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This article presents an extension to the nonlinear model predictive control (MPC) for tracking scheme able to guarantee convergence even in cases of nonconvex output admissible sets. This is achieved by incorporating a convexifying homeomorphism in the optimization problem, allowing it to be solved in the convex space. A novel class of nonconvex sets is also defined for which a systematic procedure to construct a convexifying homeomorphism is provided. This homeomorphism is then embedded in the MPC optimization problem in such a way that the homeomorphism is no longer required in closed form. Finally, the effectiveness of the proposed method is showcased through an illustrative example.

In this article, we present an implementation of a low-memory footprint model predictive control (MPC)-based controller in programmable logic controllers (PLCs). Automatic code generation of standardized IEC 61131–3 PLC programming languages is used to solve the MPC’s optimization problem online. The implementation is designed for its application in a realistic industrial environment, including timing considerations and accounting for the possibility of the PLC not being exclusively dedicated to the MPC controller. We describe the controller architecture and algorithm, show the results of its memory footprint with regard to the problem dimensions, and present the results of its implementation to control a hardware-in-the-loop multivariable chemical plant.

The growing use of air conditioning systems has become one of the main drivers of energy consumption in buildings. Many efforts are being made to develop new designs and control strategies to improve energy efficiency and minimise electricity consumption. In this work, a model for a case study of multiple-chiller-based cooling system is presented, based on surrogate models derived from information provided by manufacturers, and the study of the economic performance index. Then, an economic predictive control strategy will aim to operate the system optimizing the efficiency of the plant. Instead of the classical two-layer economic predictive control structure, where the reference to be tracked by the controller is given by a real-time optimizer, here we consider a single-layer control strategy where the gradients with respect to the manipulated inputs of the economic performance index are included in the cost function of the model predictive controller. The resulting optimization problem to be solved on line is a QP, which considerably eases the optimization problem, while also avoiding discrepancies between layers that could lead to loss of feasibility.

How to efficiently implement Model Predictive Control (MPC) in embedded systems is a topic that is attracting a lot of research recently, due to its impact in practical applications. Implementing MPC in industrial Programmable Logic Controllers (PLCs) is of particular interest due to their widespread prevalence in the industry in comparison with other embedded systems, such as FPGAs or microcontrollers. In this paper, we present a PLC implementation of real-time embedded MPC for multivariable systems described by linear time-invariant input/output models subject to upper and lower bounds on input and output variables. The MPC algorithm uses a recently developed primal active-set method for bounded-variable least-squares problems. We highlight and address some crucial challenges that arise in implementing the MPC algorithm in a PLC. Possible extensions of the proposed methods are presented along with hardware-in-the-loop simulation results of controlling a nonlinear multivariable system using a real industrial PLC.

This article presents a sparse, low-memory footprint optimization algorithm for the implementation of the model predictive control (MPC) for tracking formulation in embedded systems. This MPC formulation has several advantages over standard MPC formulations, such as an increased domain of attraction and guaranteed recursive feasibility even in the event of a sudden reference change. However, this comes at the expense of the addition of a small amount of decision variables to the MPC's optimization problem that complicates the structure of its matrices. We propose a sparse optimization algorithm, based on an extension of the alternating direction method of multipliers, that exploits the structure of this particular MPC formulation. We describe the controller formulation and detail how its structure is exploited by means of the aforementioned optimization algorithm. We show closed-loop simulations comparing the proposed solver against other solvers and approaches from the literature., Comment: Accepted version of the article published in IEEE Transactions on Control Systems Technology (8 pages, 5 figures)

Many popular approaches in the field of robust model predictive control (MPC) are based on nominal predictions. This paper presents a novel formulation of this class of controller with proven input-to-state stability and robust constraint satisfaction. Its advantages are: (i) the design of its main ingredients are tractable for medium to large-sized systems, (ii) the terminal set does not need to be robust with respect to all the possible system uncertainties, but only for a reduced set that can be made arbitrarily small, thus facilitating its design and implementation, (iii) under certain conditions the terminal set can be taken as a positive invariant set of the nominal system, allowing us to use a terminal equality constraint, which facilitates its application to large-scale systems, and (iv) the complexity of its optimization problem is comparable to the non-robust MPC variant. We show numerical closed-loop results of its application to a multivariable chemical plant and compare it against other robust MPC formulations., Accepted version of article in Journal of Process Control (13 pages, 25 figures)

