Nonlinear Design Problem Research Articles

A non‐linear fin design problem in determining the optimum shape of spine and longitudinal fins

AbstractA non‐linear fin design algorithm is applied to estimate the optimum shapes for the spine and longitudinal fins by using the conjugate gradient method (CGM) based on the desired fin efficiency and fin volume. One of the advantages in using CGM in the inverse design problem lies in that it can handle problems having a large number of unknown parameters easily and converges very fast.The validity of the present algorithm by using the CGM to solve the non‐linear fin design problem is justified based on numerical experiments. Results show that the optimum fin shapes can always be obtained. Copyright © 2003 John Wiley & Sons, Ltd.

전역근사화 반응표면의 생성을 위한 퍼지모델링 및 퍼지규칙의 생성

진화퍼지모델링은 퍼지추론시스템과 진화연산의 장점을 결합한 모델링 방법으로써 전역근사최적화를 수행한다. 본 논문에서는 진화퍼지모델링의 가장 중요한 과정 중 하나인 퍼지규칙의 생성방법으로써 퍼지클러스터링을 제안한다. 퍼지클러스터링을 실험 혹은 시뮬레이션의 결과에 적용함으로써, 비선형성이 강하고 복잡한 설계문제를 적절하게 묘사할 수 있는 퍼지 규칙을 생성할 수 있다. 퍼지클러스터링의 결과로 얻어지는 클러스터에 대한 실험치의 소속정도를 활용하여 진화퍼지모델링의 효율을 향상시킬 수 있다. 제안된 방법의 유효성을 검증하기 위해 실제 자동차 내장재에 설계문제를 선정하여 전역근사화를 수행하였다. 클러스터 수와 퍼지규칙의 선택과 관련하여 여러 다양한 경우에 대해서 진화퍼지모델링을 수행하여 그 결과를 비교하였고 이를 통하여 제안된 방법이 시스템을 묘사하는 적절한 퍼지규칙을 생성하고 모델링의 오차를 만족할 만한 수준으로 유지하면서 계산시간을 줄일 수 있음을 확인하였다. As a modeling method where the merits of fuzzy inference system and evolutionary computation are put together, evolutionary fuzzy modeling performs global approximate optimization. The paper proposes fuzzy clustering as fuzzy rule generation process which is one of the most important steps in evolutionary fuzzy modeling. With application of fuzzy clustering into the experiment or simulation results, fuzzy rules which properly describe non-linear and complex design problem can be obtained. The efficiency of evolutionary fuzzy modeling can be improved utilizing the membership degrees of data to clusters from the results of fuzzy clustering. To ensure the validity of the proposed method, the real design problem of an automotive inner trim is applied and the global approximation is achieved. Evolutionary fuzzy modeling is performed for several cases which differ in the number of clusters and the criterion of rule selection and their results are compared to prove that the proposed method can provide proper fuzzy rules for a given system and reduce computation time while maintaining the errors of modeling as a satisfactory level.

Nonlinear adaptive control of master–slave system in teleoperation

This paper is devoted to the nonlinear control design problem to achieve stability of master–slave manipulators in teleoperation system and its transparency in the sense of motion/force tracking. Nonlinear adaptive controllers are bilaterally designed for both master and slave sites to guarantee the stability of whole system and motion tracking performance. Global boundedness of the overall adaptive system and asymptotic motion (velocity/position) tracking are established. Especially, the concept of “virtual master manipulator” is introduced to increase degree of freedom of control design for force tracking performance. The resulting force tracking error depends only on the acceleration of the designed virtual master manipulator. Accurate dynamic parameters of manipulators, their acceleration information as well as models of human operator and environment are not required in the control design. Another important feature of our approach is the relaxation for the trade-off between motion and force tracking performances.

