bandit problem

In the multiarmed bandit problem the dilemma between exploration and exploitation in reinforcement learning is expressed as a model of a gambler playing a slot machine with multiple arms. A policy chooses an arm in each round so as to minimize the number of times that arms with suboptimal expected rewards are pulled. We propose the minimum empirical divergence (MED) policy and derive an upper bound on the finite-time regret which meets the asymptotic bound for the case of finite support models. In a setting similar to ours, Burnetas and Katehakis have already proposed an asymptotically optimal policy. However, we do not assume any knowledge of the support except for its upper and lower bounds. Furthermore, the criterion for choosing an arm, minimum empirical divergence, can be computed easily by a convex optimization technique. We confirm by simulations that the MED policy demonstrates good performance in finite time in comparison to other currently popular policies.     

Finite-time adaptive neural control for uncertain nonlinear time-delay systems with actuator delay and full-state constraints

This paper investigates finite-time adaptive neural tracking control for a class of nonlinear time-delay systems subject to the actuator delay and full-state constraints. The difficulty is to consider full-state time delays and full-state constraints in finite-time control design. First, finite-time control method is used to achieve fast transient performances, and new Lyapunov–Krasovskii functionals are appropriately constructed to compensate time delays, in which a predictor-like term is utilized to transform input delayed systems into delay-free systems. Second, neural networks are utilized to deal with the unknown functions, the Gaussian error function is used to express the continuously differentiable asymmetric saturation nonlinearity, and barrier Lyapunov functions are employed to guarantee that full-state signals are restricted within certain fixed bounds. At last, based on finite-time stability theory and Lyapunov stability theory, the finite-time tracking control question involved in full-state constraints is solved, and the designed control scheme reduces learning parameters. It is shown that the presented neural controller ensures that all closed-loop signals are bounded and the tracking error converges to a small neighbourhood of the origin in a finite time. The simulation studies are provided to further illustrate the effectiveness of the proposed approach.     

Optimal control of distributed multiagent systems with finite-time group flocking

The flocking of multiple intelligent agents, inspired by the swarm behavior of natural phenomena, has been widely used in the engineering fields such as in unmanned aerial vehicle (UAV) and robots system. However, the performance of the system (such as response time, network throughput, and resource utilization) may be greatly affected while the intelligent agents are engaged in cooperative work. Therefore, it is concerned to accomplish the distributed cooperation while ensuring the optimal performance of the intelligent system. In this paper, we investigated the optimal control problem of distributed multiagent systems (MASs) with finite-time group flocking movement. Specifically, we propose two optimal group flocking algorithms of MASs with single-integrator model and double-integrator model. Then, we study the group consensus of distributed MASs by using modern control theory and finite-time convergence theory, where the proposed optimal control algorithms can drive MASs to achieve the group convergence in finite-time while minimizing the performance index of the intelligence system. Finally, experimental simulation shows that MASs can keep the minimum energy function under the effect of optimal control algorithm, while the intelligent agents can follow the optimal trajectory to achieve group flocking in finite time.     

Recursive Learning Automata Approach to Markov Decision Processes

In this note, we present a sampling algorithm, called recursive automata sampling algorithm (RASA), for control of finite-horizon Markov decision processes (MDPs). By extending in a recursive manner Sastry's learning automata pursuit algorithm designed for solving nonsequential stochastic optimization problems, RASA returns an estimate of both the optimal action from a given state and the corresponding optimal value. Based on the finite-time analysis of the pursuit algorithm by Rajaraman and Sastry, we provide an analysis for the finite-time behavior of RASA. Specifically, for a given initial state, we derive the following probability bounds as a function of the number of samples: 1) a lower bound on the probability that RASA will sample the optimal action and 2) an upper bound on the probability that the deviation between the true optimal value and the RASA estimate exceeds a given error.     

Kernels, regularization and differential equations

Many common machine learning methods such as support vector machines or Gaussian process inference make use of positive definite kernels, reproducing kernel Hilbert spaces, Gaussian processes, and regularization operators. In this work these objects are presented in a general, unifying framework and interrelations are highlighted.With this in mind we then show how linear stochastic differential equation models can be incorporated naturally into the kernel framework. And vice versa, many kernel machines can be interpreted in terms of differential equations. We focus especially on ordinary differential equations, also known as dynamical systems, and it is shown that standard kernel inference algorithms are equivalent to Kalman filter methods based on such models.In order not to cloud qualitative insights with heavy mathematical machinery, we restrict ourselves to finite domains, implying that differential equations are treated via their corresponding finite difference equations.     

无刷直流电动机系统的有限时间同步

有限时间同步能够确保两个系统在有限的时间内实现同步,具有重要的研究意义.但常见的控制器往往只能确保两个系统渐近同步,而能够实现有限时间同步的控制器目前尚不多见,且存在控制器复杂,不连续易产生抖振现象等缺陷.为此,本文设计了一种简单连续的有限时间同步控制器,实现了主–从无刷直流电动机系统(the brushless DC motor system,BLDCM)的有限时间同步.首先建立了基于该控制器的主–从有限时间同步框架.然后,从理论上证明了两个相同的BLDCM系统有限时间同步的充分性同步判据.最后,通过数值实例验证了所得判据的有效性.     

