On H/sub 2/ control of systems with multiple I/O delays

The H/sub 2/ optimal control problem of systems with multiple I/O delays is solved. The problem is tackled by first transforming it to what is called the two-sided regulator problem. The latter is solved using orthogonal projection arguments and spectral factorization. The resulting controller is an interconnection of rational blocks, nonrational blocks having finite impulse response, and delay operators, all of which are implementable.     

Control of systems with I/O delay via reduction to a one-block problem

In this paper, the standard (four-block) H/sup /spl infin// control problem for systems with a single delay in the feedback loop is studied. A simple procedure of the reduction of the problem to an equivalent one-block problem having particularly simple structure is proposed. The one-block problem is then solved by the J-spectral factorization approach, resulting in the so-called dead-time compensator (DTC) form of the controller. The advantages of the proposed procedure are its simplicity, intuitively clear derivation of the DTC form of the H/sup /spl infin// controller, and extensibility to the multiple delay case.     

H2 optimization for systems with adobe input delays: A loop shifting approach

This paper studies the $H^2$ optimization problem for systems with adobe input delay. These are systems having only two (possibly vector) input channels: one is delay free and the other is delayed. We present a solution based on the reduction of the problem to an equivalent delay-free problem via simple loop shifting arguments. This results in a solution based on two standard algebraic Riccati equations, which are associated with the delay-free version of the problem. The optimal controller is in the dead-time compensator form. We also derive an explicit and transparent expression for the cost of delay and (in the case when the problem is solvable without the delayed channel) a numerically stable form of the optimal solution, which includes exponentials of Hurwitz matrices only. The approach is readily extendible to more general multiple input/output delay cases.     

用动态规划法求解延时/面积最小化工艺映射

本文提出了一个求解延时／面积最小化工艺映射动态规划法．它首先基干线性延时模型，给出了用动态规划法求解延时最小化工艺映射的步骤；然后从树型网络的面积计算公式入手，用动态规划法近似计算面积最小化工艺映射；最后用“线性加权和法”把延时／面积最小化工艺映射转变为单目标最优化问题求解．     

On ℋ∞ control for dead-time systems

A mixed sensitivity ℋ_∞ problem is solved for dead-time systems. It is shown that for a given bound on the ℋ_∞-norm causal stabilizing controllers exist that achieve this bound if and only if a related finite-dimensional Riccati equation has a solution with a certain nonsingularity property. In the case of zero time delay, the Riccati equation is a standard Riccati equation and the nonsingularity condition is that the solution be nonnegative definite. For nonzero time delay, the nonsingularity condition is more involved but still allows us to obtain controllers. All suboptimal controllers are parameterized, and the central controller is shown to be a feedback interconnection of a finite-dimensional system and a finite memory system, both of which can be implemented. Some ℋ_∞ problems are rewritten as pure rational ℋ _∞, problems using a Smith predictor parameterization of the controller     

H2 approximation of multiple input/output delay systems

Many physical multivariable processes can be sufficiently described as linear models with multiple input/output delays. To simplify the synthesis and analysis of control problem, a reduced-complexity model is often desired. In this paper, an H₂ model reduction scheme is introduced for stable linear systems with multiple input/output delays. The reduced model can be a finite dimensional linear model, or a linear model with a time delay. In the latter case the approximation can be improved drastically without increasing the order of the finite dimensional part. The stability is preserved in the approximating models by employing a parametrization of linear stable systems. The optimal parameters can be obtained by solving an optimization problem using a gradient-based method. Two chemical numerical examples are used to show the effectiveness of the proposed scheme.     

Formulas on Preview and Delayed H∞ Control

A generalized H^infin control problem, which covers preview and delayed control strategies, is discussed based on a state-space approach. By introducing a Hamiltonian matrix, which is associated with a delay-free generalized plant, the analytic solution to the corresponding operator Riccati equation is newly established. Based on the result obtained here, the H^infin control problem is solved and, for typical control problems (e.g., H^infin and linear quadratic (LQ) control for multiple input delay systems, H^infin preview control), some interpretations are provided on the resulting control system     

Rationalization of singularly perturbed continuous systems with time delays

The state equation of a continuous time system with time delay is nonlinear. Therefore, its transfer function is irrational, which is difficult to solve. However, the transfer function of a discrete time state equation with time delay is rational. Hence, the problem can be solved easily. A rationalization of the singularly perturbed continuous system of single and multiple time delays is presented by setting a delay coefficient. The technique is a powerful tool when solving the singularly perturbed continuous equation with single and multiple time delays instead of when using numerical methods such as the Runge-Kutta algorithm.     

