A linearization algorithm for optimizing control systems subject to singular value inequalities

The design of feedback linear multivariable systems subject to inequality constraints frequently leads to nonlinear programming problems involving singular values of matrix transfer functions. We present a readily implementable and globally convergent algorithm for solving such problems. It exploits the structure inherent in singular values differently than do other existing methods.     

An exact penalty function algorithm for solving general constrained parameter optimization problems

An exact penalty function type of algorithm is proposed to solve a general class of constrained parameter optimization problems. The proposed algorithm has the property that any solution obtained by it will always satisfy the problem constraints, and that it will obtain a solution to the constrained problem, within a given specified tolerance, by solving a single unconstrained problem, i.e. it is not necessary to solve a sequence of unconstrained optimization problems. The algorithm applies a modification of Rosenbrock's (Rosenbrock, 1960) polynomial boundary penalty function, and a negative exponential penalty function with moving parameters, to modify the objective function in the neighborhood of the constrained region; a robust unconstrained algorithm (Davison and Wong, 1975) is then used to solve the resulting unconstrained optimization problem. Some standard test functions are included to show the performance of the algorithhm. Application of the algorithm is then made to solve some computer-aided design problems occurring in the area of control system synthesis.     

A new approach for solving singular systems in topology optimization using Krylov subspace methods

In topology optimization, elements without any contribution to the improvement of the objective function vanish by decrease of density of the design parameter. This easily causes a singular stiffness matrix. To avoid the numerical breakdown caused by this singularity, conventional optimization techniques employ additional procedures. These additional procedures, however, raise some problems. On the other hand, convergence of Krylov subspace methods for singular systems have been studied recently. Through subsequent studies, it has been revealed that the conjugate gradient method (CGM) does not converge to the local optimal solution in some singular systems but in those satisfying certain condition, while the conjugate residual method (CRM) yields converged solutions in any singular systems. In this article, we show that a local optimal solution for topology optimization is obtained by using the CRM and the CGM as a solver of the equilibrium equation in the structural analysis, even if the stiffness matrix becomes singular. Moreover, we prove that the CGM, without any additional procedures, realizes convergence to a local optimal solution in that case. Computer simulation shows that the CGM gives almost the same solutions obtained by the CRM in the case of the two-bar truss problem.     

An interval algorithm for multi-objective optimization

This paper presents an interval algorithm for solving multi-objective optimization problems. Similar to other interval optimization techniques, [see Hansen and Walster (2004)], the interval algorithm presented here is guaranteed to capture all solutions, namely all points on the Pareto front. This algorithm is a hybrid method consisting of local gradient-based and global direct comparison components. A series of example problems covering convex, nonconvex, and multimodal Pareto fronts is used to demonstrate the method.     

Polynomial modeling for time-varying systems based on a particle swarm optimization algorithm

In this paper, an effective particle swarm optimization (PSO) is proposed for polynomial models for time varying systems. The basic operations of the proposed PSO are similar to those of the classical PSO except that elements of particles represent arithmetic operations and variables of time-varying models. The performance of the proposed PSO is evaluated by polynomial modeling based on various sets of time-invariant and time-varying data. Results of polynomial modeling in time-varying systems show that the proposed PSO outperforms commonly used modeling methods which have been developed for solving dynamic optimization problems including genetic programming (GP) and dynamic GP. An analysis of the diversity of individuals of populations in the proposed PSO and GP reveals why the proposed PSO obtains better results than those obtained by GP.     

Multi-objective reliability optimization for dissimilar-unit cold-standby systems using a genetic algorithm

A genetic algorithm approach is used to solve a multi-objective discrete reliability optimization problem in a k dissimilar-unit non-repairable cold-standby redundant system. Each unit is composed of a number of independent components with generalized Erlang distributions arranged in a series–parallel configuration. There are multiple component choices with different distribution parameters available for being replaced with each component of the system. The objective of the reliability optimization problem is to select the best components, from the set of available components, to be placed in the standby system in order to minimize the initial purchase cost of the system, maximize the system MTTF (mean time to failure), minimize the system VTTF (variance of time to failure) and also maximize the system reliability at the mission time. Finally, we apply a genetic algorithm with double strings using continuous relaxation based on reference solution updating (GADSCRRSU) to solve this multi-objective problem, using goal attainment formulation. The results are also compared against the results of a discrete-time approximation technique to show the efficiency of the proposed GA approach.     