The application of multilevel converters to renewable energy systems is a growing topic due to their advantages in energy efficiency. Regarding its control, model predictive control (MPC) has become very appealing due to its natural consideration of discrete inputs, its optimization capability, and the present-day availability of powerful processing hardware. The main drawback of MPC compared to other control techniques in this field is that the control input is held constant during the sampling period, and it is usually difficult or even impossible to reduce this sampling period because of hardware limitations. For this reason, a multirate MPC algorithm is proposed, which allows to change the control input several times within the sampling period. The optimization problem is simplified and made suboptimal to substantially decrease computational burden. This approach is tested in simulation on a three-phase, five-level diode-clamped converter (DCC) operating in inverted mode with a three-phase resistive load. Results show significant reduction in harmonic distortion at the cost of an increase in the number of commutations with respect to a standard MPC operating at the same sampling period., 6 pages, 7 figures, to be published in IFAC World Congress 2020 Proceedings

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0) In this paper, we address the problem of modeling error in economically optimal control. A single layer controller is proposed that integrates the economical part of the Real Time Optimization (RTO), the dynamic part of the Model Predictive Control (MPC) and the Modifier Adaptation strategy (MA), resulting in a controller with the following characteristics: a) recursive feasibility guarantee of the controller; b) asymptotic closed-loop stability for any change in the economic cost function; c) convergence guarantee to the economic optimum of the real plant (offset-free) for any change in the cost function of the controller; and d) simple implementation of the controller. We show the behaviour of the proposal by means of a motivating example that highlights the performance of the proposed algorithm

Data centers are energy-hungry infrastructures that provide cloud computing services. The growing number of data centers in use has led to a drastic increment of the energy consumption associated to these facilities, causing environmental concerns. For that reason, efficient management strategies are needed in order to reduce the energy consumption while the quality of service is kept. This paper presents a unified management approach for the thermal and workload distribution problem in data centers, shaped as a Model Predictive Control problem. The corresponding optimization problem is intractable for conventional solvers because the model is based on multiple queues and the decision variables are a mix of integer and real valued ones. A highly parallelizable particle based optimization algorithm is proposed to solve the optimization problem. Numerical simulations are provided in order to illustrate the effectiveness of the strategy.

Sherpa/Romeo: Versión aceptada en repositorios institucionales tras 24 meses de embargo https://v2.sherpa.ac.uk/id/publication/4278 This paper presents a robust learning-based predictive control strategy for nonlinear systems subject to both input and output constraints, under the assumption that the model function is not known a priori and only input–output data are available. The proposed controller is obtained using a nonparametric machine learning technique to estimate a prediction model. Based on this prediction model, a novel stabilizing robust predictive controller without terminal constraint is proposed. The design procedure is purely based on data and avoids the estimation of any robust invariant set, which is in general a hard task. The resulting controller has been validated in a simulated case study.

This paper presents a novel model predictive control (MPC) formulation for set-point tracking. Stabilizing predictive controllers based on terminal ingredients may exhibit stability and feasibility issues in the event of a reference change for small to moderate prediction horizons. In the MPC for tracking formulation, these issues are solved by the addition of an artificial equilibrium point as a new decision variable, providing a significantly enlarged domain of attraction and guaranteeing recursive feasibility for any reference change. However, it may suffer from performance issues if the prediction horizon is not large enough. This paper presents an extension of this formulation where a harmonic artificial reference is used in place of the equilibrium point. The proposed formulation achieves even greater domains of attraction and can significantly outperform other MPC formulations when the prediction horizon is small. We prove the asymptotic stability and recursive feasibility of the proposed controller, as well as provide guidelines for the design of its main ingredients. Finally, we highlight its advantages with a case study of a ball and plate system., Comment: Accepted version of the article published in IEEE Transactions on Automatic Control (14 pages, 11 figures)

A data-based predictive controller is proposed, offering both robust stability guarantees and online learning capabilities. To merge these two properties in a single controller, a double-prediction approach is taken. On the one hand, a safe prediction is computed using Lipschitz interpolation on the basis of an offline identification dataset, which guarantees safety of the controlled system. On the other hand, the controller also benefits from the use of a second online learning-based prediction as measurements incrementally become available over time. Sufficient conditions for robust stability and constraint satisfaction are given. Illustrations of the approach are provided in a simulated case study Feder (UE) DPI2016‐76493‐C3‐1‐R Universidad de Sevilla VI‐PPIT Ministerio de Economía y Competitividad (MINECO). España DPI2016‐76493‐C3‐1‐R

