In this paper, we present a novel prediction technique based on Kriging methods. Here, instead of assuming that the dynamics of the system are completely unknown and build a complete black-box model of the system, we opt to inject previous knowledge of the system into the black-box model in order to improve the performance of the obtained predictor. This can be easily done by adding new constraints to the Kriging predictor. These can be added in a hard-constraint or a soft-constraint manner, obtaining different results depending on this choice. Also, embedding physics-based conditions into the predictor is compatible with both the local-data based Kriging and the kernel-based Kriging technique, allowing for a flexible modeling depending on the application. Finally, the proposed predictors were tested against their state-of-the-art versions to show their effectiveness in a numerical example.

In this paper, we present a data-driven methodology to predict and control the behaviour of nonlinear and non-autonomous systems based on kernel functions. The technique computes the forecasting by means of a linear combination of past data. The weights used to compute the prediction are obtained by solving a convex optimization problem that stems from a novel kriging formulation. A Control Lyapunov Function (CLF) based controller using the presented predictor is also built. Finally, numerical examples of both prediction and control are presented, showing the efficacy of the proposed approach.

This paper presents a new methodology to obtain prediction regions of the output of a dynamical system. The proposed approach uses stored past outputs of the system and it is entirely data-based. Only two hyperparameters are necessary to apply the proposed methodology. These scalars are chosen so that the size of the obtained regions is minimized while fulfilling the desired empirical probability in a validation set. In this paper, methods to optimally estimate both hyperparameters are provided. The provided prediction regions are convex and checking if a given point belongs to a computed prediction region amounts to solving a convex optimization problem. Also, approximation methods to build ellipsoidal prediction regions are provided. These approximations are useful when explicit descriptions of the regions are necessary. Finally, some numerical examples and comparisons for the case of a non-linear uncertain kite system are provided to prove the effectiveness of the proposed methodology.

In the field of variable speed electric drives, the predictive method based on virtual voltage vectors has recently appeared. This method allows to reduce the voltage contribution in the x-y subspace, in which no torque is produced, but losses. This not only limits the losses but also reduces the tuning complexity of the predictive controller. The virtual voltage vectors are obtained by combining tension vectors belonging to different small, medium and large crowns in addition to the null vectors. In a typical application, first the crown(s) to be used are chosen and then the virtual vectors are developed. The predictive controller uses in each sampling period the most suitable virtual vector. In this work we propose the use of several sets of virtual vectors coming from different combinations of crowns. For each operating point of the electric drive, the set that provides the best values of a certain goodness criterion is used. The proposed method is experimentally validated using a six-phase induction machine.

En el campo de los accionamientos eléctricos de velocidad variable ha aparecido recientemente el método predictivo basado en vectores virtuales de tensión. Este método permite reducir la contribuci´on del voltaje en el subespacio x-y, en el cual no se produce par, sino pérdidas. De este modo no sólo se limitan las pérdidas sino que se reduce la complejidad de sintonía del controlador predictivo. Los vectores virtuales de tensión se obtienen mediante combinación de vectores de tensión pertenencientes a distintas coronas pequeña, media y grande además de los vectores nulos. En una aplicación típica se elige en primer lugar la(s) corona(s) a usar y después se desarrollan los vectores virtuales. El controlador predictivo usa en cada periodo de muestreo el vector virtual más adecuado. En este trabajo se propone el uso de varios conjuntos de vectores virtuales provenientes de diferentes combinaciones de coronas. Para cada punto de operación del accionamiento eléctrico se utiliza el conjunto que proporciona mejores valores de cierto criterio de bondad. El método propuesto es validado experimentalmente usando una máquina de inducción de seis fases.

This article combines data and tube-based predictive control to deal with systems with bounded parametric uncertainty. This integration generates robustly feasible control sequences that can also be exploited in cooperative scenarios where controllers learn from each other’s data. In particular, the approach is based on a database that contains information from previous executions of the same and other controllers handling similar systems. By the combination of feasible histories plus an auxiliary control law that deals with bounded uncertainties, which only needs to be stabilizing for at least one of the system realizations within the uncertainty set, this scheme provides a finite-horizon predictive controller that guarantees exponential stability and robust constraint satisfaction. The validity and benefits of the proposed scheme are shown in case studies with linear and non-linear dynamics.