On designing observers for time-delay systems with non-linear disturbances

In this paper, the observer design problem is studied for a class of time-delay non-linear systems. The system under consideration is subject to delayed state and non-linear disturbances. The time-delay is allowed to be time-varying, and the non-linearities are assumed to satisfy global Lipschitz conditions. The problem addressed is the design of state observers such that, for the admissible time-delay as well as non-linear disturbances, the dynamics of the observation error is globally exponentially stable. An effective algebraic matrix inequality approach is developed to solve the non-linear observer design problem. Specifically, some conditions for the existence of the desired observers are derived, and an explicit expression of desired observers is given in terms of some free parameters. A simulation example is included to illustrate the practical applicability of the proposed theory.

Relay Based Gain and Phase Margins Iterative PID Controller Design

In this paper it is addressed the problem of achieving gain and phase margin specifications on a closed loop system with a PID controller. The nonlinear design problem is solved iteratively using relay feedback experiments to estimate the gain and phase margin at each iteration. The relay tests are fast and easy to perform, which makes the procedure suitable for industrial applications. The iterative scheme is illustrated with simulation examples using desired gain and phase margin specifications.

Reduced-Order Nonlinear Discrete-Time Observer Design Using Functional Equations

The present research work proposes a new approach to the reduced-order nonlinear discrete-time observer design problem. Based on the early ideas that influenced the development of the linear Luenberger observer, the proposed approach develops a nonlinear analogue. The formulation of the reduced-order nonlinear discrete-time observer design problem is realized via a system of first-order linear nonhomogeneous functional equations, and a rather general set of necessary and sufficient conditions for solvability is derived using results from functional equations theory. The solution to the above system of functional equations can be proven to be locally analytic and this enables the development of a series solution method, that is easily programmable with the aid of a symbolic software package.

Discrete-time nonlinear observer design using functional equations

The present research work proposes a new approach to the discrete-time nonlinear observer design problem. Based on the early ideas that influenced the development of the linear Luenberger observer, the proposed approach develops a nonlinear analogue. The formulation of the discrete-time nonlinear observer design problem is realized via a system of first-order linear nonhomogeneous functional equations, and a rather general set of necessary and sufficient conditions for solvability is derived using results from functional equations theory. The solution to the above system of functional equations can be proven to be locally analytic and this enables the development of a series solution method, that is easily programmable with the aid of a symbolic software package.

Genetic algorithm approach to fixed-order mixed H/sub 2//H/sub /spl infin/#x221E;/ optimal deconvolution filter designs

The mixed H/sub 2//H/sub /spl infin// optimal deconvolution filter is proposed to achieve the H/sub 2/ optimal reconstruction and a desired robustness against the effect of uncertainties in signal processing from the H/sub /spl infin// norm perspective. However, the conventional mixed H/sub 2//H/sub /spl infin// optimal design filters are very complicated and are not practical for industrial applications. For simplicity of implementation and conservation of operation time, the fixed-order mixed H/sub 2//H/sub /spl infin// optimal deconvolution filter design is interesting for engineers in signal processing from the practical design perspective. In this study, to avoid the trap of local minima, a design method based on the genetic algorithm is introduced to treat the nonlinear optimization design problem of the fixed-order mixed H/sub 2//H/sub /spl infin// deconvolution filter. The convergence property of our design algorithm is also discussed. Finally, an example is presented to illustrate the design procedure and confirm the robustness performance of the proposed method.

Optimal configuration design of structures using the binary enumeration technique

This paper presents an optimization methodology for the design of structural members. The objective is to develop a fully stressed design while satisfying constraints on the maximum stress value and maintenance of the connectivity of finite elements in the model. This work is based on altering the finite element model of structure by removing or keeping elements in the discretized design. Such a problem is categorized into a large-scale, non-convex and non-linear discrete problem. Thus, it can have many local optimum solutions and it is important to develop methodologies that find global optimum solutions as opposed to local. In this study, to solve the problem, a discrete optimization technique based on enumeration method is used. To improve the computational efficiency, the non-linear design problem has been linearized. An error intensity analysis is implemented to account for the difference between the non-linear and the linearized values. To illustrate the approach, several design examples are presented and examined.