H∞ Estimation for Uncertain Systems With Limited Communication Capacity

This paper investigates the problem of robust H_infin estimation for uncertain systems subject to limited communication capacity. The parameter uncertainty belongs to a given convex polytope and the communication limitations include measurement quantization, signal transmission delay, and data packet dropout, which appear typically in a network environment. The problem of H_infin filter design is first solved for a nominal system subject to the aforementioned information limitations, which is then extended to the uncertain case based on the notion of quadratic stability. To further reduce the overdesign in the quadratic framework, this paper also proposes a parameter-dependent filter design procedure, which is much less conservative than the quadratic approach. The quadratic and parameter-dependent approaches provide alternatives for designing robust H_infin filters with different degrees of conservativeness and computational complexity. Two examples, including a mass-spring system, are utilized to illustrate the design procedures proposed in this paper.     

Dynamic disturbance rejection controllers for neutral time delay systems with application to a central heating system

In the present paper the problem of disturbance rejection of single input-single output neutral time delay systems with multiple measurable disturbances is solved via dynamic controllers. In particular, the general form of the controller matrices is presented, while the necessary and sufficient conditions for the controller to be realizable are offered. The proposed technique is applied to a test case neutral time delay central heating system. In particular, the nonlinear model of the plant and its linearized approximation are presented. Based on the linearized model, a two-stage controller is designed in order to regulate the room temperature and the boiler effluent temperature. The performance of the closed loop system is investigated through computational experiments.     

On the decoupling of multivariable control systems with time delays†

The decoupling problem is solved for an m-input m-output linear time-invariant system with multiple delays in the state and/or the control. The conditions under which such a system can be decoupled are found and the class of the feedback decoupling operators is given. These operators are realized by means of digital filters. Then, the more general linear model in which the input effects directly the output is considered which, upon the introduction of both feedback and feedforward, is shown to be decoupled, Two illustrative examples are included to support the theoretical results.     

Hankel norm approximation for well-posed linear systems

The sub-optimal Hankel norm approximation problem is solved for a well-posed linear system with generating operators (A,B,C) and transfer function G satisfying some mild assumptions. In the special case of the sub-optimal Nehari problem, an explicit parameterization of all solutions is obtained in terms of the system parameters A, B, C and G(0).     

基于遗传算法的一种生物序列比对方法

生物序列比对是对DNA（或RNA,蛋白质）序列,寻找和确定它们的相似部分或稳定区域.二重序列比对问题可采用动态规划方法求得其最优解;多重序列比对问题是一个NP完全的组合优化问题,有待进一步探索与研究.通过合理的编码表示,采用相应的遗传算子,设计了一种求生物序列比对的遗传算法.并对几组DNA序列进行了测试.     

A study on synergy of multiple crossover operators in a hierarchical genetic algorithm applied to structural optimisation

Development of crossover operators is based on three different mechanisms: mating selection mechanism, offspring generation mechanism and offspring selection mechanism. Most crossover operators are able to get exploration or exploitation of the domain depending on the way they handle the current diversity of the population. Each crossover operator directs the search towards a different region in the neighbourhood of the parents. The quality of the elements belonging to the visited region depends on the particular problem to be solved. This is confirmed by the well known No Free Lunch (NFL) theorems. The simultaneous use of diverse crossover operators on the population may induce more efficient algorithms. The aim of this paper is to analyse and to study complementary properties resulting from synergy effects using several crossover operators in particular for a hierarchical genetic algorithm. The reached improvements using multiple crossover operators will be analysed through some standard optimisation examples of hybrid composite structures.     

