• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.12
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• pp.3053-3060
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• 2000

Alternative formulation is presented for robust optimization problems and an efficient computational scheme for reliability estimation is proposed. Both design variables and design parameters considered as random variables about their nominal values. To ensure the robustness of objective performance a new cost function bounding the performance and a new constraint limiting the performance variation are introduced. The constraint variations are regulated by considering the probability of feasibility. Each probability constraint is transformed into a sub-optimization problem and then is resolved with the modified advanced first order second moment(AFOSM) method for computational efficiency. The proposed robust optimization method has advantages that the mean value and the variation of the performance function are controlled simultaneously and the second order sensitivity information is not required even in case of gradient based optimization. The suggested method is examined by solving three examples and the results are compared with those for deterministic case and those available in literature.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.100-104
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• 1993

In Part 1, we derived robust stability conditions for an LTI interconnected to time-varying nonlinear perturbations belonging to several classes of nonlinearities. These conditions were presented in terms of positive definite solutions to LMI. In this paper we address a problem of synthesizing feedback controllers for linear time-invariant systems under structured time-varying uncertainties, combined with a worst-case H$_{2}$ performance. This problem is introduced in [7, 8, 15, 35] in case of time-invariant uncertainties, where the necessary conditions involve highly coupled linear and nonlinear matrix equations. Such coupled equations are in general difficult to solve. A convex optimization approach will be employed in this synthesis problem in order to avoid solving highly coupled nonlinear matrix equations that commonly arises in multiobjective synthesis problem. Using LMI formulation, this convex optimization problem can in turn be cast as generalized eigenvalue minimization problem, where an attractive algorithm based on the method of centers has been recently introduced to find its solution [30, 361. In the present paper we will restrict our discussion to state feedback case with Popov multipliers. A more general case of output feedback and other types of multipliers will be addressed in a future paper.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.699-717
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• 2012

In this paper, we deal with the robust mixed $H_2/H_{\infty}$ guaranteed-cost control problem involving uncertain neutral stochastic distributed delay systems. More precisely, the aim of this problem is to design a robust mixed $H_2/H_{\infty}$ guaranteed-cost controller such that the close-loop system is stochastic mean-square exponentially stable, and an $H_2$ performance measure upper bound is guaranteed, for a prescribed $H_{\infty}$ attenuation level ${\gamma}$. Therefore, the fast convergence can be fulfilled and the proposed controller is more appealing in engineering practice. Based on the Lyapunov-Krasovskii functional theory, new delay-dependent sufficient criteria are proposed to guarantee the existence of a desired robust mixed $H_2/H_{\infty}$ guaranteed cost controller, which are derived in terms of linear matrix inequalities(LMIs). Furthermore, the design problem of the optimal robust mixed $H_2/H_{\infty}$ guaranteed cost controller, which minimized an $H_2$ performance measure upper bound, is transformed into a convex optimization problem with LMIs constraints. Finally, two simulation examples illustrate the design procedure and verify the expected control performance.

• Structural Engineering and Mechanics
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• v.84 no.4
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• pp.489-502
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• 2022

This paper is aimed at developing an optimization-based Finite Element model updating approach for structural damage identification and quantification. A modal flexibility-based error function is introduced, which uses modal assurance criterion to formulate the updating problem as an optimization problem. Because of the inexplicit input/output relationship between the candidate solutions and the error function's output, a robust and efficient optimization algorithm should be employed to evaluate the solution domain and find the global extremum with high speed and accuracy. This paper proposes a new multi-stage Selective Particle Swarm Optimization (SPSO) algorithm to solve the optimization problem. The proposed multi-stage strategy not only fixes the premature convergence of the original Particle Swarm Optimization (PSO) algorithm, but also increases the speed of the search stage and reduces the corresponding computational costs, without changing or adding extra terms to the algorithm's formulation. Solving the introduced objective function with the proposed multi-stage SPSO leads to a smart feedback-wise and self-adjusting damage detection method, which can effectively assess the health of the structural systems. The performance and precision of the proposed method are verified and benchmarked against the original PSO and some of its most popular variants, including SPSO, DPSO, APSO, and MSPSO. For this purpose, two numerical examples of complex civil engineering structures under different damage patterns are studied. Comparative studies are also carried out to evaluate the performance of the proposed method in the presence of measurement errors. Moreover, the robustness and accuracy of the method are validated by assessing the health of a six-story shear-type building structure tested on a shake table. The obtained results introduced the proposed method as an effective and robust damage detection method even if the first few vibration modes are utilized to form the objective function.