On the Connections Between Stabilization, Network Routing and Receding Horizon Optimal Control Problems

The paper is devoted to a general nonlinear regulator design problem. In this context some connections between discrete version of the receding horizon control problem and the generalized network routing problem are considered. Except “standard” definition of the Lyapunov function with the help of the Bellman optimal cost-to-go function, it is shown, that the optimizing mapping corresponds to the Bellman-Ford routing algorithm. As such, it can be implemented asynchronously, e.g. in a Hopfield type neural network. The obtained routing tables will be control rules of an optimal receding horizon regulator. At the end some results of the application of this approach to an inverted pendulum control problem are presented.

Nonlinear observer design using Lyapunov’s auxiliary theorem

The present work proposes a new approach to the nonlinear observer design problem. Based on the early ideas that influenced the development of the linear Luenberger observer theory, the proposed approach develops a nonlinear analogue. The formulation of the observer design problem is realized via a system of singular first-order linear PDEs, and a rather general set of necessary and sufficient conditions for solvability is derived by using Lyapunov’s auxiliary theorem. The solution to the above system of PDEs is locally analytic and this enables the development of a series solution method, that is easily programmable with the aid of a symbolic software package.

Buffer allocation for an integer nonlinear network design problem

The Buffer Allocation Problem (BAP) is a nonlinear, multi-objective one in integer variables and there exists no closed-form solution for the objective function. An efficient and effective search methodology is utilized to generate sub-optimal solutions to the problem for series, merge, and split topologies with M/M/C/K queueing stations. Computational results demonstrate the effectiveness of this search methodology.

The Equivalence of Constrained and Weighted Designs in Multiple Objective Design Problems

Abstract Several competing objectives may be relevant in the design of an experiment. The competing objectives may not be easy to characterize in a single optimality criterion. One approach to these design problems has been to weight each criterion and find the design that optimizes the weighted average of the criteria. An alternative approach has been to optimize one criterion subject to constraints on the other criteria. An equivalence theorem is presented for the Bayesian constrained design problem. Equivalence theorems are essential in verifying optimality of proposed designs, especially when (as in most nonlinear design problems) numerical optimization is required. This theorem is used to show that the results of Cook and Wong on the equivalence of the weighted and constrained problems apply much more generally. The results are applied to Bayesian nonlinear design problems with several objectives.

The Equivalence of Constrained and Weighted Designs in Multiple Objective Design Problems

Abstract Several competing objectives may be relevant in the design of an experiment. The competing objectives may not be easy to characterize in a single optimality criterion. One approach to these design problems has been to weight each criterion and find the design that optimizes the weighted average of the criteria. An alternative approach has been to optimize one criterion subject to constraints on the other criteria. An equivalence theorem is presented for the Bayesian constrained design problem. Equivalence theorems are essential in verifying optimality of proposed designs, especially when (as in most nonlinear design problems) numerical optimization is required. This theorem is used to show that the results of Cook and Wong on the equivalence of the weighted and constrained problems apply much more generally. The results are applied to Bayesian nonlinear design problems with several objectives.

Nonlinear Dynamic Ship Positioning

Thruster saturation in high sea states can occur due to lack of thruster power in respond to low frequency or high frequency sea disturbances. This can lead to inaccuracy in ship positions and possible control loop instability. Using the Single Input Describing Function (SDDF) to convert the static nonlinear elements into a quasi-linear system, robust control design techniques such as H∞ and μ. Methods are extended to the nonlinear control design problems to incorporate the thruster nonlinear dynamics. Based on the SIDF approximation, the inverse SIDF compensation is also used to cancel the dominant non-linearities. The remnant of the nonlinear effects can then be included in the controller robustness requirement. These methods are then compared with the case where the nonlinear elements can be replaced by a unity linear element. Simulation studies for a Ship Dynamic Positioning System are presented to compare the robustness of the proposed methods.

