Artículos (Ingeniería de Sistemas y Automática)

URI permanente para esta colecciónhttps://hdl.handle.net/11441/11342

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  • Acceso AbiertoArtículo
    Corrigendum to “Tuning of modern speed drives using IFOC: A case study for a five-phase induction machine
    (Elsevier, 2024-11) Barrero García, Federico; Garrido Satué, Manuel; Colodro Ruiz, Francisco; Arahal, Manuel R.; Universidad de Sevilla. Departamento de Ingeniería Electrónica; Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática; Universidad de Sevilla. TIC275: Investigación y Desarrollo en Electrónica, Automática y Tecnologías Emergentes
  • Acceso AbiertoArtículo
    Tuning of modern speed drives using IFOC: A case study for a five-phase induction machine
    (Elsevier, 2024-12) Barrero García, Federico; Garrido Satué, Manuel; Colodro Ruiz, Francisco; Ruiz Arahal, Manuel; Universidad de Sevilla. Departamento de Ingeniería Electrónica; Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática; Ministerio de Ciencia, Innovación y Universidades (MICINN). España; Universidad de Sevilla. TIC275: Investigación y Desarrollo en Electrónica, Automática y Tecnologías Emergentes
    Electric machines have existed since the beginning of the 19th century. Although variable-speed drive technology has evolved considerably during the last years, the indirect field-oriented control technique has been in use as a standard control method since the 1960s, using an outer speed loop and an inner current loop. This paper deals with the non-trivial problem of tuning the outer speed controller of modern variable-speed drives, where experimental results are provided to show the need for new tuning methods. The influence of non-modeled effects on the performance of the drive is illustrated considering the dynamical effect of the mechanical speed sensing procedure using optical devices. This effect has not been generally considered. However, it is shown that it has a notable effect on tuning for high performance drives. This is especially true when considering some figures of merits of relevance for drives, such as the torque ripple. A Pareto analysis is proposed to reveal trade-offs between typical figures of merit to establish new tuning methods. To focus our contribution, a five-phase induction drive is considered as the case study, using a finite-state model predictive controller for the stator current control and PI regulators for the outer speed control loop.
  • Acceso AbiertoArtículo
    Trade-Off Analysis of Drive Dynamics Considering Speed and Current Loops
    (MDPI, 2024-08) Arahal, Manuel R.; Garrido Satué, Manuel; Colodro Ruiz, Francisco; Martínez Heredia, Juana María; Universidad de Sevilla. Departamento de Ingeniería Electrónica; Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Universidad de Sevilla. TIC275: Investigación y Desarrollo en Electrónica, Automática y Tecnologías Emergentes; Universidad de Sevilla. TEP201: Ingeniería de Automatización, Control y Robótica
    Electric drive control is an important area of research due to its ubiquity. In particular, multi-phase induction machines are an important field due to their inherent robustness. Tuning of the inner loop (speed) and outer loop (current) is typically tackled separately. The problem of trade-off analysis for the tuning of both loops has never been tackled before, which motivates the present study. This paper examines the complex and non-linear relationships between commonly used performance indicators in variable speed applications. The paper shows that there are links between performance indicators for both loops. This prompts a more detailed study of concurrent tuning. Also, it is shown that said links are, in a variable speed drive, dependent on the operating point. This requires studying more than just one operating point. Experimental results for a five-phase induction motor are used to validate the analysis.
