Papers by Alejandro Anderson
Water Quality Map Extraction from Field Measurements Targetting Robotic Simulations
IFAC-PapersOnLine, 2022
Resumen: Recently, a Model Predictive Control (MPC) scheme suitable for closedloop re-identificat... more Resumen: Recently, a Model Predictive Control (MPC) scheme suitable for closedloop re-identification was proposed which solves, in a non-conservative form, the potential conflict between the persistent excitation of the system and the stabilization. The scheme uses the concept of probabilistic invariance to define the target set, exploiting in that way the knowledge of the probabilistic distribution of the excitation signal to design a non-competitive two-objective MPC formulation. In this work, we prove some theoretical properties of the scheme that have fundamental practical consequences, including the finite-time convergence to the target set and a lower probability bound about the period of time the state remains in that set for the identification procedure. We also include new simulation results comparing the performance of the proposed approach with those of a previous deterministic formulation.
Control predictivo robusto apto para la identificación de sistemas en lazo cerrado
El Control Predictivo basado en modelos (MPC) es una estrategia de control avanzado ampliamente u... more El Control Predictivo basado en modelos (MPC) es una estrategia de control avanzado ampliamente utilizada (y estudiada) tanto en ámbitos académicos como industriales. Entre sus principales virtudes se encuentra la de ser una estrategia optimizante, con robustez frente a perturbaciones o discrepancias entre planta y modelo, y la de considerar de forma explícita restricciones en las variables de estado, de entrada y de salida del sistema que se quiere controlar. Para su formulación - intrínsecamente ligada al estudio de sistemas dinámicos - pueden alcanzarse diferentes niveles de abstracción, de modo de garantizar,bajo ciertas hipótesis generales, estabilidad, factibilidad recursiva, robustez y optimalidad según criterios exógenos al problema de control.Más allá de sus evidentes ventajas, el uso explícito de objetivos tipo conjunto ha sido poco explotado en la literatura. Esta generalización - la de pasar de objetivos dados por puntos de equilibrios a objetivos dados por conjuntos invariantes - ha mostrado ser de suma utilidad en diferentes aplicaciones, sino en la mayoría. Partiendo de que en la realidad raramente se encuentren objetivos puntuales (entendiendo por tal la abstracción matemática que representa el punto), es habitual encontrar en aplicaciones tan diversas como lo son las industriales o las biomédicas, lo que se conoce como control por zonas, que no es más que una primera generalización que considera como objetivo de control un conjunto (agregación) de puntos de equilibrio. La extensión que le sigue es la de considerar conjuntos que también permitan el movimiento de los estados en su interior (régimen transitorio), y allí la generalización por excelencia del concepto de equilibrio son los conjuntos invariantes.De este modo, y con independencia del tamaño que estos conjuntos puedan tener en torno al equilibrio formal que contienen, se abre un marco conceptual diferente para las formulaciones de MPC. Primero, el nuevo control considerará alcanzado el objetivo una vez que el sistema alcance el conjunto, pero dada su condición de invariante, el sistema ya no abandonará a este, a menos que se presente una perturbación o un cambio de objetivo. En ese caso, sin embargo, el control se activará nuevamente, devolviendo el sistema al conjunto objetivo.En este escenario, y dado que dentro del conjunto objetivo el sistema estará, en cierto modo, en lazo abierto (el controlador sólo prohibirá la aplicación de acciones de control fuera de cierto conjunto), pueden realizarse otras operaciones, como ser la excitación y posterior recolección de datos para una re-identificación. Y esto puede hacerse en forma segura, dada la supervisión que ejercerá el control para casos en que el conjunto objetivo sea abandonado. Más aún, bajo el concepto novedoso de conjuntos invariantes probabilísticos, esta operación puede realizarse en regiones arbitrariamente reducidas, si se está dispuestoa permitir 'escapes' esporádicos del conjunto, con una probabilidad baja. Más allá de este tipo de aplicaciones, el marco general de MPC basado en conjuntos, permite también, desde un punto de vista puramente teórico, garantizar la atractividad en tiempo finito de esos conjuntos, bajo ciertas suposiciones simples, como ser, la de que los conjuntos sean, además de invariantes, contractivos. Más aún, a partir de esta convergencia en tiempo finito, se puede