• Korean Journal of Computational Design and Engineering
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• v.14 no.3
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• pp.207-216
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• 2009

Modern engineering design problems involve complexity of disciplinary coupling and difficulty of problem formulation. Multidisciplinary design optimization can overcome the complexity and design optimization software or frameworks can lessen the difficulty. Recently, a growing number of new multidisciplinary design optimization techniques have been proposed. However, each technique has its own pros and cons and it is hard to predict a priori which technique is more efficient than others for a specific problem. In this study, a software system has been developed to directly solve MDO problems with minimal input required. Since the system is based on MATLAB, it can exploit the optimization toolbox which is already developed and proven to be effective and robust. The framework is devised to change an MDO technique to another as the optimization goes on and it is called a reconfigurable MDO framework. Several numerical examples are shown to prove the validity of the reconfiguration idea and its effectiveness.

• International Journal of Control, Automation, and Systems
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• v.2 no.4
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• pp.407-422
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• 2004

A new method for the design of predictive controllers for SISO systems is presented. The proposed technique allows uncertainties and constraints to be concluded in the design of the control law. The goal is to design, at each sample instant, a predictive feedback control law that minimizes a performance measure and guarantees of constraints are satisfied for a set of models that describes the system to be controlled. The predictive controller consists of a finite horizon parametric-optimization problem with an additional constraint over the manipulated variable behavior. This is an end-constraint based approach that ensures the exponential stability of the closed-loop system. The inclusion of this additional constraint, in the on-line optimization algorithm, enables robust stability properties to be demonstrated for the closed-loop system. This is the case even though constraints and disturbances are present. Finally, simulation results are presented using a nonlinear continuous stirred tank reactor model.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.95.2-95
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• 2001

Disturbance observer(DOB) based controller design is one of the most popular methods in the field of motion control. In this paper, a generalized disturbance compensation framework, called as robust internal-loop compensator(RIC) is introduced and an advanced design method of DOB is proposed based on the RIC. Mixed sensitivity optimization problem, which is the main issue of DOB design, is solved through the parameterization of DOB in the RIC framework. Different from conventional methods, Q-filter is separated in the mixed sensitivity optimization problem and the systematic design law for the DOB is proposed. This guarantees the robustness and optimality of the DOB and also enables the design for unstable plants.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.34-39
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• 1991

In this paper, we provide a treatment of the $H^{\infty}$-mixed sensitivity optimization approach to feedback system design. With compromising between the effect of a disturbance at the plant output and the effect of plant perturbations, we propose an algorithm to design robust controller. A $H^{\infty}$-optimization problem is to be equivalent to a Hankel-approximation, this enables the problem to be solved using state-space methods based on balanced realizations.s.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.10
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• pp.1109-1114
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• 2012

The performance of a system can be affected by various variables such as manufacturing tolerances, uncertainties of material properties, and environmental factors acting on the system. Robust design optimization has attracted much attention in the design of products because it can find the best design solution that minimizes the variance of the response while considering the distribution of the variables. However, the computational cost and accuracy of optimization have thus far been a challenging problem. In this study, robust design optimization using the multiplicative decomposition method is proposed in order to solve these problems. Because the proposed method calculates the mean and variance of the system directly from the kriging metamodel using the multiplicative decomposition method, it can be used to search for a robust optimum design accurately and efficiently. Several mathematical and engineering examples are used to demonstrate the feasibility of the proposed method.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1999.10a
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• pp.359-369
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• 1999

The paper describes the study of concurrent subspace optimization(CSSO) for coupled multidisciplinary design optimization (MDO) techniques in mechanical systems. This method is a solution to large scale coupled multidisciplinary system, wherein the original problem is decomposed into a set of smaller, more tractable subproblems. Key elements in CSSO are consisted of global sensitivity equation(GSE), subspace optimization (SSO), optimum sensitivity analysis(OSA), and coordination optimization problem(COP) so as to inquiry valanced design solutions finally, Automatic differentiation has an ability to provide a robust sensitivity solution, and have shown the numerical numerical effectiveness over finite difference schemes wherein the perturbed step size in design variable is required. The present paper will develop the automatic differentiation based concurrent subspace optimization(AD-CSSO) in MDO. An automatic differentiation tool in FORTRAN(ADIFOR) will be employed to evaluate sensitivities. The use of exact function derivatives in GSE, OSA and COP makes Possible to enhance the numerical accuracy during the iterative design process. The paper discusses how much influence on final optimal design compared with traditional all-in-one approach, finite difference based CSSO and AD-CSSO applying coupled design variables.