  • Acceso AbiertoArtículo
    Simulation of Full Wavefield Data with Deep Learning Approach for Delamination Identification
    (MDPI, 2024-07) Ullah, Saeed; Kudela, Pawel; Ijjeh, Abdalraheem A.; Chatzi, Eleni; Ostachowicz, Wieslaw; Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática; National Science Center. Poland
    In this work, a novel approach of guided wave-based damage identification in composite laminates is proposed. The novelty of this research lies in the implementation of ConvLSTM-based autoencoders for the generation of full wavefield data of propagating guided waves in composite structures. The developed surrogate deep learning model takes as input full wavefield frames of propagating waves in a healthy plate, along with a binary image representing delamination, and predicts the frames of propagating waves in a plate, which contains single delamination. The evaluation of the surrogate model is ultrafast (less than 1 s). Therefore, unlike traditional forward solvers, the surrogate model can be employed efficiently in the inverse framework of damage identification. In this work, particle swarm optimisation is applied as a suitable tool to this end. The proposed method was tested on a synthetic dataset, thus showing that it is capable of estimating the delamination location and size with good accuracy. The test involved full wavefield data in the objective function of the inverse method, but it should be underlined as well that partial data with measurements can be implemented. This is extremely important for practical applications in structural health monitoring where only signals at a finite number of locations are available.
  • Acceso AbiertoArtículo
    Conformal predictions for probabilistically robust scalable machine learning classification
    (Springer, 2024-09) Carlevaro, Alberto; Alamo, Teodoro; Dabbene, Fabrizio; Mongelli, Maurizio; Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática; Consejo Nacional de Investigación de Italia (Consiglio Nazionale delle Ricerche)
    Conformal predictions make it possible to define reliable and robust learning algorithms. But they are essentially a method for evaluating whether an algorithm is good enough to be used in practice. To define a reliable learning framework for classification from the very beginning of its design, the concept of scalable classifier was introduced to generalize the concept of classical classifier by linking it to statistical order theory and probabilistic learning theory. In this paper, we analyze the similarities between scalable classifiers and conformal predictions by introducing a new definition of a score function and defining a special set of input variables, the conformal safety set, which can identify patterns in the input space that satisfy the error coverage guarantee, i.e., that the probability of observing the wrong (possibly unsafe) label for points belonging to this set is bounded by a predefined ε error level. We demonstrate the practical implications of this framework through an application in cybersecurity for identifying DNS tunneling attacks. Our work contributes to the development of probabilistically robust and reliable machine learning models.
  • Acceso AbiertoArtículo
    A priori data-driven robustness guarantees on strategic deviations from generalised Nash equilibria
    (Elsevier, 2024-09) Pantazis, Georgios; Fele, Filiberto; Margellos, Kostas; Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática; Ministerio de Ciencia, Innovación y Universidades (MICINN). España; European Union (UE); European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Engineering and Physical Sciences Research Council (UK)
    In this paper we focus on noncooperative games with uncertain constraints coupling the agents’ decisions. We consider a setting where bounded deviations of agents’ decisions from the equilibrium are possible, and uncertain constraints are inferred from data. Building upon recent advances in the so called scenario approach, we propose a randomised algorithm that returns a nominal equilibrium such that a pre-specified bound on the probability of violation for yet unseen constraints is satisfied for an entire region of admissible deviations surrounding it—thus supporting neighbourhoods of equilibria with probabilistic feasibility certificates. For the case in which the game admits a potential function, whose minimum coincides with the social welfare optimum of the population, the proposed algorithmic scheme opens the road to achieve a trade-off between the guaranteed feasibility levels of the region surrounding the nominal equilibrium, and its system-level efficiency. Detailed numerical simulations corroborate our theoretical results.
  • Solo MetadatosArtículo
    Controlled Shaking of Trees With an Aerial Manipulator
    (Institute of Electrical and Electronics Engineers (IEEE), 2024) González Morgado, Antonio; Cuniato, Eugenio; Tognon, Marco; Heredia Benot, Guillermo; Siegwart, Roland; Ollero Baturone, Aníbal; Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática; AEROTRAIN Marie Skłodowska-Curie; MARTIN; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Universidad de Sevilla. TEP151: Robótica, Visión y Control.