finalmente extender el dominio de atracción de los controles MPC a su máximo posible (máximo que depende sólo del sistema y sus restricciones), por medio de una secuencia de leyes implícitas, que al contar con la garantía dealcance en tiempo finito, van llevando el sistema de un conjunto a otro, estrictamente interior, de modo de alcanzar cualquier equilibrio admisible.En este marco, el objetivo general de la presente tesis es ampliar las fronteras de los desarrollos teóricos del MPC basados en conjuntos invariantes, con objetivos concretos como son los de mejorar las condiciones de estabilidad, ampliar los dominios de atracción y permitir aplicaciones de tipo duales, es decir, aplicaciones en donde parte del objetivo se lleva a cabo dentro del conjunto invariante considerado como objetivos de control.Fil: Anderson, Alejandro 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; Argentin
arXiv (Cornell University), Jun 15, 2020
While many epidemiological models have being proposed to understand and handle COVID-19, too litt... more While many epidemiological models have being proposed to understand and handle COVID-19, too little has been invested to understand how the virus replicates in the human body and potential antiviral can be used to control the replication cycle. In this work, using a control theoretical approach, validated mathematical models of SARS-CoV-2 in humans are properly characterized. A complete analysis of the main dynamic characteristic is developed based on the reproduction number. The equilibrium regions of the system are fully characterized, and the stability of such a regions, formally established. Mathematical analysis highlights critical conditions to decrease monotonically SARS-CoV-2 in the host, such conditions are relevant to tailor future antiviral treatments. Simulation results show the potential benefits of the aforementioned system characterization.
arXiv (Cornell University), Oct 1, 2019
This paper presents a novel set-based model predictive control for tracking, which provides the l... more This paper presents a novel set-based model predictive control for tracking, which provides the largest domain of attraction, even with the minimal predictive/control horizon. The formulation-which consists of a single optimization problem-shows a dual behavior: one operating inside the maximal controllable set to the feasible equilibrium set, and the other operating at the N-controllable set to the same equilibrium set. Based on some finite-time convergence results, asymptotic stability of the resulting closed-loop is proved, while recursive feasibility is ensured for any change of the setpoint. The properties and advantages of the proposal have been tested on simulation models.
arXiv (Cornell University), Dec 31, 2020
Mathematical models describing SARS-CoV-2 dynamics and the corresponding immune responses in pati... more Mathematical models describing SARS-CoV-2 dynamics and the corresponding immune responses in patients with COVID-19 can be critical to evaluate possible clinical outcomes of antiviral treatments. In this work, based on the concept of virus spreadability in the host, antiviral effectiveness thresholds are determined to establish whether or not a treatment will be able to clear the infection. In addition, the virus dynamic in the host-including the time-to-peak and the final monotonically decreasing behavior-is chracterized as a function of the treatment initial time. Simulation results, based on nine real patient data, show the potential clinical benefits of a treatment classification according to patient critical parameters. This study is aimed at paving the way for the different antivirals being developed to tackle SARS-CoV-2.
Finite-time convergence results in Model Predictive Control
Asymptotic stability (convergence and $\epsilon-\delta$ stability) of invariant sets under model ... more Asymptotic stability (convergence and $\epsilon-\delta$ stability) of invariant sets under model predictive control (MPC) strategies have been extensively studied in the last decades. Lyapunov theory is in some sense the common denominator of the different forms to achieve such results. However, the meaningful problem of the finite-time convergence (for a given fixed control horizon) has not received much attention in the literature (with some remarkable exceptions). In this work a novel set-based MPC that ensures finite-time convergence in a natural way is presented. The contractivity and non-empty interior conditions of the target set, the consideration of an appropriate input set and the continuity of the dynamic model are the main hypothesis to be made. An upper bound for the convergence time is also provided.