A 3D multi-grid algorithm for the Chan–Vese model of variational image segmentation

Variational segmentation models provide effective tools for image processing applications. Although existing models are continually refined to increase their capabilities, solution of such models is often a slow process, since fast methods are not immediately applicable to nonlinear problems. This paper presents an efficient multi-grid algorithm for solving the Chan–Vese model in three dimensions, generalizing our previous work on the topic in two dimensions, but this direct generalized method is low performance or unfeasible. So here, we first present two general smoothers for a nonlinear multi-grid method and then give our three new adaptive smoothers which can choose optimal a parameter of the smoothers automatically, also we analyse them using a local Fourier analysis and our theorem to inform how to obtain an optimal parameter and the best smoother selection. Finally, various advantages of our recommended algorithm are illustrated, using both synthetic and real images.     

An iterated local search heuristic for multi-capacity bin packing and machine reassignment problems

This paper proposes an efficient Multi-Start Iterated Local Search for Packing Problems (MS-ILS-PPs) metaheuristic for Multi-Capacity Bin Packing Problems (MCBPP) and Machine Reassignment Problems (MRP). The MCBPP is a generalization of the classical bin-packing problem in which the machine (bin) capacity and task (item) sizes are given by multiple (resource) dimensions. The MRP is a challenging and novel optimization problem, aimed at maximizing the usage of available machines by reallocating tasks/processes among those machines in a cost-efficient manner, while fulfilling several capacity, conflict, and dependency-related constraints. The proposed MS-ILS-PP approach relies on simple neighborhoods as well as problem-tailored shaking procedures. We perform computational experiments on MRP benchmark instances containing between 100 and 50,000 processes. Near-optimum multi-resource allocation and scheduling solutions are obtained while meeting specified processing-time requirements (on the order of minutes). In particular, for 9/28 instances with more than 1000 processes, the gap between the solution value and a lower bound measure is smaller than 0.1%. Our optimization method is also applied to solve classical benchmark instances for the MCBPP, yielding the best known solutions and optimum ones in most cases. In addition, several upper bounds for non-solved problems were improved.     

A survey of state vectors

The theory of Turing machines, which is basic to proving the various limitations of computers, is quite well known. The theory of finite state automata, the basic hardware models such as Moore machines, Mealy machines, and their generalizations, are similarly well known. Our purpose here is to survey basic work done between 1958 and 1975 on still another mathematical model for computer science, the state vector model. In this model there are many variables, each with its own current value, rather than a single state; this makes the model closer to what happens in a real computer.     

Quantum computation with write-only memory

In classical computation, a “write-only memory” (WOM) is little more than an oxymoron, and the addition of WOM to a (deterministic or probabilistic) classical computer brings no advantage. We prove that quantum computers that are augmented with WOM can solve problems that neither a classical computer with WOM nor a quantum computer without WOM can solve, when all other resource bounds are equal. We focus on realtime quantum finite automata, and examine the increase in their power effected by the addition of WOMs with different access modes and capacities. Some problems that are unsolvable by two-way probabilistic Turing machines using sublogarithmic amounts of read/write memory are shown to be solvable by these enhanced automata.     

基于量子逻辑的图灵机及其通用性

基于量子逻辑的自动机理论是量子计算模型的一个重要研究方向.该文研究了基于量子逻辑的图灵机(简称量子图灵机)及其一些变形,给出了包括非确定型量子图灵机l-VTM,确定型量子图灵机l-VDTM以及相应类型的多带量子图灵机,并引入量子图灵机基于深度优先与宽度优先识别语言的两种不同定义方式,证明了这两种定义方式在量子逻辑意义下是不等价的.进一步证明了l-VTM、l-VDTM与相应类型的多带量子图灵机之间的等价性.其次,给出了量子递归可枚举语言及量子递归语言的定义,并给出了二者的层次刻画,证明了l-VTM与l-VDTM不等价,但两者作为量子递归语言的识别器是等价的.最后,文中讨论了基于量子逻辑的通用图灵机的存在性问题,给出了一套合理编码系统,证明了基于量子逻辑的通用图灵机在其所取值的正交模格无限时不存在,而在其所取值的正交模格有限时是存在的.     