    In recent years, the fields of application of aerial manipulators have expanded, ranging from infrastructure inspection to physical interaction with flexible elements, such as branches and trees. This article presents the controlled shaking of a tree with an aerial manipulator. Our work aims at contributing to applications like the identification of tree parameters for environmental health monitoring or the collection of samples and fruits by vibration. To this end, we propose a control strategy for controlled shaking of flexible systems. We adopt a self-excited oscillation strategy that induces vibrations at the natural frequency of the system, at which the greatest amplification and therefore the greatest vibrations occur. Likewise, this work presents a simplified 1 degree of freedom (DoF) model based on the Rayleigh–Ritz method to analyze dynamic interaction between a tree and the aerial manipulator with the controlled shaking strategy. The proposed control strategy is evaluated through indoor experiments, where an aerial manipulator shakes an indoor tree made of bamboo canes. Experimental results show how the proposed model can estimate properly the amplitude of the vibration and the frequency of the vibration, depending on the grasping point and the control gain of the self-excited oscillation strategy.
  • Acceso AbiertoArtículo
    Data-driven learning and control of nonlinear system dynamics: A robust-learning approach via Sontag’s control formula
    (Springer Nature, 2024) Becerra-Mora, Yeyson; Acosta Rodríguez, José Ángel; Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática; Universidad de Sevilla; Universidad de Sevilla. TEP995: Multi-robot and Control Systems
    This work falls into the field of discovering the dynamic equations of stabilizable nonlinear systems, via a learning-and-control algorithm to process the data sets of trajectories previously obtained. To this end, an interlaced method to learn and control nonlinear system dynamics from a set of demonstrations is proposed, under a constrained optimization framework for the unsupervised learning process. The nonlinear system is modeled as a mixture of Gaussians and Sontag’s formula together with its associated Control Lyapunov Function is proposed for learning and control. Lyapunov stability and robustness in noisy data environments are guaranteed, as a result of the inclusion of control in the learning-optimization problem. The performances are validated through a well-known dataset of demonstrations with handwriting complex trajectories, succeeding in all of them and outperforming previous methods under bounded disturbances, possibly coming from inaccuracies, imperfect demonstrations, or noisy datasets. As a result, the proposed interlaced solution yields a good performance trade-off between reproductions and robustness. Therefore, this work sheds some more light on the automatic discovery of nonlinear dynamics from noisy raw data.
  • EmbargoArtículo
    Digital twin of an absorption chiller for solar cooling
    (Elsevier, 2023-05) Ortiz Machado, Diogo; Chicaiza Salazar, William David; Escaño González, Juan Manuel; Gallego Len, Antonio Javier; Gustavo, Andrade A. de; Normey Rico, Julio Elías; Bordons Alba, Carlos; Camacho, Eduardo F.; Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática; Ministerio de Ciencia e Innovación (MICIN). España; Universidad de Sevilla.TEP116: Automatica y Robotica Industrial
    The aim of this study is to create a digital twin of a commercial absorption chiller for control and optimization purposes. The chiller is a complex system that is affected by solar intermittency and non-linearities. The authors use Adaptive Neuro-fuzzy Inference System (ANFIS) to model the chiller's behavior during transients and part-load events. The chiller is divided into four sub-models, each modeled by ANFIS, and trained and validated using data from 15 days of operation. The ANFIS models are precise, accurate, and fast, with a worst-case Mean Absolute Percentage Error (MAPE) of 3.30% and reduced error dispersion (σE=0.88) and Standard Error (SE=0.01). The models outperformed literature models in terms of MAPE, with MAPEs of 1.12%, 2.21%, and 3.24% for the High Temperature Generator (HTG), absorber + condenser, and evaporator outlet temperatures, respectively. The computational execution time of the model is also a valuable asset, with an average simulation step taking less than 0.20 ms and a total simulation time of 8.9 s for three days of operation. The resulting digital twin is suitable for Model Predictive Control applications and fast what-if analysis and optimization due to its gray-box representation and computational speed.