无线电能传输系统参数优化

无线供电系统中线圈、线圈间互感、补偿电容、谐振频率各个参数之间相互制约、相互影响,系统的设计是一个多参数、多变量的优化问题。以往的参数优化一般是单参数优化而且只优化到互感,并没有优化到具体的匝数,系统设计需要较大修正。为解决此问题,在得到系统的传输功率和效率模型的基础上,利用线圈匝数与自感互感的关系,以PS型拓扑为优化对象,给出了系统的非线性数学规划模型,利用遗传算法得出了系统的最优设计参数。最后,通过实验研究证明了理论分析与设计方法的正确性。     

A simulation optimization approach in production planning of failure prone manufacturing systems

In this paper, the implementation of a new method to control the production rate of manufacturing systems, based on the combination of stochastic optimal control theory, discrete event simulation, experimental design and response surface methodology is outlined. The system under study consists of several parallel machines, multiple-product manufacturing system. Machines are subject to failures and repairs and their capacity process is assumed to be a finite state Markov chain throughout the analytical control model. The problem is to choose the production rates so as to minimize the expected discounted cost of inventory/backlog over an infinite horizon. We first show that, for constant demand rates and exponential failure and repair times distributions of the machines, the hedging point policy is optimal. The structure of the hedging point policy is then parameterized by factors representing the thresholds of involved products. With such a policy, simulation experiments are combined to experimental design and response surface methodology to estimate the optimal control policy. We obtain that the hedging point policy is also applicable to a wide variety of complex problems including non-exponential failure and repair times distributions and random demand rates. Analytical solutions may not be easily obtained for such complex situations.     

Perturbation analysis for production control and optimization of manufacturing systems

We use stochastic fluid models (SFM) to capture the operation of threshold-based production control policies in manufacturing systems without resorting to detailed discrete event models. By applying infinitesimal perturbation analysis (IPA) to a SFM of a workcenter, we derive gradient estimators of throughput and buffer overflow metrics with respect to production control parameters. It is shown that these gradient estimators are unbiased and independent of distributional information of supply and service processes involved. In addition, based on the fact that they can be evaluated using data from the observed actual (discrete event) system, we use them as approximate gradient estimators in simple iterative schemes for adjusting thresholds (hedging points) on line seeking to optimize an objective function that trades off throughput and buffer overflow costs.     

A unified framework for designing textures using energy optimization

A unified framework is proposed for designing textures using energy optimization and deformation. Our interactive scheme has the ability to globally change the visual properties of texture elements, and locally change texture elements with little user interaction. Given a small sample texture, the design process starts with applying a set of global deformation operations (rotation, translation, mirror, scale and flip) to the sample texture to obtain a set of deformed textures automatically. Then we further make the local deformation to the deformed textures interactively by replacing the local-texture elements regions from other textures. By utilizing the energy optimization method, interactive selections and deformations of local-texture elements are accomplished simply through indicating the positions of texture elements very roughly with a brush tool. Finally the deformed textures are further utilized to create large textures with the fast layer-based texture deformation algorithm, and the wavelet-based energy optimization. Our experimental results demonstrate that the proposed approach can help design a large variety of textures from a small example, change the locations of texture elements, increase or decrease the density of texture elements, and design cyclic marbling textures.     

Optimal design of linear control systems by an interactive optimization method

When designing linear control systems, one of the most difficult problems is that the designer almost has no theoretical basis for the determination of proper parameters in order to obtain a system with desired specifications. Poles and directions of eigenvectors in the pole assignment method or weighting matrices of the quadratic criterion function in the optimal regulator method are such parameters. The designer has to determine them by trial-and-error using computer simulation. The purpose of this paper is to propose an approach to helping determine proper parameters in linear control system design by the state space methods. In the case where the desired specifications are not given explicitly, the approach applies an interactive optimization method called the Interactive Simplex method to search the most suitable parameters directly in the parameter space. But, if the specifications are given explicitly, the design problem can be formulated as a multiobjective optimization problem. In this case, weights which indicate relative importance of different specifications are introduced and the Interactive Simplex method is applied in the weight space to indirectly find the most appropriate parameters. The approach is implemented as part of a CAD system. The designer has only to make pairwise comparisons of response curves which are shown on a graphics display terminal in order to obtain the most preferred control system. Two illustrative examples are demonstrated to indicate the efficiency of the approach.     

Integrating linear physical programming within collaborative optimization for multiobjective multidisciplinary design optimization

Multidisciplinary design optimization (MDO) is a concurrent engineering design tool for large-scale, complex systems design that can be affected through the optimal design of several smaller functional units or subsystems. Due to the multiobjective nature of most MDO problems, recent work has focused on formulating the MDO problem to resolve tradeoffs between multiple, conflicting objectives. In this paper, we describe the novel integration of linear physical programming within the collaborative optimization framework, which enables designers to formulate multiple system-level objectives in terms of physically meaningful parameters. The proposed formulation extends our previous multiobjective formulation of collaborative optimization, which uses goal programming at the system and subsystem levels to enable multiple objectives to be considered at both levels during optimization. The proposed framework is demonstrated using a racecar design example that consists of two subsystem level analyses — force and aerodynamics — and incorporates two system-level objectives: (1) minimize lap time and (2) maximize normalized weight distribution. The aerodynamics subsystem also seeks to minimize rearwheel downforce as a secondary objective. The racecar design example is presented in detail to provide a benchmark problem for other researchers. It is solved using the proposed formulation and compared against a traditional formulation without collaborative optimization or linear physical programming. The proposed framework capitalizes on the disciplinary organization encountered during large-scale systems design.     