Permanence regions for switched linear systems under waiting-time constraints
IFAC-PapersOnLine, 2022
IEEE Latin America Transactions, Jun 1, 2016
Recently, a Model Predictive Control (MPC) suitable for closed-loop re-identification was propose... more Recently, a Model Predictive Control (MPC) suitable for closed-loop re-identification was proposed, which solves the potential conflict between the persistent excitation of the system and the stabilization of the closed-loop by extending the equilibrium-pointstability to the invariant-set-stability. The proposed objective set, however, derives in large regions that contain conservatively the excited system evolution. In this work, based on the concept of probabilistic invariant sets, the controller target sets are substantially reduced ensuring the invariance with a sufficiently large probability (instead of deterministically), giving the resulting MPC controller the necessary flexibility to be applied in a wide range of systems.
Systems & Control Letters, Jul 1, 2022
The interest in non-linear impulsive systems (NIS) has been growing due to its impact in applicat... more The interest in non-linear impulsive systems (NIS) has been growing due to its impact in application problems such as disease treatments (diabetes, HIV, influenza, among many others), where the control action (drug administration) is given by short-duration pulses followed by time periods of null values. Within this framework the concept of equilibrium needs to be extended (redefined) to allows the system to keep orbiting (between two consecutive pulses) in some state space regions out of the origin, according to usual objectives of most real applications. Although such regions can be characterized by means of a discrete-time system obtained by sampling the NIS at the impulsive times, no agreements have reached about their asymptotic stability (AS). This paper studies the asymptotic stability of control equilibrium orbits for NSI, based on the underlying discrete time system, in order to establish the conditions under which the AS for the latter leads to the AS for the former. Furthermore, based on the latter AS characterization, an impulsive Model Predictive Control (i-MPC) that feasibly stabilizes the non-linear impulsive system is presented. Finally, the proposed stable MPC is applied to two control problems of interest: the intravenous bolus administration of Lithium and the administration of antiretrovirals for HIV treatments.
Systems & Control Letters, Aug 1, 2018
This work extends a recent set-based Model Predictive Control (MPC) scheme for closed loop reiden... more This work extends a recent set-based Model Predictive Control (MPC) scheme for closed loop reidentification that solves the potential conflict between the simultaneous persistent excitation of the system and the stabilization of the closed-loop system. Based on the original scheme proposed in González et al. (2014), this manuscript extends those results by taking into account model uncertainties and by exploiting the knowledge of the probability distribution of the excitation signal used to identify the plant. The robust extension solves the main drawback of the previous work, which was limited to a nominal analysis while the need of re-identification assumes the presence of model uncertainties. In addition, the probabilistic analysis allows the use of smaller target sets computed as Probabilistic Invariant Sets (PIS), improving the system performance during the identification procedure. Simulation results show the practical benefits of the novel robust strategy.
Communications in Nonlinear Science and Numerical Simulation, Apr 1, 2021
Switched systems in which the manipulated control action is the time-depending switching signal d... more Switched systems in which the manipulated control action is the time-depending switching signal describe many engineering problems, mainly related to biomedical applications. In such a context, to control the system means to select an autonomous system-at each time step-among a given finite family. Even when this selection can be done by solving a Dynamic Programming (DP) problem, such a solution is often difficult to apply, and state/control constraints cannot be explicitly considered. In this work a new set-based Model Predictive Control (MPC) strategy is proposed to handle switched systems in a tractable form. The optimization problem at the core of the MPC formulation consists in an easy-to-solve mixed-integer optimization problem, whose solution is applied in a receding horizon way. Two biomedical applications are simulated to test the controller: (i) the drug schedule to attenuate the effect of viral mutation and drugs resistance on the viral load, and (ii) the drug schedule for Triple Negative breast cancer treatment. The numerical results suggest that the proposed strategy outperform the schedule for available treatments.
