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Model predictive control strategy is based on the iterative resolution of a constrained optimization problem. In this context, the feasibility represents a central issue. The present paper concentrates on the use of the invariant sets to guarantee the feasibility of the predictive control law for reference tracking applications. In a first stage, two basic algorithms to approximate the maximal invariant...
Several authors have proposed algorithms for approximate explicit MPC (Bemporad and Filippi, 2003). These algorithms have in common that they develop a stability criterion for approximate explicit MPC that require the approximate cost function to be within a certain distance from the optimal cost function. In this paper, stability is instead ascertained by considering only the cost function of the...
Mining ventilation is an interesting example of a large scale system with high environmental impact where advanced control strategies can bring major improvements. The challenge in this work is focused on the mining ventilation since as much as 50 % or more of the energy consumed by the mining process may go into the ventilation (including heating the air). It is clear that investigating automatic...
This paper considers discrete-time, uncertain piecewise affine (PWA) systems affected by both parameter variations and bounded disturbances. We are interested in the characterization of attainability, understood as the reachability of a state space region, associated to a certain invariance property. Our approach computes in the first stage the maximal set in the state space from which states can...
This papers proposes a novel climate control strategy for mine extraction rooms based on the receding horizon optimal control scheme. Being a model-based procedure, the development of a pertinent prediction model is one of the keystones. According to recent technological advances, we consider that distributed measurements are available and provided by a wireless network. An enhanced modeling approach,...
The paper deals with robust predictive control based on a LMI approach. With respect to the well established case of linear models, with a global polytopic uncertainty, in the present approach the conservativeness reduction is assured by allowing different local descriptions of the uncertainty. The prediction model can thus be interpreted as a multi-model description of the plant to be controlled...
The paper uses an explicit nonlinear control law constructed upon an approximating solution of a constrained finite-time optimal control (CFTOC) problem. The methodology is based on the piecewise affine approximation of a nonlinear models and the exact explicit solution of a multiparametric optimisation problem associated with a model predictive control (MPC) scheme. The technique is applied to a...
This contribution deals with the computational issues encountered in the construction of invariant sets, the presented results being useful in the more general framework of piecewise linear systems. The main contribution of the present paper is the efficient computation of upper and lower bounds of the maximal positive invariant (MPI) sets. These turn to be meaningful approximations when iterative...
This paper is dealing with the receding horizon optimal control techniques having as main goal the reduction of the computational effort inherent to the use of on-line optimization routines. The off-line construction of the explicit solution for the associated multiparametric optimization problems is advocated with a special interest in the presence of nonlinearities in the constraints description...
The present paper deals with the computation of distances between polyhedral sets. The classical reference in this sense is the Hausdorff formulation, but several alternative distance functions can be cited. Their geometrical properties are revisited here together with the induced metrics over this specific class of convex bodies. The genuine goal of the analysis is to clarify which are the reasonable...
The present paper proposes a geometrical approach for the multiparametric linear programs (mp-LP). The interest for this topic is motivated by the need for explicit formulations in the constrained predictive control (with non-quadratic cost indexes). It is shown how the double description of the feasible domains can offer access to the entire family of optimal mappings from the parameters space to...
This paper deals with the control laws based on parametric programming and concentrates on the a posteriori robustification of the resulting piecewise linear laws. The generalized predictive control case is studied, the controller qualities being enhanced by making use of the model arguments (those accounting for the noise influence on the system) as additional degrees of freedom. The technique helps...
The paper considers the discrete time-invariant linear systems affected by input disturbances and construct the explicit description of the constrained generalized predictive control (GPC) law taking in account the constraints existence from the design stage. The explicit formulation of the predictive controllers gives a useful insight on the closed loop capabilities. The GPC is a special case of...
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