This paper deals with an economic predictive controller for the optimal operation of a plant under the assumption that the only measurement of the system is the economic cost function to be minimized. In order to predict the evolution of the economic cost for a given input trajectory, an oracle with a NARX structure is proposed. Sufficient conditions to ensure the existence of such oracle are given, and based on this oracle, a novel predictive controller is proposed. Under certain assumptions, including ideal accurate estimation, it is proven that the proposed oracle-based economic predictive controller provides the same solution of a standard economic MPC based on the model plant, inheriting the properties of this class of controllers. The proposed oracle-based economic predictive controller is applied to a quadruple-tank process example.

One of the challenges of model predictive control is achieving a large domain of attraction with a small prediction horizon, in order to reduce the computation time and ease its implementation in embedded platforms. The domain of attraction can be enlarged by increasing the prediction horizon, at the expense of an increase in the number of decision variables, or by enlarging the terminal set. In MPC for tracking the terminal set is enlarged by the addition of an artificial equilibrium point as a decision variable, while maintaining stability of the closed loop system. In this paper we propose an extension of the MPC for tracking formulation that adds a single harmonic signal as an artificial reference. We show that a significant increase of the domain of attraction is achieved with the addition of a low number of decision variables, especially for low values of the prediction horizon.

Model predictive control allows to provide high performance and safety guarantees in the form of constraint satisfaction. These properties, however, can be satisfied only if the underlying model, used for prediction, of the controlled process is sufficiently accurate. One way to address this challenge is by data-driven and machine learning approaches, such as Gaussian processes, that allow to refine the model online during operation. We present a combination of an output feedback model predictive control scheme and a Gaussian process-based prediction model that is capable of efficient online learning. To this end, the concept of evolving Gaussian processes is combined with recursive posterior prediction updates. The presented approach guarantees recursive constraint satisfaction and input-to-state stability with respect to the model-plant mismatch. Simulation studies underline that the Gaussian process prediction model can be successfully and efficiently learned online. The resulting computational load is significantly reduced via the combination of the recursive update procedure and by limiting the number of training data points while maintaining good performance., 29 pages, 13 figures, 3 tables, 1 algorithm, revision submitted to International Journal of Robust and Nonlinear Control

We present an output feedback nonlinear model predictive control approach that uses a Gaussian process model for prediction. We show nominal stability assuming that the Gaussian process model is able to represent the real process and establish input-to-state stability assuming a bounded error between the real process and the Gaussian model approximation. These results are achieved using a predictive control formulation without terminal region. The approach is illustrated using a continuous stirred-tank reactor benchmark problem.

In this paper, we propose an extension to the existing Model Predictive Control scheme for tracking. This extension is able to provide a solution for the case where the set of steady-state admissible outputs is non-convex. This is achieved by means of a transformation that maps the output set into a convex set. In the proposed scheme, the cost function and constraints of the usual tracking MPC are modified, so that the controller can drive the system to any point in the admissible steady-state domain without violating any constraints. The paper discusses the feasibility and stability of the proposed approach and a final simulation demonstrates the effectiveness of the approach.

This paper presents an economic model predictive controller, under the assumption that the only measurable signal of the plant is the economic cost to be minimized. In order to forecast the evolution of this economic cost for a given input trajectory, a prediction model with a NARX structure, the so-called oracle, is proposed. Sufficient conditions to ensure the existence of such oracle are studied, proving that it can be derived for a general nonlinear system if the economic cost function is a Morse function. Based on this oracle, economic model predictive controllers are proposed, and their stability is demonstrated in nominal conditions under a standard dissipativity assumption. The viability of these controllers in practical settings (where the oracle may provide imperfect predictions for generic inputs) is proven by means of input-to-state stability. These properties have been illustrated in a case study based on a continuously stirred tank reactor., Preprint submitted to Computers & Chemical Engineering. 19 pages, 6 figures

