Enlarging the domain of attraction of MPC controllers

This paper presents a method for enlarging the domain of attraction of nonlinear model predictive control (MPC). The usual way of guaranteeing stability of nonlinear MPC is to add a terminal constraint and a terminal cost to the optimization problem such that the terminal region is a positively invariant set for the system and the terminal cost is an associated Lyapunov function. The domain of attraction of the controller depends on the size of the terminal region and the control horizon. By increasing the control horizon, the domain of attraction is enlarged but at the expense of a greater computational burden, while increasing the terminal region produces an enlargement without an extra cost. In this paper, the MPC formulation with terminal cost and constraint is modified, replacing the terminal constraint by a contractive terminal constraint. This constraint is given by a sequence of sets computed off-line that is based on the positively invariant set. Each set of this sequence does not need to be an invariant set and can be computed by a procedure which provides an inner approximation to the one-step set. This property allows us to use one-step approximations with a trade off between accuracy and computational burden for the computation of the sequence. This strategy guarantees closed loop-stability ensuring the enlargement of the domain of attraction and the local optimality of the controller. Moreover, this idea can be directly translated to robust MPC.Ministerio de Ciencia y Tecnología DPI2002-04375-c03-0

Computationally efficient min-max MPC

2005 IFAC 16th Triennial World Congress, Prague, Czech RepublicMin-Max MPC (MMMPC) controllers (Campo and Morari, 1987) suffer from a great computational burden that is often circumvented by using upper bounds of the worst possible case of a performance index. These upper bounds are usually computed by means of LMI techniques. In this paper a more efficient approach is shown. This paper proposes a computationally efficient MMMPC control strategy in which the worst case cost is approximated by an upper bound which can be easily computed using 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. Simulation examples are given in the paper

Enlarging the domain of attraction of MPC controller using invariant sets

2002 IFAC15th Triennial World Congress, Barcelona, SpainThis paper presents a method for enlarging the domain of attraction of nonlinear model predictive control (MPC). The useful way of guaranteeing stability of nonlinear MPC is to add a terminal constraint and a terminal cost in the optimization problem. The terminal constraint is a positively invariant set for the system and the terminal cost is an associated Lyapunov function. The domain of attraction of the controller depends on the size of the terminal region and the prediction horizon. By increasing the prediction horizon, the domain of attraction is enlarged but at expense of a greater computational burden. A strategy to enlarge the domain of attraction of MPC without increasing the prediction horizon is presented. The terminal constraint is replaced by a contractive terminal constraint which is given by a sequence of control invariant sets for the system. This strategy guarantees closed loop stability under the same assumptions

Robust stability of min-max MPC controllers for nonlinear systems with bounded uncertainties

Sixteenth International Symposium on Mathematical Theory of Networks and Systems 05/07/2004 Leuven, BélgicaThe closed loop formulation of the robust MPC has been shown to be a control technique capable of robustly stabilize uncertain nonlinear systems subject to constraints. Robust asymptotic stability of these controllers has been proved when the uncertainties are decaying. In this paper we extend the existing results to the case of uncertainties that decay with the state but do not tend to zero. This allows us to consider both plant uncertainties and external disturbances in a less conservative way. First, we provide some results on robust stability under the considered kind of uncertainties. Based on these, we prove robust stability of the min-max MPC. In the paper we show how the robust design of the local controller is translated to the min-max controller and how the persistent term of the uncertainties determines the convergence rate of the closed-loop system.Ministerio de Ciencia y Tecnología DPI-2001-2380-03-01Ministerio de Ciencia y Tecnología DPI-2002-4375-C02-0

Computational burden reduction in Min-Max MPC

Min–max model predictive control (MMMPC) is one of the strategies used to control plants subject to bounded uncertainties. The implementation of MMMPC suffers a large computational burden due to the complex numerical optimization problem that has to be solved at every sampling time. This paper shows how to overcome this by transforming the original problem into a reduced min–max problem whose solution is much simpler. In this way, the range of processes to which MMMPC can be applied is considerably broadened. Proofs based on the properties of the cost function and simulation examples are given in the paper

Applying a Cognitive-Behavioral Model to Conceptualize Burnout and Coping for Teachers in Urban Schools

