Fuzzy set based multiobjective allocation of resources and its applications

AbstractThis paper presents results of research into the use of the Bellman-Zadeh approach to decision making in a fuzzy environment for solving multiobjective optimization problems. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. The use of the Bellman-Zadeh approach has served as a basis for solving a problem of multiobjective allocation of resources (or their shortages) and developing a corresponding adaptive interactive decision-making system (AIDMS1). Its calculating kernel permits one to solve maxmin problems using an algorithm based on a nonlocal search (modification of the Gelfand's and Tsetlin's “long valley” method). The AIDMS1 includes procedures for considering linguistic variables to reflect conditions that are difficult to formalize as well as procedures for constructing and correcting vectors of importance factors for goals. The use of these procedures permits one to realize an adaptive approach to processing information of a decision maker to provide successive improving of the solution quality. C++ windows of the AIDMS1 are presented for input, output, and special possibilities related to considering linguistic variables and constructing and correcting vectors of importance factors. The results of the paper are universally applicable and are already being used to solve power engineering problems

ℋ∞ And ℋ2 Guaranteed Costs Computation For Uncertain Linear Systems

This paper proposes an LMIs characterization of guaranteed ℋ∞ and ℋ2 norms costs for linear systems with convex bounded parameter uncertainties. Both continuous-time and discrete-time systems are addressed.282183188Boyd, S., Balakrishnan, V., A regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its ℒ∞ norm (1990) System Control Letters, 15, pp. 1-7Boyd, S., El-Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities in System and Control Theory, , Philadelphia, Pennsylvania, U.S.A.: SIAMBruinsman, N.A., Steinbuch, M., A fast algorithm to compute the ℋ∞ norm of a transfer function matrix (1990) System Control Letters, 14, pp. 287-293Chang, B.C., Li, X.P., Yeh, H.H., Banda, S.S., Computation of the ℋ∞ norm of a transfer function (1990) Proceedings of the American Control Conference, pp. 2578-2582. , San Diego, California, U.S.AConsiglio, A., How to control stock markets (1994) International Journal of Systems Science, 25, pp. 2245-2253Doyle, J.C., Glover, K., Khargonekar, P.P., Francis, B.A., State-space solutions to standard ℋ2 and ℋ∞ control problems (1989) IEEE Transactions on Automatic Control, 34, pp. 831-847Geromel, J.C., Peres, P.L.D., Souza, S.R., ℋ2 guaranteed cost control for uncertain continuous-time linear systems (1992) System Control Letters, 19, pp. 23-27ℋ2 guaranteed cost control for uncertain discrete-time linear systems (1993) International Journal of Control, 57, pp. 853-864ℋ∞ control of discrete-time uncertain systems (1994) IEEE Transactions on Automatic Control, 39, pp. 1072-1075A convex approach to the mixed ℋ2/ℋ∞ control problem for discrete-time uncertain systems (1995) SIAM Journal on Control Optimization, 33, pp. 1816-1833Hinrichsen, D., Kelb, B., Linnemann, A., An algorithm for the computation of the structured complex stability radius (1989) Automatica, 25, pp. 771-775Kavranoglu, D., ℋ∞ norm approximation of systems by constant matrices and related results (1994) IEEE Transactions on Automatic Control, 39, pp. 1006-1009Khargonekar, P.P., Rotea, M.A., Mixed ℋ2/ℋ∞ control: A convex optimization approach (1991) IEEE Transactions on Automatic Control, 36, pp. 824-837Peres, P.L.D., Geromel, J.C., Souza, S.R., ℋ∞ guaranteed cost control for uncertain continuous time linear systems (1993) System Control Letters, 20, pp. 413-418ℋ∞ control design by static output feedback (1994) IFAC Symposium on Robust Control Design, pp. 243-248. , Rio de Janeiro, BrazilRobel, G., On computing the infinity norm (1989) IEEE Transactions on Automatic Control, 34, pp. 882-884Zhou, K., Khargonekar, P.P., Stoustrup, J., Niemann, H.H., Robust performance of systems with structured uncertainties in state space (1995) Automatica, 31, pp. 249-25

Relating Two State Feedback H∞ Control Approaches

In this paper, two different approaches to the H∞ control by state feedback are related and discussed. The first approach is based on the solvability of an algebraic Riccati equation and the second one explores the convexity of the set defined by a matrix inequality. New insights are provided in order to establish the relationship between the set of stabilizing gains obtained from the two different approaches. The results are illustrated through two examples.92778