An Efficient Maximization Algorithm With Implications in Min-Max Predictive Control

n this technical note, an algorithm for binary quadratic programs defined by matrices with band structure is proposed. It was shown in the article by T. Alamo, D. M. de la Pentildea, D. Limon, and E. F. Camacho, ldquoConstrained min-max predictive control: modifications of the objective function leading to polynomial complexity,rdquo IEEE Tran. Autom. Control , vol. 50, pp. 710-714, May 2005, that this class of problems arise in robust model predictive control when min-max techniques are applied. Although binary quadratic problems belongs to a class of NP-complete problems, the computational burden of the proposed maximization algorithm for band matrices is polynomial with the dimension of the optimization variable and exponential with the band size. Computational results and comparisons on several hundred test problems demonstrate the efficiency of the algorithm

Min–max MPC using a tractable QP problem

Min–max model predictive controllers (MMMPC) suffer from a great computational burden that is often circumvented by using approximate solutions or upper bounds of the worst possible case of a performance index. This paper proposes a computationally efficient MMMPC control strategy in which a close approximation of the solution of the min–max problem is computed using a quadratic programming problem. The overall computational burden is much lower than that of the min–max problem and the resulting control is shown to have a guaranteed stability. A simulation example is given in the paper

Min-Max MPC based on a computationally efficient upper bound of the worst case cost

Min-Max MPC (MMMPC) controllers [P.J. Campo, M. Morari, Robust model predictive control, in: Proc. American Control Conference, June 10–12, 1987, pp. 1021–1026] suffer from a great computational burden which limits their applicability in the industry. Sometimes upper bounds of the worst possible case of a performance index have been used to reduce the computational burden. This paper proposes a computationally efficient MMMPC control strategy in which the worst case cost is approximated by an upper bound based on a diagonalization scheme. The upper bound can be computed with O(n3) operations and using only simple matrix operations. This implies that the algorithm can be coded easily even in non-mathematical oriented programming languages such as those found in industrial embedded control hardware. A simulation example is given in the paper

Min-max model predictive control as a quadratic program

This paper deals with the implementation of min-max model predictive control for constrained linear systems with bounded additive uncertainties and quadratic cost functions. This type of controller has been shown to be a continuous piecewise affine function of the state vector by geometrical methods. However, no algorithm for computing the explicit solution has been given. In this paper, we show that the min-max optimization problem can be expressed as a multi-parametric quadratic program, and so, the explicit form of the controller may be determined by standard multi-parametric techniques

Model predictive control techniques for hybrid systems

This paper describes the main issues encountered when applying model predictive control to hybrid processes. Hybrid model predictive control (HMPC) is a research field non-fully developed with many open challenges. The paper describes some of the techniques proposed by the research community to overcome the main problems encountered. Issues related to the stability and the solution of the optimization problem are also discussed. The paper ends by describing the results of a benchmark exercise in which several HMPC schemes were applied to a solar air conditioning plant.Ministerio de Eduación y Ciencia DPI2007-66718-C04-01Ministerio de Eduación y Ciencia DPI2008-0581

An Application of Cooperative Game Theory to Distributed Control

18th World CongressThe International Federation of Automatic ControlMilano (Italy) August 28 - September 2, 2011In this paper we propose to study the underlying properties of a given distributed control scheme in which a set of agents switch between different communication strategies that define which network links are used in order to regulate to the origin a set of unconstrained linear systems. The problems of how to decide the time-varying communication strategy, share the benefits/costs and detect which are the most critical links in the network are solved using tools from game theory. The proposed scheme is demonstrated through a simulation example

What's wrong with this rebuttal?

A recent rebuttal to criticism of Bell's analysis is shown to be defective by fault of failure to consider all hypothetical conditions input into the derivation of Bell Inequalitites.Comment: 2 page

Effect of the stop-signal modality on brain electrical activity associated with suppression of ongoing actions

To clarify how the modality of stop signals affects the ability to suppress ongoing actions, we compared behavioural indices and event-related potentials (ERPs) recorded in healthy volunteers performing visual and auditory stop-signal tasks. Auditory stop signals were associated with faster reaction times and shorter stop-N2 and stop-P3 latencies. Given that the tasks did not differ in attentional/arousal processes (go-P3 or stop-P3 amplitudes) or motor preparation (LRP amplitude, onset or latency), our results suggest that stop signal modality mainly affects bottom-up sensory processes (faster auditory processing). The ERP waveform obtained by subtracting successfully stopped from unsuccessfully stopped trials showed similar amplitude and topography in both tasks, indicating that the strength of top-down processes related to inhibition was independent of modality. The findings contribute further knowledge about the variables associated with efficient inhibition and have practical implications for the design of settings or interventions to improve reactive inhibition.This work was supported by funding from the Galician Government (Consellería de Cultura, Educación e Ordenación Universitaria; axudas para a consolidación e Estruturación de unidades de investigación competitivas do Sistema universitario de Galicia [grant number GPC2014/047]. A.J. G-V was supported by a grant from the Deputación da Coruña (Bolsas de investigación en ciencias da saúde 2017) and Xunta de Galicia (Axudas de apoio á etapa de formación posdoutoral 2018)