In this paper, we extend the state-space kriging（SSK） modeling technique presented in a previous work by the authors in order to consider non-autonomous systems. SSK is a data-driven method that computes predictions as linear combinations of past outputs. To model the nonlinear dynamics of the system, we propose the kernel-based state-space kriging（K-SSK）, a new version of the SSK where kernel functions are used instead of resorting to considerations about the locality of the data. Also, a Kalman filter can be used to improve the predictions at each time step in the case of noisy measurements. A constrained tracking nonlinear model predictive control（NMPC） scheme using the black-box input-output model obtained by means of the K-SSK prediction method is proposed. Finally, a simulation example and a real experiment are provided in order to assess the performance of the proposed controller.

In this technical note we study the computation of the Maximal Output Admissible Set for linear systems subject to polynomial constraints. The computation of an inner approximation of the Maximal Output Admissible Sets requires the determination of constraint redundancy. We use a procedure to determine polynomial constraint redundancy based on a consequence of Putinar's Positivstellensatz. Further, we present a modification of the algorithm to compute the Maximal Output Admissible Set with improved performance. Lastly, demonstrate the potential for practical applications in two case studies of spacecraft rendezvous and control of an electromagnetic actuator.

This paper presents a robust finite-horizon control scheme based on data that produces feasible control sequences. The scheme makes use of a database that includes information from prior experiences of the same and others controllers handling similar systems. By the convex combination of feasible histories plus an auxiliary control law that deals with uncertainties, this scheme can be used as a robust historian-based predictive controller. Further application could include a cooperative learning-based strategy in which multiple controllers share their previous executions to gain collective benefits in terms of performance. The validity of the proposed controller is tested in a simulated case study.

This work presents a new methodology to obtain probabilistic interval predictions of a dynamical system. The proposed strategy uses stored past system measurements to estimate the future evolution of the system. The method relies on the use of dissimilarity functions to estimate the conditional probability density function of the outputs. A family of empirical probability density functions, parameterized by means of two scalars, is introduced. It is shown that the proposed family encompasses the multivariable normal probability density function as a particular case. We show that the presented approach constitutes a generalization of classical estimation methods. A validation scheme is used to tune the two parameters on which the methodology relies. In order to prove the effectiveness of the presented methodology, some numerical examples and comparisons are provided.

Constant torque motors are needed for rotary screw compressors that are used for cooling and other applications. In such systems, the torque demanded by the load is approximately the same over the whole range of mechanical speeds. In this paper, the use of multi-phase induction machines is investigated for this type of application. The requirement of low stator current distortion is considered. A scheduled approach is used to provide the best possible tuning for each operating point, similar to the concept of gain scheduling control. Simulations and laboratory tests are used to assess the proposal and compare it with finite-state predictive control. The experiments show that a trade-off situation appears between the ripple content in stator currents in the torque-producing and harmonic planes. As a consequence, the controller tuning appears as an important step. The proposed method considers various figures of merit with cost function tuning, resulting in a scheduled scheme that provides improved results. It is shown that the approach leads to a reduction in current ripple, which is advantageous for this particular application.

El control predictivo de corrientes de estátor precisa una estimación de las corrientes rotóricas que son, usualmente, no medibles. Estas corrientes afectan a la evolución de la corriente de estátor y por tanto afectan a las predicciones usadas por el controlador. El procedimiento habitual consiste en estimar el efecto que producen dichas corrientes mediante una técnica simple que añade a la predicción el error del periodo de muestreo anterior. En este artí­culo se presenta un nuevo método de estimación basado en el circuito equivalente de la máquina de inducción. Se presentan resultados de simulación y experimentales para el caso particularmente más complejo de una motor polifásico en los que se demuestra la superioridad del método.

Predictive control of stator currents is a model-based technique needing an estimation of rotor currents, which are normally not measured. These currents affect the evolution of the stator currents and, therefore, also affect the predictions used by the controller. The usual procedure consists in correcting their effect by a simple feedback technique. In this article, the estimation of rotor currents is tackled based in the induction machine equivalent circuit. The proposed estimation procedure aims at improving the predictions with respect to the usual procedure. Simulation and experimental results are provided for the particularly demanding case of a multi-phase induction machine, showing the superiority of the proposal.