  • Acceso AbiertoArtículo
    Model-Based Control for Power Converters With Variable Sampling Time: A Case Example Using Five-Phase Induction Motor Drives
    (Institute of Electrical and Electronics Engineers Inc. (IEEE), 2019-08) Arahal, Manuel R.; Martín Torres, Cristina; Barrero, Federico; González Prieto, Ignacio; Durán, Mario J.; Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática; Universidad de Sevilla. Departamento de Ingeniería Eléctrica; Universidad de Sevilla. Departamento de Ingeniería Electrónica; Ministerio de Economía y Competitividad (MINECO). España; Universidad de Sevilla; Universidad de Sevilla. TEP196: Sistemas de Energía Eléctrica; Universidad de Sevilla. TIC201: ACE-TI
    Discrete-time control of power converters without modulation blocks have been considered in recent times in modern high-performance electromechanical drives, particularly with the appearance of model predictive control in its finite set version. The shortcomings produced by the fixed discretization of time used in this kind of control systems has been analyzed, and several methods have been put forward to deal with them. Most of the alternatives increase the complexity of the controller introducing different analytical modulation methods. However, a variable sampling time can be a simpler and more natural solution, at the expense of using a less-known paradigm for implementation. This paper introduces a new control approach based on a model of the system as in predictive controllers but using variable sampling time. It can be applied to modern power converters and drives, including conventional three-phase or advanced multiphase ones. Experimental results are provided to test the ability of the controller using a five-phase induction motor drive as a case example.
  • Acceso AbiertoArtículo
    Influence of Covariance-Based ALS Methods in the Performance of Predictive Controllers With Rotor Current Estimation
    (Institute of Electrical and Electronics Engineers Inc. (IEEE), 2017-04) Rodas, Jorge; Martín Torres, Cristina; Arahal, Manuel R.; Barrero, Federico; Gregor, Raúl; Universidad de Sevilla. Departamento de Ingeniería Eléctrica; Ministerio de Ciencia e Innovación (MICIN). España; Universidad de Sevilla; Universidad de Sevilla. TEP196: Sistemas de Energía Eléctrica
    The use of online rotor current estimators with predictive current controllers has been very recently stated in five-phase induction motor drives, where the closed-loop performance of the system is improved by using suboptimal estimators based on Kalman filters. In this paper, the interest of using optimization methods in the definition of the Kalman filter, like the covariance technique, is analyzed. Obtained system performances using optimal and suboptimal rotor current estimators are experimentally compared.
  • Acceso AbiertoArtículo
    Multiphase rotor current observers for current predictive control: A five-phase case study
    (Elsevier, 2016-04) Martín Torres, Cristina; Arahal, Manuel R.; Barrero, Federico; Durán, Mario J.; Universidad de Sevilla. Departamento de Ingeniería Eléctrica; Junta de Andalucía; Ministerio de Economía y Competitividad (MINECO). España; Universidad de Sevilla. TEP196: Sistemas de Energía Eléctrica
    The use of multiphase drives has gained importance in recent times due to some advantages that they provide over conventional three-phase ones. High performance stator current control can be achieved by means of direct command of voltage source inverter. In this context finite-state model predictive control is a very flexible strategy that has been recently proposed and analyzed. Nevertheless, its implementation must solve the problem of estimating rotor quantities, being the conventional solution a simple backtracking procedure. In this respect, observers appear as an attractive alternative. However, while they have been used with FOC, sensorless drives and for fault detection, they have not been used yet for predictive control of drives as a way to provide rotor values estimates. In this paper the authors propose to incorporate a full-order rotor current observer in a finite-state model predictive controller of a five-phase induction machine. Pole placement design based on Butterworth filters is used. The new estimation scheme and the standard procedure are compared. By means of experimental tests, the differences between both approaches and the benefits of including a rotor observer are illustrated and verified.