Article number 109614 The goal of this paper is to present a systematic method to compute reference dependent positively in- variant sets for systems subject to constraints. To this end, we first characterize these sets as level sets of reference dependent Lyapunov functions. Based on this characterization and using Sum of Squares theory, we provide a polynomial certificate for the existence of such sets. Subsequently, through some algebraic manipulations, we express this certificate in terms of a Semi-Definite Programming problem which maximizes the size of the resulting reference dependent invariant sets. We then present some results implementing the proposed method to an example and propose some variants that may help in reducing possible numerical issues. Finally, the proposed approach is employed in the Model Predictive Control for Tracking scheme to compute the terminal set, and in the Explicit Reference Governor framework to compute the so-called Dynamic Safety Margin. The effectiveness of the proposed method in each of the schemes is demonstrated through simulation studies. Ministerio de Economía y Competitividad de España DPI2016-76493-C3-1-R Ministerio de Ciencia e Innovación (España) PID2019-106212RB-C41

In this paper we propose a novel economic robust predictive controller for periodic operation. The proposed controller joins dynamic and economic trajectory planning and robust predictive controller for tracking in a single layer taking into account bounded disturbances, algebraic constraints and periodic operation. We study the closed-loop system properties of the proposed controller and provide a design procedure that guarantees that the perturbed closed-loop system converges asymptotically to the optimal economic reachable periodic trajectory, constraint satisfaction and recursive feasibility. The proposed controller has been applied to control a cluster of interconnected micro-grids. Each nano-grid is connected to an electric utility and has a renewable energy source, a cluster of batteries and a metal hydride based hydrogen storage system. The cluster must satisfy a periodic energy demand while maximizing the profit of the energy sold to the electric utility taking into account time varying prices.

In this study, the authors propose a stabilising data-based model predictive controller for systems subject to constraints in which the prediction model is inferred from experimental data of the plant using a machine learning technique. The inference method is a modification of the kinky inference tailored for model predictive control. In particular, the modified method has a lower computational effort and provides smoother predictions than the original method. The controller formulation considers soft constraints in the outputs, hard constraints in the inputs and guarantees closed-loop robust stability as well as performance by means of the use of different control and prediction horizons and a weighted terminal cost. Under the assumption that the model of the system is Holder continuous, they prove that the closed-loop system is input-to-state stable with respect to the estimation errors. The results are demonstrated in a case study of a continuously stirred-tank reactor.

This paper presents stabilizing Model Predictive Controllers (MPC) to be applied to black-box systems subject to constraints in the inputs and the outputs. The prediction model of the controllers is inferred from experimental data of the inputs and outputs of the plant. Using a nonparametric machine learning technique called SPKI, the estimated (possibly nonlinear) model function is provided. Based on this, a predictive controller with stability guaranteed by design is proposed. Robust stability and recursive feasibility is ensured by using tightened constraints in the optimisation problem but without adding a terminal constraint on the optimisation problem. The proposed predictive controller has been validated in a simulation case study.

This paper presents a novel tracking predictive controller for constrained nonlinear systems capable to deal with sudden and large variations of a piece-wise constant setpoint signal. The uncertain nature of the setpoint may lead to stability and feasibility issues if a regulation predictive controller based on the stabilizing terminal constraint is used. The tracking model predictive controller presented in this paper extends the MPC for tracking for constrained linear systems to the more complex case of constrained nonlinear systems. The key idea is the addition of an artificial reference as a new decision variable. The considered cost function penalizes the deviation of the predicted trajectory with respect to the artificial reference as well as the distance between the artificial reference and the setpoint. Closed-loop stability and recursive feasibility for any setpoint are guaranteed, thanks to an appropriate terminal cost and extended stabilizing terminal constraint. Also, two simplified formulations are shown: the design based on a terminal equality constraint and the design without terminal constraint. The resulting controller ensures recursive feasibility for any changing setpoint. In the case of unreachable setpoints, asymptotic stability of the optimal reachable setpoint is also proved. The properties of the controller have been tested on a constrained continuous stirred tank reactor simulation model and have been experimentally validated on a four-tanks plant. Fil: Limón, Daniel. Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática. Escuela Superior de Ingenieros Industriales; España Fil: Ferramosca, Antonio. Universidad Tecnológica Nacional. Facultad Regional Reconquista; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina Fil: Alvarado, Ignacio. Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática. Escuela Superior de Ingenieros Industriales; España Fil: Alamo, Teodoro. Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática. Escuela Superior de Ingenieros Industriales; España