A fuzzy self-tuning parallel genetic algorithm for optimization

The genetic algorithm (GA) is now a very popular tool for solving optimization problems. Each operator has its special approach route to a solution. For example, a GA using crossover as its major operator arrives at solutions depending on its initial conditions. In other words, a GA with multiple operators should be more robust in global search. However, a multiple operator GA needs a large population size thus taking a huge time for evaluation. We therefore apply fuzzy reasoning to give effective operators more opportunity to search while keeping the overall population size constant. We propose a fuzzy self-tuning parallel genetic algorithm (FPGA) for optimization problems. In our test case FPGA there are four operators—crossover, mutation, sub-exchange, and sub-copy. These operators are modified using the eugenic concept under the assumption that the individuals with higher fitness values have a higher probability of breeding new better individuals. All operators are executed in each generation through parallel processing, but the populations of these operators are decided by fuzzy reasoning. The fuzzy reasoning senses the contributions of these operators, and then decides their population sizes. The contribution of each operator is defined as an accumulative increment of fitness value due to each operator's success in searching. We make the assumption that the operators that give higher contribution are more suitable for the typical optimization problem. The fuzzy reasoning is built under this concept and adjusts the population sizes in each generation. As a test case, a FPGA is applied to the optimization of the fuzzy rule set for a model reference adaptive control system. The simulation results show that the FPGA is better at finding optimal solutions than a traditional GA.     

An adaptive hybrid genetic algorithm for the three-matching problem

This paper presents a hybrid genetic algorithm (GA) with an adaptive application of genetic operators for solving the 3-matching problem (3MP), an NP-complete graph problem. In the 3MP, we search for the partition of a point set into minimal total cost triplets, where the cost of a triplet is the Euclidean length of the minimal spanning tree of the three points. The problem is a special case of grouping and facility location problems. One common problem with GA applied to hard combinatorial optimization, like the 3MP, is to incorporate problem-dependent local search operators into the GA efficiently in order to find high-quality solutions. Small instances of the problem can be solved exactly, but for large problems, we use local optimization. We introduce several general heuristic crossover and local hill-climbing operators, and apply adaptation to choose among them. Our GA combines these operators to form an effective problem solver. It is hybridized as it incorporates local search heuristics, and it is adaptive as the individual recombination/improvement operators are fired according to their online performance. Test results show that this approach gives approximately the same or even slightly better results than our previous, fine tuned GA without adaptation. It is better than a grouping GA for the partitioning considered. The adaptive combination of operators eliminates a large set of parameters, making the method more robust, and it presents a convenient way to build a hybrid problem solver     

On the dead-time compensation from L/sup 1/ perspectives

It is known that both H/sup 2/ and H/sup /spl infin// optimization problems for dead-time systems are solved by controllers having the so-called modified Smith predictor (dead-time compensator) structure. This note shows that this is also true for the L/sup 1/ control problem. More precisely, it is demonstrated that the use of the modified Smith predictor enables one to reduce the standard L/sup 1/ problem for systems with a single loop delay to an equivalent delay-free problem. The (sub)optimal solution therefore always contains the modified Smith predictor.     

Linear quadratic regulation for linear time-varying systems with multiple input delays

This paper studies the classic linear quadratic regulation (LQR) problem for both continuous-time and discrete-time systems with multiple input delays. For discrete-time systems, the LQR problem for systems with single input delay has been studied in existing literature, whereas a solution to the multiple input delay case is not known to our knowledge. For continuous-time systems with multiple input delays, the LQR problem has been tackled via an infinite dimensional system theory approach and a frequency/time domain approach. The objective of the present paper is to give an explicit solution to the LQR problem via a simple and intuitive approach. The main contributions of the paper include a fundamental result of duality between the LQR problem for systems with multiple input delays and a smoothing problem for an associated backward stochastic system. The duality allows us to obtain a solution to the LQR problem via standard projection in linear space. The LQR controller is simply constructed by the solution of one backward Riccati difference (for the discrete-time case) or differential (for the continuous-time case) equation of the same order as the plant (ignoring the delays).     

On equivalence classes of fuzzy connectives-the case of fuzzyintegrals

An equivalence relation between connectives (or operators) in the framework of multiple criteria decision-making is introduced. Two operators are said to be equivalent if they lead to the same ranking of alternatives. Some general results to find equivalence classes of operators are given through the concept of level surfaces. In a second part, these results are applied to the case of discrete fuzzy integrals, which are considered here as n-place operators. First, some general results on the situation of fuzzy integrals among fuzzy operators are given and then the equivalence classes of fuzzy integrals     

基于5G的塔机远程控制系统

在建筑施工现场, 塔式起重机现有的操控方式存在安全风险高、操作人员利用率低等问题. 对此, 提出基于5G MEC的塔机远程控制系统, 能够实现不同地理位置的多台塔机、多个客户端的灵活接入和综合管控. 通过对状态数据、控制数据、媒体流数据的转发控制采用模块化设计及有针对性的策略, 保证了基于5G通讯的低时延在应用层面得以实现, 对于多设备多客户端的分布式远程控制应用具有一定的参考价值.