A method for model selection using reinforcement learning when viewing design as a sequential decision process

In an emerging paradigm, design is viewed as a sequential decision process (SDP) in which mathematical models of increasing fidelity are used in a sequence to systematically contract sets of design alternatives. The key idea behind SDP is to sequence models of increasing fidelity to provide sequentially tighter bounds on the decision criteria thereby removing inefficient designs from the tradespace with the guarantee that the antecedent model only removes design solutions that are dominated when analyzed using the more detailed, high-fidelity model. In general, efficiency in the SDP is achieved by using less expensive (low-fidelity) models early in the design process, before using high-fidelity models later on in the process. However, the set of multi-fidelity models and discrete decision states result in a combinatorial combination of model sequences, some of which require significantly fewer model evaluations than others. Unfortunately, the optimal modeling policy can not be determined at the onset of the SDP because the computational costs of executing all models on all designs and the discriminatory power of the resulting bounds are unknown. In this paper, the model selection problem is formulated as a finite Markov decision process (MDP) and an online reinforcement learning (RL) algorithm, namely, Q-learning, is used to obtain and follow an approximately optimal modeling policy, thereby overcoming the optimal modeling policy limitation of the current SDP. The outcome is a Reinforcement Learning based Design (RL-D) methodology able to learn efficient sequencing of models from sample estimates of the computational cost and discriminatory power of different models while analyzing design alternatives in the tradespace throughout the design process. Through application to two different design examples, the RL-D is shown to (1) effectively identify the approximate optimal modeling policy and (2) efficiently converge upon a choice set.

     

高超声速飞行器有限时间饱和跟踪控制

针对高超声速飞行器纵向模型存在外界干扰和模型参数不确定性情形下的有限时间跟踪问题进行了研究分析.针对外界干扰上界已知,基于快速积分滑模理论,设计了有限时间快速积分滑模控制器.当外界干扰上界未知时,结合具有低通滤波器性能的自适应算法,通过引入辅助系统设计了实际有限时间自适应快速积分滑模控制器,能够处理输入饱和问题.对所设计的两个控制器利用李雅普诺夫理论给出了严格理论证明,得到整个闭环系统分别为有限时间稳定的、实际有限时间稳定的,并能够保证系统其它状态变量在较短的时间内趋于稳态值.对不同类型参考信号进行了数字仿真,进一步验证了所设计两个控制器的有效性和鲁棒性.     

Decentralised adaptive neural connectively finite-time control for a class of p-normal form large-scale nonlinear systems

ABSTRACT

This paper focuses on the decentralised adaptive finite-time connective stabilisation problem for a class of p-normal form large-scale nonlinear systems at the first. By combining the adding a power integrator technique, the neural network technique and the finite-time Lyapunov stability theory, the decentralised adaptive neural finite-time controllers are designed, which can guarantee the large-scale system is finite-time connectively stable. In order to avoid the effect of neural network estimation error on satisfying the finite-time criteria, the combination vectors are composed by the weights and the estimation errors of the neural networks. The maximal upper bounds of the combination vector norms are taken as the adaptive parameters. Because of employing neural networks, the restriction of the unknown nonlinear terms in some literature about finite-time control is relaxed. Two simulation examples are provided to prove the effectiveness and advantage of the proposed control method.     

Event-triggered-based finite-time cooperative path following control for underactuated multiple marine surface vehicles

This paper develops an event-triggered-based finite-time cooperative path following (CPF) control scheme for underactuated marine surface vehicles (MSVs) with model parameter uncertainties and unknown ocean disturbances. First, a finite-time extended state observer (FTESO) is proposed, in which the FTESO can estimate the velocities and compound disturbances in finite time. Then, the finite-time LOS guidance law based on velocity estimation values is designed to obtain the desired surge velocity and the desired yaw rate. In order to realize the cooperative control of multiple paths in finite time, the cooperative control law for the path variable is designed. In addition, the relative threshold event-triggered control (ETC) mechanism is incorporated into the formation control algorithm, and an event-triggered-based finite-time CPF controller is designed, which not only effectively reduces the update frequency of controller and the mechanical loss of actuator but also improves the control performance of system. Furthermore, by using homogeneous method, Lyapunov theory, and finite-time stability theory, it is proved that under the proposed finite-time CPF control scheme, the formation errors can converge to a small neighborhood around origin in finite time. Finally, numerical simulation results illustrate the effectiveness of the proposed control scheme.     

A novel adaptive high-order sliding mode control based on integral sliding mode

This paper presents an adaptive high-order sliding mode control scheme targeting for uncertain minimum phase nonlinear single-input-single-output (SISO) systems, which can be equivalently formulated as the finite-time stabilization of high-order input-output dynamics subject to the uncertainties of parameters such as a chain of integrators. The proposed controller is derived from the concept of integral sliding mode and consists of two parts, one part of which achieves the finite-time stabilization of the high-order input-output dynamics without uncertainties by solving a finite-horizon optimal control problem with a free-final-state. The other part adopts the adaptive sliding mode control technique considering the practical bounded uncertainties, by which a modified switching gain adaptation algorithm is developed so that the on-line switching gain selection can be executed and the upper bounds of the uncertainties are not requisite in advance. As a result, a high-order sliding mode is established, ensuring the sliding variables and its high-order derivatives converge to an arbitrarily small vicinity of the origin in finite time. Therefore, the proposed controller achieves fixed convergence time and further improves strong robustness against bounded uncertainties with lower chattering and the easy implementation. Simulation results are presented in detail to verify the effectiveness and feasibility of the proposed algorithm.