Mixed L_1/H-infinity control for uncertain linear singular systems

The mixed L1/H-infinity control problem for a class of uncertain linear singular systems is considered using a matrix inequality approach.The purpose is to design a state feedback control law such that the resultant closed-loop system is regular,impulse-free,stable and satisfies some given mixed L1/H-infinity performance.A sufficient condition for the existence of such control law is given in terms of a set of matrix inequalities by the introduction of inescapable set and *-norm.When these matrix inequaliti...     

The scenario approach for systems and control design

The ‘scenario approach’ is an innovative technology that has been introduced to solve convex optimization problems with an infinite number of constraints, a class of problems which often occurs when dealing with uncertainty. This technology relies on random sampling of constraints, and provides a powerful means for solving a variety of design problems in systems and control. The objective of this paper is to illustrate the scenario approach at a tutorial level, focusing mainly on algorithmic aspects. Its versatility and virtues will be pointed out through a number of examples in model reduction, robust and optimal control.     

自愈软件系统设计与实现方法

针对自愈软件系统功能层与自愈层交织带来的设计复杂性问题,提出系统横向模型驱动设计思想,给出一种以故障模型为中心的系统设计与实现方法。该方法能够将系统功能层与自愈层隔离,使它们的设计与实现相对独立,根据系统特点在不同阶段通过故障模型加以耦合,这种松耦合方式有利于降低系统整体设计的复杂性,提高可配置性、可重用性以及可维护性。通过一个具有自愈特性的捷联惯性导航系统仿真软件的设计与实现,验证了该设计思想与方法的可行性和有效性。     

Admissible output consensus control for singular swarm systems

For swarm systems consisting of agents described by high-order linear singular systems, admissible output consensus problems are investigated. By using observability decomposition and eigenvalue decomposition techniques, a sufficient condition for admissible output consensus and a necessary and sufficient condition for admissible limited control energy output consensus are obtained. Furthermore, it is shown that stabilisability of the agents is a sufficient condition for admissible output consensualisability, and an approach to solve the protocol design problem is presented. Finally, a numerical example is provided to demonstrate the effectiveness of protocol design approach.     

Application of multiobjective optimization in aircraft control systems design

Multiobjective optimization techniques are applied in the design of an aircraft lateral control system. A large manned reentry vehicle and a fighter aircraft are considered. An algorithm suggested by Lin's Proper Inequality Constraints method, is implemented in the numerical computation of Pareto-optimal solutions. Subsequently, a trade-off analysis of several Pareto-optimal solutions is conducted.     

一种用于PID控制参数优化的混合果蝇算法

针对果蝇优化算法（ FOA）收敛速度快但寻优精度低的缺点,为了改善果蝇算法的优化性能,提出一种混合果蝇优化算法（ HFOA）。HFOA采用分段优化的思想,在优化过程后期采用收敛稳定性较好的粒子群优化（ PSO）算法优化果蝇算法中果蝇个体飞行距离和味道浓度的判定值,采用误差性能指标积分准则ITAE作为适应度函数,并将优化方案应用于一类不稳定系统的PID控制。Matlab仿真验证表明：HFOA计算高效,具有良好的稳定性,收敛精度高,进而验证了HFOA应用于PID控制参数优化是可行而有效的。     

Free material optimization for stress constraints

Free material design deals with the question of finding the lightest structure subject to one or more given loads when both the distribution of material and the material itself can be freely varied. We additionally consider constraints on local stresses in the optimal structure. We discuss the choice of formulation of the problem and the stress constraints. The chosen formulation leads to a mathematical program with matrix inequality constraints, so-called nonlinear semidefinite program. We present an algorithm that can solve these problems. The algorithm is based on a generalized augmented Lagrangian method. A number of numerical examples demonstrate the effect of stress constraints in free material optimization. Dedicated to Pauli Pedersen on the occasion of his 70th birthday.     

Computer aided design of multivariable nonlinear control systems using frequency domain techniques

The application of frequency domain methods to the study of a class of multivariable nonlinear feedback systems is considered within the context of a comprehensive interactive graphics design procedure and a new computational method is outlined for the determination of limit cycle operation which emphasises the effects of off diagonal system elements. It is shown how compensation can be applied using classical graphical design methods to avoid critical regions in the frequency domain. Two examples of use are given.