  • Acceso AbiertoArtículo
    Control of Solar Energy Systems
    (Annual Review, 2024-07) Camacho, Eduardo F.; Ruiz-Moreno, Sara; Aguilar López, José María; Gallego Len, Antonio Javier; García Rodríguez, Ramón Andrés; Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática; European Research Council (ERC); Ministerio de Ciencia, Innovación y Universidades (MICINN). España
    This review deals with the control of parabolic trough collector (PTC) solar power plants. After a brief introduction, we present a description of PTC plants. We then provide a short literature review and describe some of our experiences. We also describe new control trends in PTC plants. Recent research has focused on (a) new control methods using mobile sensors mounted on drones and unmanned ground vehicles as an integral part of the control systems; (b) spatially distributed solar irradiance estimation methods using a variable fleet of sensors mounted on drones and unmanned ground vehicles; (c) strategies to achieve thermal balance in large-scale fields; (d) new model predictive control algorithms using mobile solar sensor estimates and predictions for safer and more efficient plant operation, which allow the effective integration of solar energy and combine coalitional and artificial intelligence techniques; and (e) fault detection and diagnosis methods to ensure safe operation.
  • Acceso AbiertoArtículo
    Tracking-Based Distributed Equilibrium Seeking for Aggregative Games
    (IEEE, 2024-02) Carnevale, Guido; Fabiani, Filippo; Fele, Filiberto; Margellos, Kostas; Notarstefano, Giuseppe; Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática; Ministerio de Asuntos Exteriores y Cooperación Internacional. Italia; Ministerio de Ciencia, Innovación y Universidades. España; Agencia Estatal de Investigación. España; European Union (UE); European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)
    We propose fully-distributed algorithms for Nash equilibrium seeking in aggregative games over networks. We first consider the case where local constraints are present and we design an algorithm combining, for each agent, (i) the projected pseudo-gradient descent and (ii) a tracking mechanism to locally reconstruct the aggregative variable. To handle coupling constraints arising in generalized settings, we propose another distributed algorithm based on (i) a recently emerged augmented primal-dual scheme and (ii) two tracking mechanisms to reconstruct, for each agent, both the aggregative variable and the coupling constraint satisfaction. Leveraging tools from singular perturbations analysis, we prove linear convergence to the Nash equilibrium for both schemes. Finally, we run extensive numerical simulations to confirm the effectiveness of our methods and compare them with state-of-the-art distributed equilibrium-seeking algorithms.
  • Acceso AbiertoArtículo
    Distributed Allocation and Scheduling of Tasks With Cross-Schedule Dependencies for Heterogeneous Multi-Robot Teams
    (Institute of Electrical and Electronics Engineers (IEEE), 2024) Arbanas Ferreria, Barbara; Petrovic, Tamara; Orsag, Matko; Martínez de Dios, José Ramiro; Bogdan, Stjepan; Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática; European Union (UE); Universidad de Sevilla. TEP151: Robotica, Visión y Control
    To enable safe and efficient use of multi-robot systems in everyday life, a robust and fast method for coordinating their actions must be developed. In this paper, we present a distributed task allocation and scheduling algorithm for missions where the tasks of different robots are tightly coupled with temporal and precedence constraints. The approach is based on representing the problem as a variant of the vehicle routing problem, and the solution is found using a distributed metaheuristic algorithm based on evolutionary computation (CBM-pop). Such an approach allows a fast and near-optimal allocation and can therefore be used for online applications. Simulation results show that the approach has better computational speed and scalability without loss of optimality compared to the state-of-the-art distributed methods. An application of the planning procedure to a practical use case of a greenhouse maintained by a multi-robot system is given.
  • Acceso AbiertoArtículo
    Stability and control of VSC-based HVDC systems: A systematic review
    (ELSEVIER, 2024) Mohammadi, Fazel; Azizi, Neda; Moradi, Hassan; Rouzbehi, Kumars; Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática; Universidad de Sevilla. TEP-116: Automática y Robótica Industrial
    The technological development in the area of power electronics has paved the way for the construction of High Voltage Direct Current (HVDC) systems. The utilization of HVDC grids alongside conventional High Voltage Alternating Current (HVAC) grids poses several challenges, especially, from stability and control points of view. Indeed, moving towards such systems in the context of conventional Alternating Current (AC) power systems cannot be possible without ensuring the overall stability of hybrid HVAC/HVDC grids. This paper analyzes different aspects of the stability of Voltage Source Converter (VSC)-based HVDC grids and presents various methods of improving stability based on a systematic and comprehensive review. In addition, this paper provides a concise classification of various control methods to improve the operation of such grids and the advantages of each method.