In this paper a new model predictive controller for tracking arbitrary periodic references is presented. The proposed controller is based on a single layer that unites dynamic trajectory planning and control. A design procedure to guarantee that the closed loop system converges asymptotically to the optimal admissible periodic trajectory while guaranteeing constraint satisfaction is provided. In addition, the constraints of the optimization problem solved by the controller do not depend on the reference, allowing for sudden changes in the reference without loosing feasibility. The properties of the proposed controller are demonstrated with a simulation example of a ball and plate system. MINECO-Spain and FEDER under project DPI2013-48243-C2-2-R University of Seville under contracts 2014/425 and 2014/758 European Research Council under the European Unions Seventh Framework Programme (FP/2007- 2013)/ ERC Grant Agreement n. 307608

This paper discusses the stability properties of a robust nonlinear model predictive control (NMPC) scheme that is based on a multi-stage optimization formulation. The use of a scenario tree to represent the uncertainty makes it possible to formulate a closed-loop robust approach with recourse which improves the open-loop approach in terms of performance and domain of attraction. We show that a straightforward formulation of a multi-stage NMPC scheme does not guarantee Input-to-State stability (ISS) in a deterministic setting, in contrast to the results that one gets using stochastic stability concepts. Since for many applications deterministic stability guarantees are desired, we provide an alternative formulation to achieve deterministic ISS and recursive feasibility guarantees for the case of discrete values of the uncertainty. The design and the performance of the proposed schemes are illustrated by simulations for a highly nonlinear example.

This paper presents the application of economic predictive control to minimize the cost of operating a nonisolated microgrid connected to an electric utility (EU) subject to a periodic internal demand. The microgrid considered is composed of a set of photovoltaic panels and two storage systems and it can buy and sell energy to an EU. The first storage system is composed of a cluster of batteries of lead acid, and the second storage system is based on hydrogen storage. A function that describes the economic cost of operating the plant taking into account aspects such as electric market costs, degradation of the microgrid, and amortization costs is proposed. Based on this cost and considering the periodic nature of the plant, an economic predictive controller capable of adapting to sudden changes on the cost function while guaranteeing stability and recursive feasibility has been successfully tested on a realistic nonlinear model of an experimental configurable testbed located in the laboratories of the University of Seville.

This paper presents the application of economic predictive control to minimize the cost of operating a non-isolated micro-grid connected to an electric utility subject to a periodic internal demand. A function that describes the economic cost of operating the plant taking into account aspects such as electric market costs, degradation of the micro-grid and amortization costs is proposed. Based on this cost and considering the periodic nature of the plant, an economic predictive controller capable of adapting to sudden changes on the cost function while guaranteeing stability and recursive feasibility has been successfully tested using the LTI model of an experimental congurable test-bed located at the laboratories of the University of Seville.

Summary In model predictive control (MPC), the input sequence is computed, minimizing a usually quadratic cost function based on the predicted evolution of the system output. In the case of nonlinear MPC (NMPC), the use of nonlinear prediction models frequently leads to non-convex optimization problems with several minimums. This paper proposes a new NMPC strategy based on second order Volterra series models where the original performance index is approximated by quadratic functions, which represent a lower bound of the original performance index. Convexity of the approximating quadratic cost functions can be achieved easily by a suitable choice of the weighting of the control increments in the performance index. The approximating cost functions can be globally minimized by convex optimization techniques in order to compute the input sequence. The minimization of the performance index is carried out by an iterative optimization procedure, which guarantees convergence to the solution. Furthermore, for a nominal prediction model, asymptotic stability for the proposed NMPC strategy can be shown. In the case of considering an estimation error in the prediction model, input-to-state practical stability is assured. The control performance of the NMPC strategy is illustrated by experimental results. Copyright © 2014 John Wiley & Sons, Ltd.

Model Predictive Control (MPC) is the most used advanced control strategy in the industries, mainly due to its capability to fulfill economic objectives, taking into account a dynamic simplified model of the plant, constraints, and stability requirements. In the last years, several economic formulations of MPC have been presented, which get over the standard setpointtracking formulation. The goal of this work is to provide, by means of application to a highly nonlinear plant, a comparison of different strategies, focusing mainly on economic optimality, computational burden, and economic performance. Fil: Ferramosca, Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina Fil: González, Alejandro Hernán. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina Fil: Limon, Daniel. Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática; España Fil: Bustos, Germán Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina Fil: Godoy, José Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina Fil: Marchetti, Jacinto Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina

The mathematical model used in Min–Max MPC (MMMPC) to predict the future trajectory of the system explicitly considers disturbances and uncertainties. Based on the future trajectory, the control sequence is computed minimizing the worst case cost with respect to all possible trajectories of the disturbances and uncertainties. This approach leads to a more robust control performance but also complicates the practical implementation of MMMPC due to the high computational burden required to solve the optimization problem. This computational burden is even worse if a nonlinear prediction model is used. In fact, to the best of the authors’ knowledge, there have not yet been reported any applications of nonlinear MMMPC to real processes. In this paper a nonlinear MMMPC strategy based on a second order Volterra series model is presented. The particular structure of the used prediction model allows to obtain an explicit formulation of the worst case cost and its computation in polynomial time. Real time applications with typical prediction and control horizons are possible because of the reduced complexity of the proposed control strategy. Furthermore, input-to-state practical stability for the proposed control strategy is guaranteed under certain conditions. The MMMPC strategy is implemented and validated in experiments with a continuous stirred tank reactor whose temperature dynamics are approximated by a second order Volterra series model. The control performance of the proposed MMMPC strategy is illustrated by the obtained experimental results.

This study presents an analysis about state estimation and dead-time compensation effect over constrained control systems with bounded disturbances and dead-time. It is shown that input-to-state stability and constraint satisfaction can be guaranteed by using an equivalent dead-time free system with measurable states and modified disturbances. This result may be useful to simplify synthesis and analysis of a given constrained control strategy. A linear output feedback control scheme and a tube-based model predictive control strategy are used as motivating examples.

The objective of this paper is to present recent results on model predictive control for tracking in the context of economic operation of a industrial plants. The well-established hierarchical economic control is based on a Real Time Optimizer that calculates the economic target to the advanced controller, in this case model predictive controllers. The change of the economic parameters or constraints, or the existence of disturbances and modelling errors make that this target may change throughout the plant evolution. The MPC for tracking is an appealing formulation to deal with this issue since maintain the recursive feasibility and convergence under any change of the target. Thus, this MPC formulation is summarized as well as its properties. In virtue of these properties, it is demonstrated how the economic operation can be improved by integrating the Steady State Target Optimizer in the MPC. Then it is also shown how the proposed MPC can deal with practical problems such us zone control or distributed control. Finally, the economic control of the plant can be enhanced by adopting an economic MPC approach. A formulation capable to ensure economic optimality and target tracking is also shown.

Computational simplicity is one of the most important aspects to take into account in robust model predictive control (MPC). In dead-time processes, it is common to use an augmented state-space representation in order to apply robust MPC strategies but, this procedure may affect computational aspects. In this paper, explicit dead-time compensation will be used to avoid augmented representation. This technique will be analyzed in terms of robust stability and constraint satisfaction for discrete-time linear systems. The results of this discussion will be applied to a robust tube-based MPC strategy which is able to guarantee robust stability and constraint satisfaction of a dead-time system by considering a prediction model without dead-time. Moreover, taking advantage of the proposed scheme, the robust MPC will be particularized for first-order plus dead-time models which simplifies significantly controller synthesis. The proposed dead-time compensation method will be applied to different robust MPC strategies in two case studies: (i) a simulated quadruple-tank system, and (ii) an experimental scaled laboratory heater process.

In the process industries it is often desirable that advanced controllers, such as model predictive controllers (MPC), control the plant ensuring stability and constraints satisfaction, while an economic criterion is minimized. Usually the economic objective is optimized by an upper level Real Time Optimizer (RTO) that passes steady state targets to a lower dynamic control level. The drawback of this structure is that the RTO employs complex stationary nonlinear models to perform the optimization and has a sampling time larger than the controller one. As a consequence, the economic setpoints calculated by the RTO may be inconsistent for the dynamic layer. In this paper an MPC that explicitly integrates the RTO structure into the dynamic control layer is presented. To overcome the complexity of this one-layer formulation a first order approximation of the RTO cost function is proposed, which provides a low-computational-cost suboptimal solution. It is shown that the proposed strategy ensures convergence and recursive feasibility under any change of the economic function. The strategy is tested in a simulation on a subsystem of a fluid catalytic cracking (FCC) unit.

Recently, there has been a renewed interest in the development of distributed model predictive control (MPC) techniques capable of inheriting the properties of centralized predictive controllers, such as constraint satisfaction, optimal control, closed-loop stability, etc. The objective of this paper is to design and implement in a four-tank process several distributed control algorithms that are under investigation in the research groups of the authors within the European project HD-MPC. The tested controllers are centralized and decentralized model predictive controllers schemes for tracking and several distributed MPC schemes based on (i) cooperative game theory, (ii) sensivity-based coordination mechanisms, (iii) bargaining game theory, and (iv) serial decomposition of the centralized problem. In order to analyze the controllers, a control test is proposed and a number of performance indices are defined. The experimental results of the benchmark provide an overview of the performance and the properties of several state-of-the-art distributed predictive controllers.