Computing Control Invariant Sets for Waiting-Time Switched Systems: A Study Case of Glucose Regulation
IEEE Control Systems Letters
Map Meshing Impact on the Efficiency of Nonlinear Set-based Model Predictive Control for Water Quality Assessment
IFAC-PapersOnLine
Proceedings of the 19th International Conference on Informatics in Control, Automation and Robotics
Acquiring vast and reliable data of physicochemical parameters is critical to environment monitor... more Acquiring vast and reliable data of physicochemical parameters is critical to environment monitoring. In the context of water quality analysis, data collection solutions have to overcome challenges related to the scale of environments to be explored. Sites to monitor can be large or remote. These challenges can be approached by the use of Unmanned Vehicles (UVs). Robots provide both flexibility on intervention plans and technological methods for real-time data acquisition. Being autonomous, UVs can explore areas difficult to access or far from the shore. This paper presents a nonlinear Model Predictive Control (MPC) for UV-based exploration. The strategy aims to improve the data collection of physicochemical parameters with the use of an Unmanned Surface Vehicle (USV) targeting water quality analysis. We have performed simulations based on real field experiments with a SPYBOAT® on the Heron Lake in Villeneuve d'Ascq, France. Numerical results suggest that the proposed strategy outperforms the schedule of mission planning and exploration for large areas.
Control predictivo robusto apto para la identificación de sistemas en lazo cerrado
El Control Predictivo basado en modelos (MPC) es una estrategia de control avanzado ampliamente u... more El Control Predictivo basado en modelos (MPC) es una estrategia de control avanzado ampliamente utilizada (y estudiada) tanto en ámbitos académicos como industriales. Entre sus principales virtudes se encuentra la de ser una estrategia optimizante, con robustez frente a perturbaciones o discrepancias entre planta y modelo, y la de considerar de forma explícita restricciones en las variables de estado, de entrada y de salida del sistema que se quiere controlar. Para su formulación - intrínsecamente ligada al estudio de sistemas dinámicos - pueden alcanzarse diferentes niveles de abstracción, de modo de garantizar,bajo ciertas hipótesis generales, estabilidad, factibilidad recursiva, robustez y optimalidad según criterios exógenos al problema de control.Más allá de sus evidentes ventajas, el uso explícito de objetivos tipo conjunto ha sido poco explotado en la literatura. Esta generalización - la de pasar de objetivos dados por puntos de equilibrios a objetivos dados por conjuntos invariantes - ha mostrado ser de suma utilidad en diferentes aplicaciones, sino en la mayoría. Partiendo de que en la realidad raramente se encuentren objetivos puntuales (entendiendo por tal la abstracción matemática que representa el punto), es habitual encontrar en aplicaciones tan diversas como lo son las industriales o las biomédicas, lo que se conoce como control por zonas, que no es más que una primera generalización que considera como objetivo de control un conjunto (agregación) de puntos de equilibrio. La extensión que le sigue es la de considerar conjuntos que también permitan el movimiento de los estados en su interior (régimen transitorio), y allí la generalización por excelencia del concepto de equilibrio son los conjuntos invariantes.De este modo, y con independencia del tamaño que estos conjuntos puedan tener en torno al equilibrio formal que contienen, se abre un marco conceptual diferente para las formulaciones de MPC. Primero, el nuevo control considerará alcanzado el objetivo una vez que el sistema alcance el conjunto, pero dada su condición de invariante, el sistema ya no abandonará a este, a menos que se presente una perturbación o un cambio de objetivo. En ese caso, sin embargo, el control se activará nuevamente, devolviendo el sistema al conjunto objetivo.En este escenario, y dado que dentro del conjunto objetivo el sistema estará, en cierto modo, en lazo abierto (el controlador sólo prohibirá la aplicación de acciones de control fuera de cierto conjunto), pueden realizarse otras operaciones, como ser la excitación y posterior recolección de datos para una re-identificación. Y esto puede hacerse en forma segura, dada la supervisión que ejercerá el control para casos en que el conjunto objetivo sea abandonado. Más