  • Acceso AbiertoArtículo
    An MPC-based algorithm for estimating the spatial DNI of cloud shaded regions using a robotic sensor system
    (IEEE, 2024-04) Aguilar López, José María; García Rodríguez, Ramón Andrés; Camacho, Eduardo F.; Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática; European Research Council (ERC); European Union (UE); Universidad de Sevilla. TEP116: Automática y Robótica Industrial
    This paper presents an original algorithm based on the Model Predictive Control strategy for estimating the direct normal irradiance of cloud shaded regions using a mobile robotic sensor system to improve the control of a solar thermal power plant. This new algorithm generates the waypoints of the robot team solving a minimisation problem where the objective function combines several criteria, including the measurements taken by the team. The novel method has been tested by simulation with groups of different numbers of unmanned aerial vehicles using the shape of real cloud shadows projected on the ground extracted from images and it improves the estimation error and the estimation time of previous algorithms.
  • Acceso AbiertoArtículo
    A decentralized approach for the aerial manipulator robust trajectory tracking
    (PLOS, 2024-03) Tlatelpa-Osorio, Yarai Elizabeth; Rodríguez-Cortés, Hugo; Acosta Rodríguez, José Ángel; Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática; Consejo Nacional de Ciencia y Tecnología (CONACYT). México; Universidad de Sevilla. TEP995: Multi-robot And Control Systems
    This paper introduces a new decentralized control strategy for an unmanned aerial manipulator (UAM) constrained to the vertical plane. The control strategy comprises two loops: the first compensates for the aerial vehicle’s impact on the manipulator; and the second one implements independent controllers for the aerial vehicle and the manipulator. The controller for the aerial vehicle includes an estimator to compensate for the dynamic influence of the manipulator, even if it is affected by external wind-gust disturbances. The manipulator has two revolute joints; however, it is modeled as an dynamically equivalent manipulator, with one revolute and one prismatic joint. The proposed control strategy’s performance is evaluated using a simulator that includes the vehicle’s aerodynamics and the manipulator’s contact force and moment.
  • Acceso AbiertoArtículo
    An integral and MRAC-based approach to the adaptive stabilisation of a class of linear time-delay systems with unknown parameters
    (AMCS, 2024-03) Ramírez Jerónimo, Luis Felipe; Saldivar, Belem; Aguilar-Ibáñez, Carlos Fernando; Acosta Rodríguez, José Ángel; Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática; Consejo Nacional de Ciencia y Tecnología (CONACYT). México; Instituto Politécnico Nacional. México; Universidad de Sevilla. TEP995: Multi-robot And Control Systems
    The design of a novel strategy based on the model reference adaptive control method for the stabilisation of a second-order linear time-delay system with unknown parameters is presented. The proposed approach is developed under the assumption that only one state of the system is available, and the sign of the control gain is known. First, the integral operator is applied to obtain a new representation of the original system, where the whole state is known. The use of the integral operator decomposes the control problem into two subproblems that are solved by using the model reference adaptive control method and the backstepping procedure. The effectiveness of the proposed approach is illustrated through an academic example and a practical application case regarding a chemical reactor recycle system.
  • Acceso AbiertoArtículo
    State-Space Kriging: A Data-Driven Method to Forecast Nonlinear Dynamical Systems
    (IEEE, 2022-01) Carnerero Panduro, Alfonso Daniel; Rodríguez Ramírez, Daniel; Alamo, Teodoro; Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática; Agencia Estatal de Investigación. España; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Junta de Andalucía; Universidad de Sevilla. TEP950: Estimación, Predicción, Optimización y Control
    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.