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.

This paper proposes a filtered Smith predictor (FSP) delay compensation strategy for model predictive control (MPC) robustness improvement. The intrinsic MPC delay compensation is analyzed for a class of systems with a common input-delay to show that robustness can be enhanced by using a different predictor structure. Moreover, FSP robust compensation scheme is applied in a tube based MPC strategy in order to guarantee robust stability. Finally, a simulation example is presented to illustrate the usefulness of the proposed approach.

Min-max model predictive control (MPC) is one of the few techniques suitable for robust stabilization of uncertain nonlinear systems subject to constraints. Stability issues as well as robustness have been recently studied and some novel contributions on this topic have appeared in the literature. In this survey, we distill from an extensive literature a general framework for synthesizing min-max MPC schemes with an a priori robust stability guarantee. First, we introduce a general prediction model that covers a wide class of uncertainties, which includes bounded disturbances as well as state and input dependent disturbances (uncertainties). Second, we extend the notion of regional input-to-state stability (ISS) in order to fit the considered class of uncertainties. Then, we establish that the standard min-max approach can only guarantee practical stability. We concentrate our attention on two different solutions for solving this problem. The first one is based on a particular design of the stage cost of the performance index, which leads to a Hoo strategy, while the second one is based on a dual-mode strategy. Under fairly mild assumptions both controllers guarantee ISS of the resulting closed-loop system. Moreover, it is shown that the nonlinear auxiliary control law introduced in [29] to solve the H8 problem can be used,for nonlinear systems affine incontrol, in all the proposed min-max schemes and also in presence of state-independent disturbances. A simulation example illustrates the techniques surveyed in this article. .

In this paper, a novel model predictive control (MPC) for constrained (non-square) linear systems to track piecewise constant references is presented. This controller ensures constraint satisfaction and asymptotic evolution of the system to any target which is an admissible steady-state. Therefore, any sequence of piecewise admissible setpoints can be tracked without error. If the target steady state is not admissible, the controller steers the system to the closest admissible steady state. These objectives are achieved by: (i) adding an artificial steady state and input as decision variables, (ii) using a modified cost function to penalize the distance from the artificial to the target steady state (iii) considering an extended terminal constraint based on the notion of invariant set for tracking. The control law is derived from the solution of a single quadratic programming problem which is feasible for any target. Furthermore, the proposed controller provides a larger domain of attraction (for a given control horizon) than the standard MPC and can be explicitly computed by means of multiparametric programming tools. On the other hand, the extra degrees of freedom added to the MPC may cause a loss of optimality that can be arbitrarily reduced by an appropriate weighting of the offset cost term.

The objective of this paper is, on the base of existing results, to provide a general framework for synthesizing min-max MPC schemes with an a priori robust stability guarantee for nonlinear constrained systems. Using regional input-to-state stability, it is proven that the standard min-max approach can only guarantee practical stability. This is due to the choice of the stage cost. In order to avoid this problem, two different solutions have been considered: the first one is based on a particular design of the stage cost of the performance index, while the second one is based on a dual-mode strategy. It is shown that under fairly mild assumptions both controllers guarantee input-to-state stability.

Model Predictive Control (MPC) is one of the most used advanced control strategy in the industries, mainly due to its capability to fulfill economic objectives, taking into account a simplified dynamic model of the plant, constraints, and stability requirements. In the last years, several economic formulations of MPC have been presented, which overcome the standard setpoint-tracking formulation. The goal of this work is to provide, by means of application to a highly nonlinear plant, a comparison of different strategies, focusing mainly on economic optimality, computational burden, and economic performance (understood as transient economic optimality).