This letter presents a new method for modeling dynamical systems. The method uses historical data of the outputs to predict the evolution of the system. The proposed method is based on Direct Weight Optimization and the Kriging method. These data-based methods provide predictions as linear combinations of past outputs after solving a quadratic optimization problem. We introduce a novel methodology that we named state-space Kriging, which models the time evolution of the weighting parameters using a state-space formalism. In this way, the potential of Kriging, along with classical estimation methods, as the Kalman filter, can be leveraged to forecast the output of a nonlinear dynamical system. The optimization problems involved are easy to solve, and analytical solutions are provided. Some numerical examples and comparisons are provided to demonstrate the effectiveness of our proposal.

The goal of this paper is to present a systematic method to compute reference dependent positively invariant 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.

The optimal execution of stock trades is a relevant and interesting problem as it is key in maximizing profits and reducing risks when investing in the stock market. In the case of large orders, the problem becomes even more complex as the impact of the order in the market has to be taken into account. The usual solution is to split large orders into a set of smaller suborders that must be executed within a prescribed time window. This leads to the problem of deciding when in the time window execute each suborder. There are popular ways of executing the trading of these split orders like those which try to track the "Time Weighted Average Price" and the "Volume Weighted Average Price", usually called TWAP and VWAP orders. This paper presents a strategy to optimize the splitting of large trade orders over a given time window. The strategy is based on the solution of an optimization problem that is applied following a receding horizon approach. This approach reduces the impact of prediction errors due to the uncertain market dynamics, by using new values of the price time series as they are available as time goes on. Suborder size constraints are taken into account in both market and limit orders. The strategy relies on price and traded volume forecast but it is independent of the prediction technique used. The performance index weighs not only the financial cost of the suborders, but also the impact on the market and the forecasting accuracy. A tailored optimization algorithm is proposed for efficiently solving the corresponding optimization problem. Most of the computations of the algorithm can be parallelized. Finally, the proposed approach has been tested through a case study composed by stocks of the Chinese A-share market.

Stock price forecasting is a relevant and challenging problem that has attracted a lot of interest from engineers and scientists. In this paper we apply two techniques for stock price and price intervals forecasting. Both techniques, derived from previous works by the authors, are based on the use of local data extracted from a database. These data are those that correspond to similar market states to the current one. The first technique uses these local data to compute a price forecast by finding an optimal combination of past states that equals the current state. The price forecast is then obtained by combining the past actual prices associated to the past market states. The second technique can be used to forecast prices but its main use is to forecast price intervals that will contain the real future price with a guaranteed probability. This is accomplished by building a probability distribution for the forecasted price and then setting the intervals by a choice of desired percentiles. Thus, this technique can be used in financial risk management. Both techniques are purely data driven and do not need a theoretical description or model of the price trend being forecasted. The proposed techniques adapt very easily to market changes because they use only the subset of the database that it is closer to the current state. Furthermore, the database can be updated as new data is available. Finally, both approaches are highly parallelizable, thus making possible to manage large data sets. As a case study, the proposed approaches have been applied to the k-step forecasting of the Dow Jones Industrial Average index. The results have been validated in relation with some baseline approaches, such as martingale and neural network predictors and quantile regression for the interval forecasting.

Data centers are facilities with large number of servers providing cloud services. The increasing number of data centers in the last years has generated environmental concern due to the large amount of energy consumed by them. This also includes some auxiliary services such as the cooling equipment which is known to be very costly. For that reason, efficient data center strategies are needed in order to provide an acceptable quality of service (QoS) and suitable temperature for every server while using the least amount of resources possible. This article presents some strategies to deal with the unified workload and temperature problem that appears in the data center. As the system is modeled as a queue and the control variables have an hybrid nature, some highly parallelizable particle-based optimization algorithms are proposed to solve the optimization problem. Numerical simulations are provided in order to illustrate the effectiveness of the strategy. These simulations also show the improvements obtained from the GPU computing. Finally, a probabilistic evaluation approach is developed in order to provide certificates on the probability of constraint satisfaction without increasing the computational burden of the online problem. Note to Practitioners—This article addresses the problem of deciding in real-time the number of active servers in a data center that is required to meet the quality of service (QoS) demands while keeping energy consumption at a minimum. The temperature set point of the cooling equipment must also be taken into account, as it is advisable to use the minimum cooling that keeps the servers running in safe conditions. The management strategy proposed is based on predictive control. In this way, the number of active servers and temperature set point will be chosen so that the future energy consumption is minimized while guaranteeing that QoS and safety demands are met under different possible operating conditions. Furthermore, the proposed management strategy can be tuned depending on the QoS that it is desirable to provide. The proposed strategy will lead to energy-consumption improvements while having guarantees on the data center performance.

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.