Investment Selection Model for Multicommodity Multimodal Transportation Networks

A Multicommodity Multimodal Network Design (MCMND) model is presented; the model is to be used as a planning tool for determining investment priorities for freight intercity networks. The MCMND model is designed to select the best set of investment options for a multimodal regional network, given a limited investment budget. The main component of the model comprises the solution of a nonlinear bilevel network design problem formulated to choose investments that minimize both the transportation costs incurred by users and the environmental impacts of less efficient modes of transportation. Investment options to be considered by the model involve the addition of new physical links to the network, the improvement of existing links, and the location of intermodal transfer facilities at specified nodes of the network. The representation of the multimodal network is at a level of detail appropriate for strategic planning for a large region. The demand for transportation services is fixed and exogenous to the mo...

Investment Selection Model for Multicommodity Multimodal Transportation Networks

A Multicommodity Multimodal Network Design (MCMND) model is presented; the model is to be used as a planning tool for determining investment priorities for freight intercity networks. The MCMND model is designed to select the best set of investment options for a multimodal regional network, given a limited investment budget. The main component of the model comprises the solution of a nonlinear bilevel network design problem formulated to choose investments that minimize both the transportation costs incurred by users and the environmental impacts of less efficient modes of transportation. Investment options to be considered by the model involve the addition of new physical links to the network, the improvement of existing links, and the location of intermodal transfer facilities at specified nodes of the network. The representation of the multimodal network is at a level of detail appropriate for strategic planning for a large region. The demand for transportation services is fixed and exogenous to the model. Mode choice in shipping freight is modeled in combination with flow assignment, assuming that goods are shipped at minimum total generalized costs. A new path-based stochastic user equilibrium assignment algorithm is proposed to distribute trips over the multimodal network according to a logit-type model. The Tietê-Paraná Valley in Brazil was selected for the development of a pilot application of the MCMND model to assess its efficiency when dealing with large networks. This application also served to emphasize the importance of an interface between the MCMND model and a geographic information system in solving real-life problems.

Bayesian Experimental Design: A Review

This paper reviews the literature on Bayesian experimental design. A unified view of this topic is presented, based on a decision-theoretic approach. This framework casts criteria from the Bayesian literature of design as part of a single coherent approach. The decision-theoretic structure incorporates both linear and nonlinear design problems and it suggests possible new directions to the experimental design problem, motivated by the use of new utility functions. We show that, in some special cases of linear design problems, Bayesian solutions change in a sensible way when the prior distribution and the utility function are modified to allow for the specific structure of the experiment. The decision-theoretic approach also gives a mathematical justification for selecting the appropriate optimality criterion.

Remarks on linearization of discrete-time autonomous systems and nonlinear observer design

This paper presents necessary and sufficient conditions under which a discrete-time autonomous system with outputs is locally state equivalent to an observable linear system or a system in the nonlinear observer form (Krener and Isidori, 1983). In particular, an open problem raised in Lee and Nam (1991), namely the observer linearization problem, is solved for a nonlinear system which may not be invertible (i.e., the mapping f may not be a local diffeomorphism ). As a consequence, the nonlinear observer design problem is solved by means of exact linearization techniques.

Optimal Bayesian Design of Experiments for the One-Way Random Effects Model

Since variance components are nonlinear parameters in a linear model, classical optimal designs for estimating variance components in the one-way random effects model depend on the values of the parameters. Optimal Bayesian designs are derived for the more realistic situation of unknown parameters, using the Fisher information of the variance components as a basis for comparing the designs. Balanced designs, in which the same number of measurements are taken on each unit, are shown to be optimal under various criteria for wide classes of priors in the one-way random effects model. In contrast to other nonlinear design problems, the number of support points for the design does not necessarily increase with increasingly vague prior information. Some design criteria that work well for other nonlinear design problems, such as D-optimality, do not give intuitively appealing designs for estimating variance components.