A. Cepeda

Improved computation of ellipsoidal invariant sets for saturated control systems

In this work, a new technique for the computation of ellipsoidal invariant sets for continuous-time linear systems controlled by a saturating linear control law is presented. New sufficient conditions to guarantee that an ellipsoid is a contractive invariant set for the closed-loop system is presented. The contractive nature of the invariant set ensures asymptotic stability of the controlled system. The main contributions of the paper are the following: the proposed sufficient condition is expressed in form of linear matrix inequalities constraints. The presented method includes (and consequently improves) previous results on this topic. The computational complexity of the proposed approach is analyzed. Illustrative examples are given.

Brief paper: A new concept of invariance for saturated systems

In this paper, the notions of SNS-invariance and SNS-domain of attraction are introduced. The SNS-domain of attraction serves as an estimation of the domain of attraction of a saturated system. It is shown that, in the case of single input saturated systems, any contractive set is contained in the SNS-domain of attraction. Another important characteristic of the SNS-domain of attraction is that it contains any estimation obtained by means of a linear difference inclusion of the saturated system. A simple algorithm that converges to the SNS-domain of attraction is presented. An illustrative example is given.

Estimation of the domain of attraction for saturated discrete-time systems

The domain of attraction of a given non-linear system constitutes a zone of safe operation that can avoid unnecessary operational restrictions. In this paper, an alternative approach to the estimation of the domain of attraction of a saturated linear system is presented. Given a system with m saturated control inputs, we show how to choose a linear difference inclusion (LDI) in such a way that the conservativeness in the estimation is reduced. For that purpose, an LMI problem with 2 m  + m constraints must be solved. In this paper, an algorithm that estimates the domain of attraction of the non-linear system is provided. Moreover, sufficient conditions to guarantee that the proposed algorithm obtains the greatest domain of attraction for the linear difference inclusion are given. Some illustrative examples are presented.

On the Computation of Robust Control Invariant Sets for Piecewise Affine Systems

In this paper, an alternative approach to the computation of control invariant sets for piecewise affine systems is presented. Based on two approximation operators, two algorithms that provide outer and inner approximations of the maximal robust control invariant set are presented. These algorithms can be used to obtain a robust control invariant set for the system. An illustrative example is presented.

A NEW CONCEPT OF INVARIANCE FOR SATURATED SYSTEMS

Abstract In this paper, a new concept of invariance for saturated linear systems is presented. This new notion of invariance, denoted SNS-invariance, has a number of geometrical properties that makes its use suitable for the estimation of the domain of attraction of saturated systems. The notion of SNS-domain of attraction, that serves as an estimation of the domain of attraction of a saturated system, is introduced. It is shown that, in case of single input saturated systems, any contractive set is contained in the SNS-domain of attraction. A simple algorithm that converges to the SNS-domain of attraction is presented. Some illustrative examples are given.

Computation of polyhedral H-invariant sets for saturated systems

In this paper, a unified approach to the estimation of the domain of attraction of a saturated linear system is presented. We show how to choose a linear difference inclusion (LDI) in such a way that the conservativeness in the estimation is reduced. We provide an algorithm that estimates the domain of attraction of the nonlinear system. Under mild assumptions, the proposed algorithm obtains a polyhedral invariant set that equals the maximal domain of attraction for the linear difference inclusion. An alternative approach, that obtains a sequence of invariant sets with a reduced number of constraints, is also proposed.

INPUT VARIABLE SELECTION FOR FORECASTING MODELS

The selection of input variables plays a crucial role when modelling time series. For nonlinear models there are not well developed techniques such as AIC and other criteria that work with linear models. In the case of Short Term Load Forecasting (STLF) generalization is greatly influenced by such selection. In this paper two approaches are compared using real data from a Spanish utility company. The models used are neural networks although the algorithms can be used with other nonlinear models. The experiments show that that input variable selection affects the performance of forecasting models and thus should be treated as a generalization problem.

SYNTHESIS OF ROBUST SATURATED CONTROLLERS: AN SNS-APPROACH

Abstract In this paper, the notion of SNS-domain of attraction is applied to the synthesis of saturated controllers. The notion of SNS-domain was first introduced in the framework of estimation of the domain of attraction of a discrete saturated control system. The main contribution of this paper is an algorithm that allows to obtain a saturated control law for a linear system maximizing the domain of attraction. The parameters of the controller are obtained in such a way that the size of the corresponding polyhedric SNS-domain of attraction is maximized. It is well known that, for single input systems, the greatest ellipsoidal invariant set can be obtained by means of a control law that does not saturate in the corresponding ellipsoidal set. In this paper it is shown how saturated control laws yield to greater domain of attractions when polyhedric invariant sets are considered. That is, the algorithm proposed in this paper provides a controller with a domain of attraction that contains any pre-specified ellipsoidal control invariant set obtained by means of a non saturated control law.