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An interactive fuzzy satisficing method for multiobjective optimal control problems in linear distributed-parameter systems

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FUZZY SETS AND systems 1999年第2期102卷 237-246页

作者： Sakawa, M Inuiguchi, M Kato, K Ikeda, T Hiroshima Univ Fac Engn Dept Ind & Syst Engn Higashihiroshima 739 Japan

In this paper, we propose an interactive fuzzy satisficing method for the solution of a multiobjective optimal control problem in a linear distributed-parameter system governed by a heat conduction equation. In order to reduce the control problem of this distributed-parameter system to an approximate multiobjective linear programming problem, we use a numerical integration formula and introduced the suitable auxiliary variables. By considering the vague nature of human judgements, we assume that the decision maker may have fuzzy goals for the objective functions. Having elicited the corresponding linear membership functions through the interaction with the decision maker, if the decision maker specifies the reference membership values, the corresponding Pareto optimal solution can be obtained by solving the minimax problems. Then a linear programming-based interactive fuzzy satisficing method for deriving a satisficing solution for the decision maker efficiently from a Pareto optimal solution set is presented. An illustrative numerical example is worked out to indicate the efficiency of the proposed method. (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： linear distributed-parameter systems multiobjective optimal control multiobjective linear programming fuzzy programming fuzzy goals fuzzy satisficing methods

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Parametric approach to the decoupling of linear distributed-parameter systems

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IET CONTROL THEORY AND APPLICATIONS 2010年第12期4卷 2855-2866页

作者： Deutscher, J. Harkort, C. Univ Erlangen Nurnberg Lehrstuhl Regelungstech D-91058 Erlangen Germany

In this study the input-output decoupling of linear distributed-parameter systems with distributed control and distributed measurement is considered. The decoupling problem is formulated as an eigenstructure assignment problem for distributed-parameter systems, which is solved using the parametric approach. The resulting static state feedback controller exponentially stabilises the closed-loop system and decouples the reference transfer behaviour with respect to the first p dominant closed-loop modal states. The residual dynamics are taken into account by compensating further dominant eigenvalues with transmission zeros, so that they do not influence the reference transfer behaviour. A heat conductor is used to demonstrate the design procedure which is also compared with an early lumping approach.

关键词： input output decoupling distributed measurement parametric approach distributed control closed-loop system eigenstructure assignment linear distributed-parameter systems Control system analysis and synthesis methods decentralised control decoupling problem Multivariable control systems eigenstructure assignment problem linear distributed parameter systems closed loop systems

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Backstepping Design of Robust Output Feedback Regulators for Boundary Controlled Parabolic PDEs

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2016年第8期61卷 2288-2294页

作者： Deutscher, Joachim Univ Erlangen Nurnberg Lehrstuhl Regelungstech D-91058 Erlangen Germany

In this article a backstepping-based solution of the robust output regulation problem for boundary controlled parabolic PDEs with spatially varying parameters is presented. This is achieved by stabilizing the plant extended with a finite-dimensional internal model of the exogenous signals. For the resulting PDE-ODE system with spatially varying parameters a systematic backstepping-based compensator design method is developed. The robustness of the achieved output regulation is verified for non-destabilizing model uncertainties. An uncertain parabolic system illustrates the results of the article.

关键词： Backstepping boundary control linear distributed-parameter systems parabolic systems robust output regulation

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Fourier spectral methods for numerical solving the problem of boundary control of the linear wave equation

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AIN SHAMS ENGINEERING JOURNAL 2017年第3期8卷 333-339页

作者： Zarei, Hassan Payame Noor Univ Dept Math Tehran Iran

In this paper, a Fourier spectral method is used to reduce the optimal boundary control problem for a two-dimensional wave equation to a countable number of control problems for a one-dimensional wave equation which are transformed to the optimal control problems with integral constraints using the Laplace transform. The numerical integration and differentiation methods are used to approximate the resulting problems with quadratic programming problems. An illustrative numerical example is presented to indicate the efficiency of the proposed method. (C) 2015 Ain Shams University. Production and hosting by Elsevier B.V.

关键词： Fourier spectral method linear distributed-parameter systems Optimal control Laplace transform Quadratic programming

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Structure-preserving approximation of distributed-parameter second-order systems using Krylov subspaces

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MATHEMATICAL AND COMPUTER MODELLING OF DYNAMICAL systems 2014年第4期20卷 395-413页

作者： Deutscher, J. Harkort, Ch Univ Erlangen Nurnberg Lehrstuhl Regelungstech D-91058 Erlangen Germany

In this article, the approximation of linear second-order distributed-parameter systems (DPS) is considered using a Galerkin approach. The resulting finite-dimensional approximation model also has a second-order structure and preserves the stability as well as the passivity. Furthermore, by extending the Krylov subspace methods for finite-dimensional systems of second order to DPS, the basis vectors of the Galerkin projection are determined such that the transfer behaviour of the DPS can be approximated by using moment matching. The structure-preserving approximation of an Euler-Bernoulli beam with Kelvin-Voigt damping demonstrates the results of the article.

关键词： Galerkin approach moment matching Krylov subspace methods second-order systems structure preservation linear distributed-parameter systems

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Multiobjective optimal control of the linear wave equation

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AIN SHAMS ENGINEERING JOURNAL 2014年第4期5卷 1299-1305页

作者： Zarei, Hassan Bahrmand, Mehdi Rezai Payame Noor Univ Dept Math Tehran Iran

In this paper, we propose a method for the solution of a multiobjective optimal control problem (MOOCP) in a linear distributed-parameter system governed by a wave equation. An explicit solution for the wave equation is derived and the control problem of this distributedparameter system is reduced to an approximate multiobjective programming problem. The fuzzy goals are incorporated for objectives and the equilibrium problem in terms of maximization of the degree of attainment for the aggregated fuzzy goals is considered. The solution of the equilibrium optimization problem is a Pareto optimal solution with the best satisfaction performance which is achieved by using a metaheuristic algorithm such as the simulated annealing (SA) together with the simplex method of linear programming (LP) problems. An illustrative numerical example is presented to indicate the efficiency of the proposed method and the capability of the SA in finding optimal solution compared with two popular metaheurestics. (C) 2014 Production and hosting by Elsevier B. V. on behalf of Ain Shams University.

关键词： linear distributed-parameter systems Multiobjective optimal control Multiobjective programming Fuzzy programming Fuzzy goals Metaheuristic algorithms

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