Min-max model predictive control (MPC) is one of the control techniques capable of robustly stabilize uncertain nonlinear systems subject to constraints. In this paper we extend existing results on robust stability of min-max MPC to the case of systems with uncertainties which depend on the state and the input and not necessarily decaying, i.e. state and input dependent bounded uncertainties. This allows us to consider both plant uncertainties and external disturbances in a less conservative way. It is shown that the input-to-state practical stability (ISpS) notion is suitable to analyze the stability of worst-case based controllers. Thus, we provide Lyapunov-like sufficient conditions for ISpS. Based on this, it is proved that if the terminal cost is an ISpS-Lyapunov function then the optimal cost is also an ISpS-Lyapunov function for the system controlled by the min-max MPC and hence, the controlled system is ISpS. Moreover, we show that if the system controlled by the terminal control law locally admits certain stability margin, then the system controlled by the min-max MPC retains the stability margin in the feasibility region.

The usual way to guarantee stability of model predictive control (MPC) strategies is based on a terminal cost function and a terminal constraint region. This note analyzes the stability of MPC when the terminal constraint is removed. This is particularly interesting when the system is unconstrained on the state. In this case, the computational burden of the optimization problem does not have to be increased by introducing terminal state constraints due to stabilizing reasons. A region in which the terminal constraint can be removed from the optimization problem is characterized depending on some of the design parameters of MPC. This region is a domain of attraction of the MPC without terminal constraint. Based on this result, it is proved that weighting the terminal cost, this domain of attraction of the MPC controller without terminal constraint is enlarged reaching (practically) the same domain of attraction of the MPC with terminal constraint; moreover, a practical procedure to calculate the stabilizing weighting factor for a given initial state is shown. Finally, these results are extended to the case of suboptimal solutions and an asymptotically stabilizing suboptimal controller without terminal constraint is presented.

In this note, an efficient way of implementing a constrained min-max predictive controller is presented. The new approach modifies the objective function in such a way that the resulting min-max problem can be solved in polynomial time. Different modifications are proposed. The main contribution of the note is to provide a robust constrained min-max predictive controller that can be implemented in real time. The new controller stabilizes the uncertain system.

A robust MPC for constrained discrete-time nonlinear systems with additive uncertainties is presented. The proposed controller is based on the concept of reachable sets, that is, the sets that contain the predicted evolution of the uncertain system for all possible uncertainties. If processes are nonlinear these sets are very difficult to compute. A conservative approximation based on interval arithmetic is proposed for the online computation of these sets. This technique provides good results with a computational effort only slightly greater than the one corresponding to the nominal prediction. These sets are incorporated into the MPC formulation to achieve robust stability. By choosing a robust positively invariant set as a terminal constraint, a robustly stabilising controller is obtained. Stability is guaranteed in the case of suboptimality of the computed solution. The proposed controller is applied to a continuous stirred tank reactor with an exothermic reaction.

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-c03-01

Model predictive control (MPC) is one of the few techniques which is able to handle with constraints on both state and input of the plant. The admissible evolution and asymptotically convergence of the closed loop system is ensured by means of a suitable choice of the terminal cost and terminal contraint. However, most of the existing results on MPC are designed for a regulation problem. If the desired steady state changes, the MPC controller must be redesigned to guarantee the feasibility of the optimization problem, the admissible evolution as well as the asymptotic stability. In this paper a novel formulation of the MPC is proposed to track varying references. This controller ensures the feasibility of the optimization problem, constraint satisfaction and asymptotic evolution of the system to any admissible steady-state. Hence, the proposed MPC controller ensures the offset free tracking of any sequence of piece-wise constant admissible set points. Moreover this controller requires the solution of a single QP at each sample time, it is not a switching controller and improves the performance of the closed loop system.

Trabajo presentado a la European Control Conference (ECC) celebrada en Estrasburgo (Francia) del 24 al 27 de junio de 2014., This paper addresses the management of drinking water networks (DWNs) regarding a multi-objective cost function by means of economically-oriented model predictive control (EMPC) strategies. Specifically, assuming the water demand and the energy price as periodically time-varying signals, this paper shows that the EMPC framework is flexible to enhance the control of DWNs without relying on hierarchical control schemes that require the use of real-time optimisers (RTO) or steady-state target optimisers (SSTO) in an upper layer. Four different MPC strategies are discussed in this paper: a hierarchical two-layer approach, a standard EMPC where the multi-objective cost function is optimised directly, and two different modifications of the latter, which are meant to overcome possible feasibility losses in the presence of changing operating patterns. The discussed schemes are tested andcompared by means of a case study taken from a part of the Barcelona DWN., This work has been partially funded by the EU Project EFFINET (FP7-ICT-2011-8-31855) and the DGR of Generalitat de Catalunya (SAC group Ref. 2009/SGR/1491).