Teachers in urban schools, facing a myriad of daily stressors and oftentimes without sufficient knowledge and skills to manage the social and emotional needs of their students and themselves, experience stress and burnout at levels that cause them to leave the teaching profession at alarming rates. Research pertaining to teaching stress, burnout, and coping has largely been devoted to enumerating the stressors that teachers experience, the impact of burnout on teachers and their students, and relating type of coping strategies that teachers employ. This body of literature falls short of illuminating what makes the teaching profession so inherently stressful, the cognitive and behavioral processes the mediate the experience of daily stress and burnout, and protective skills and attitudes that would prevent burnout. The current study sought to address this gap in research and practice by applying a cognitive-behavioral model to investigate the cognitive and behavioral processes that are implicated in burnout. Additionally, the present study examined coping strategies teachers utilized in managing their distress, how efficacious they felt in using these strategies, and their openness to seeking professional psychological help. Results indicated that teachers\u27 experiences are largely characterized by negative thoughts and feelings, which contribute to maladaptive physiological and behavioral processes, and that teachers who experience high levels of burnout more frequently report maladaptive physiological responses to challenging classroom situations. High burnout teachers reported more coping strategies yet felt less efficacious in their efforts. Overall, teachers were modestly open to receiving professional psychological services. Lastly, coping self-efficacy was more helpful in explaining variance in burnout than help-seeking attitudes and years of teaching experience. Suggestions for future research include investigation into how to promote the health of the cognitive, emotional, and behavioral pathways that mediate burnout. Suggestion for practice include training and support provided to teachers to educate them about the distressing nature of their profession, how to cope effectively with such stress, and potentially provide professional psychological services

Neural Network Based Min-Max Predictive Control. Application to a Heat Exchanger

IFAC Adaptation and Learning in Control and Signal Processing. Cemobbio-Como. Italy. 2001Min-max model predictive controllers (MMMPC) have been proposed for the control of linear plants subject to bounded uncertainties. The implementation of MMMPC suffers a large computational burden due to the numerical optimization problem that has to be solved at every sampling time. This fact severely limits the class of processes in which this control is suitable. In this paper the use of a Neural Network (NN) to approximate the solution of the min-max problem is proposed. The number of inputs of the NN is determined by the order and time delay of the model together with the control horizon. For large time delays the number of inputs can be prohibitive. A modification to the basic formulation is proposed in order to avoid this later problem. Simulation and experimental results are given using a heat exchanger

Implementation of min–max MPC using hinging hyperplanes. Application to a heat exchanger

Min–max model predictive control (MMMPC) is one of the few control techniques able to cope with modelling errors or uncertainties in an explicit manner. The implementation of MMMPC suffers a large computational burden due to the numerical min–max problem that has to be solved at every sampling time. This fact severely limits the range of processes to which this control structure can be applied. An implementation scheme based on hinging hyperplanes that overcome these problems is presented here. Experimental results obtained when applying the controller to the heat exchanger of a pilot plant are given.Ministerio de Ciencia y Tecnología DPI2001-2380-C02-01Ministerio de Ciencia y Tecnología DPI2002-04375-C03-0

Feedback control ideas for call center staffing

European Control Conference 2009 • Budapest, Hungary, August 23–26, 2009Call centers are nowadays a widespread solution to deal with customer support and as platform for different kind of business. Call center staffing is crucial to provide adequate service levels at acceptable costs. The task is usually accomplished using heuristics with the help of a human experts or with some static offline optimization based on operations research. Simulators based on queue theory are in some cases also used. The aim of the paper is to show that call center staffing can be posed as a feedback control problem with the advantage of getting a higher level of automation, and a wealth of results from control theory that can help to obtain the best possible staffing. In the paper the authors briefly describe the working procedures of call centers and how the staffing is usually made. They propose a feedback controller that it is used with a call center simulator. The results show that good call center staffing can be obtained even with a not very sophisticated controller

A Java based simulation for basic control

7th IFAC Symposium on Advances in Control Education 21/06/2006 MadridIn this paper we present a java based simulator for control education in basiccourses. The application has been developed using the well known tool Easy JavaSimulation.The objective of the application is to help the student to learn the design of classiccontrollers such as P,PI, PID, etc testing the tuning procedures to control the position ofan antenna controlled by a DC motor. Thus the application allows the student to choosethe parameters of the antenna and the DC motor, to choose the controller to be used andits parameters and finally to simulate the closed loop system observing the evolution ofthe signals as well as a 3-D view. Furthermore, in order to show the real behavior of thesystem, dead zone, saturation, disturbances and non-linearities can be added to the model.This application has been used by the authors to teach a basic control course at EscuelaSuperior de Ingenieros (University of Seville) as virtual laboratory.Moreover, since the application is java based, this can be used by the students from theauthors’ web pages and this can also be installed in the student’s laptop (whichever theplatform is) by downloading it from the authors web page (Limon and Salas, 2003Ministerio de Ciencia y Tecnología DPI2004-07444Ministerio de Ciencia y Tecnología DPI2003-0042