aún, bajo el concepto novedoso de conjuntos invariantes probabilísticos, esta operación puede realizarse en regiones arbitrariamente reducidas, si se está dispuestoa permitir 'escapes' esporádicos del conjunto, con una probabilidad baja. Más allá de este tipo de aplicaciones, el marco general de MPC basado en conjuntos, permite también, desde un punto de vista puramente teórico, garantizar la atractividad en tiempo finito de esos conjuntos, bajo ciertas suposiciones simples, como ser, la de que los conjuntos sean, además de invariantes, contractivos. Más aún, a partir de esta convergencia en tiempo finito, se puede finalmente extender el dominio de atracción de los controles MPC a su máximo posible (máximo que depende sólo del sistema y sus restricciones), por medio de una secuencia de leyes implícitas, que al contar con la garantía dealcance en tiempo finito, van llevando el sistema de un conjunto a otro, estrictamente interior, de modo de alcanzar cualquier equilibrio admisible.En este marco, el objetivo general de la presente tesis es ampliar las fronteras de los desarrollos teóricos del MPC basados en conjuntos invariantes, con objetivos concretos como son los de mejorar las condiciones de estabilidad, ampliar los dominios de atracción y permitir aplicaciones de tipo duales, es decir, aplicaciones en donde parte del objetivo se lleva a cabo dentro del conjunto invariante considerado como objetivos de control.Fil: Anderson, Alejandro 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; Argentin
Probabilistic Invariant Set for Closed-loop re-identification
Workshop on Information Processing and Control, 2015
Permanence regions for switched linear systems under waiting-time constraints
IFAC-PapersOnLine
Automatica
Mathematical models are instrumental to forecast the spread of pathogens and to evaluate the effe... more Mathematical models are instrumental to forecast the spread of pathogens and to evaluate the effectiveness of non-pharmaceutical measures. A plethora of optimal strategies has been recently developed to minimize either the infected peak prevalence (IPP) or the epidemic final size (EFS). While most of the control strategies optimize a simple cost function along a fixed finite-time horizon, no consensus has been reached about how to simultaneously handle the IPP, the EFS, and the avoiding of new cycles of infections rebounding. In this work, based on the characterization of the dynamical behaviour of SIR-type models under control actions (including the stability of equilibrium sets, in terms of the herd immunity), it is studied how to minimize the EFS while keeping-at any time-the IPP controlled. A procedure is proposed to tailor non-pharmaceutical interventions by separating transient from stationary control objectives and the potential benefits of the strategy are illustrated by a detailed analysis and simulation results related to the COVID-19 pandemic.
Systems & Control Letters
The interest in non-linear impulsive systems (NIS) has been growing due to its impact in applicat... more The interest in non-linear impulsive systems (NIS) has been growing due to its impact in application problems such as disease treatments (diabetes, HIV, influenza, among many others), where the control action (drug administration) is given by short-duration pulses followed by time periods of null values. Within this framework the concept of equilibrium needs to be extended (redefined) to allows the system to keep orbiting (between two consecutive pulses) in some state space regions out of the origin, according to usual objectives of most real applications. Although such regions can be characterized by means of a discrete-time system obtained by sampling the NIS at the impulsive times, no agreements have reached about their asymptotic stability (AS). This paper studies the asymptotic stability of control equilibrium orbits for NSI, based on the underlying discrete time system, in order to establish the conditions under which the AS for the latter leads to the AS for the former. Furthermore, based on the latter AS characterization, an impulsive Model Predictive Control (i-MPC) that feasibly stabilizes the non-linear impulsive system is presented. Finally, the proposed stable MPC is applied to two control problems of interest: the intravenous bolus administration of Lithium and the administration of antiretrovirals for HIV treatments.
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Papers by Alejandro Anderson