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2 Systems Science

2 2005

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Membership-set estimation with genetic algorithms in nonlinear models

Herrero J. M., Blasco X., Salcedo J. V., Ramos C.

Systems Science

2005

Vol. 31, no 2

67-76

In this article, a procedure for characterizing the feasible parameter set of nonlinear models with a membership-set uncertainty description is provided. A specific Genetic Algorithm denominated e-GA has been developed, based on Evolutionary Algorithm for Multiobjective Optimization, to find the global minima of the multimodal functions appearing when the robust identification problem is formulated. These global minima define the contour of the feasible parameter set. The procedure makes it possible to obtain the feasible parameter non-convex even disjoint set. It is not necessary for the model to be differentiable with respect to the unknown parameters. An example is presented which determines the feasible parameter set of a nonlinear model of a thermal process. In this case, noise affects the output process (interior temperature) and besides model errors appear.

LQR and predictive control tuned via BDU

Ramos C., Sanchis J., Martinez M., Herrero J. M.

Systems Science

2005

Vol. 31, no 1

15-25

This work presents the BDU technique (Bounded Data Uncertainties) and the tuning of the linear quadratic regulator (LQR) via this technique, which considers models with bounded uncertainties. The BDU method is based on constrained game-type formulations, and allows the designer to explicitly incorporate a priori information about bounds on the sizes of the uncertainties into the problem statement. Thus, on the one hand, the uncertainty effect is not over-emphasized, avoiding an overly conservative design and, on the other hand, the uncertainty effect is not under-emphasized, avoiding an overly sensitive to errors design. A feature of this technique consists of its geometric interpretation. The structure of the paper is the following, in the first section, some problems about the least-squares method in the presence of uncertainty are introduced. The BDU technique is shown in the second section and the LQR controller in the third. After that a new guided way of tuning the LQR is offered, taking into account the uncertainties bounds via the BDU. The consequence of this method is that both recursive and algebraic Riccati equations are modified. Finally, some examples are shown and the main conclusions and future work are commented.