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BIBO stabilisation of continuous-time Takagi–Sugeno systems under persistent perturbations and input saturation

Salcedo J. V., Martínez M., García-Nieto S., Hilario A.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 3

457--472

EN

This paper presents a novel approach to the design of fuzzy state feedback controllers for continuous-time non-linear systems with input saturation under persistent perturbations. It is assumed that all the states of the Takagi–Sugeno (TS) fuzzy model representing a non-linear system are measurable. Such controllers achieve bounded input bounded output (BIBO) stabilisation in closed loop based on the computation of inescapable ellipsoids. These ellipsoids are computed with linear matrix inequalities (LMIs) that guarantee stabilisation with input saturation and persistent perturbations. In particular, two kinds of inescapable ellipsoids are computed when solving a multiobjective optimization problem: the maximum volume inescapable ellipsoids contained inside the validity domain of the TS fuzzy model and the smallest inescapable ellipsoids which guarantee a minimum *-norm (upper bound of the 1-norm) of the perturbed system. For every initial point contained in the maximum volume ellipsoid, the closed loop will enter the minimum *-norm ellipsoid after a finite time, and it will remain inside afterwards. Consequently, the designed controllers have a large domain of validity and ensure a small value for the 1-norm of closed loop.

2

Membership-set estimation with genetic algorithms in nonlinear models

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

Systems Science

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2005

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Vol. 31, no 2

67-76

EN

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.

3

GPC in state space with robust observer: constraint satisfaction based on invariant sets

Salcedo J. V., Martinez M., Sanchis J., Blasco F. X.

Systems Science

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2004

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Vol. 30, no 1

77-90

EN

The Generalized Predictive Controller (GPC) [1], [2] belongs to the general class of predictive controllers. The authors have proposed an alternative (although equivalent) formulation for the GPC in state space [7]. This formulation is based on a robust observer [5], and the poles selection is closely related to the controller robustness. An important feature of predictive controllers consists of their ability to take explicitly into account hard constraints in their formulation. However, their design must be accompanied by a guarantee of feasibility. There are some papers which deal with (his problem [4], [9], [8], [3], although all of them suppose that the state of the process can be measured on-line. However, in some cases, the design of the GPC proposed by the authors cannot measure online the process states since they are artificial states, that is to say, not related to physical magnitudes. The authors in paper [6] extend the results of [3] to the GPC in the case where all the states are online measurable. So the state estimation will be presented employing the same ideas of this previous work [6]. When the states have to be observed with the robust observer proposed, the authors show that there appears in the analysis a linear but time varying system perturbed with the error in the initial estimation of states. This initial error belongs to a known and bounded set. The main result states that if it is possible to find a collection of non-empty sets K_j that converge to the maximal robust control invariant set when j increases, the feasibility of GPC control law is guaranteed for all the sampling instants. Finally, this result is verified in a numerical example with a 2 states process.