An algebraic approach to the structural properties of positive state control systems

[EN] In this paper, we deal with discrete-time linear control systems in which the state is constrained to lie in the positive orthant R_+^n independently of the inputs involved, that is, the inputs can take negative values. Such (positive state) systems appear, for example, in ecology models where the removal of individuals from a population is described. Controllability and reachability are fundamental properties of a system that show its ability to move in space, which are analyzed from an algebraic point of view throughout the text, paying special attention to the single-input case.This work has been partially supported by Ministerio de Ciencia e Innovacion through Grants DPI-2013-46982-C2-1-R and MTM-2013-43678-P.Ricarte Benedito, B.; Romero Vivó, S. (2018). An algebraic approach to the structural properties of positive state control systems. Mathematical Methods in the Applied Sciences. 41(6):2370-2378. https://doi.org/10.1002/mma.4351S2370237841

Propiedades de las matrices totalmente no positivas

Una matriz real A se dice que es totalmente (negativa) no positiva si todos sus menores son (negativos) no positivos. En este trabajo veremos la factorización LDU de una matriz totalmente no positiva e invertible a partir del método de eliminación completo de Neville sin intercambio de filas y columnas. Dicha factorización nos permitirá generar de una forma sencilla matrices totalmente (negativas) no positivas del cualquier orden a partir de matrices totalmente positivas.Ministerio de Educación y Ciencia. Dirección General de InvestigaciónUniversidad Politécnica de Valenci

Realizaciones positivas de determinados sistemas singulares

En este trabajo se estudian los sistemas singulares lineales de control a partir de las propiedades obtenidas para los sistemas estándares. Se obtienen realizaciones positivas de ciertas matrices de trasferencia con polos reales, analizando las condiciones para que la dimensión de la realización positiva sea minimal

Full rank factorization in quasi-LDU form of totally nonpositive rectangular matrices

Let A = (a(ij)) is an element of R-nxm be a totally nonpositive matrix with rank(A) = r <= min{n, m} and a(11) = 0. In this paper we obtain a characterization in terms of the full rank factorization in quasi-LDU form, that is, A = (L) over tilde DU where (L) over tilde is an element of R-nxr is a block lower echelon matrix, U is an element of R-rxm is a unit upper echelon totally positive matrix and D is an element of R-rxr is a diagonal matrix, with rank((L) over tilde) = rank(U) = rank(D) = r. We use this quasi-LDU decomposition to construct the quasi-bidiagonal factorization of A. Moreover, some properties about these matrices are studied. (C) 2013 Elsevier Inc. All rights reserved.This research was supported by the Spanish DGI grant MTM2010-18228.Cantó Colomina, R.; Ricarte Benedito, B.; Urbano Salvador, AM. (2014). Full rank factorization in quasi-LDU form of totally nonpositive rectangular matrices. Linear Algebra and its Applications. 440:61-82. https://doi.org/10.1016/j.laa.2013.11.002S618244

Sliding-mode disturbance observers for an artificial pancreas without meal announcement

[EN] Carbohydrate counting is not only a burden for patients with type 1 diabetes, but estimation errors in meal announcement could also degrade the outcomes of the current hybrid closed-loop systems. Therefore, removing meal announcement is desirable. A novel control system is addressed here to face postprandial control without meal announcement. The proposed system grounds on two applications of the sliding mode observers in dealing with disturbances: first, the equivalent output technique is used to reconstruct the meal rate of glucose appearance via a first order sliding mode observer; second, a super-twisting -based residual generator is used to detect the meals. Subsequently, a bolusing algorithm uses the information of the two observers to trigger a series of boluses based on a proportional-derivative-like strategy. An in silico validation with 30 patients in a 30-day scenario reveals that the meal detector algorithm achieves a low rate of false positives per day (0.1 (0.1), mean (SD)) and a detection time of 28.5(6.2) min. Additionally, the bolusing algorithm fulfills a non-statistically different mean glucose than the hybrid counterpart with bolus misestimation (146.69 (12.20) mg/dLvs. 144.28 (11.01) mg/dL,p>0.05), without increasing hypoglycemia (0.029 (0.077) vs. 0.004 (0.014)%, p > 0,05), although at the expense of a slightly higher time in hyperglycemia (22.51(8.72) % vs. 18.65 (7.89)%, p <0.05) due to the conservative tuning of the bolusing algorithm for the sake of safety.This work was supported by the Spanish Ministry of Economy, Industry and Competitiveness (MINECO) [grant number DPI2016-78831-C2-1-12]; the European Union [FEDER funds]: and Generalitat Valenciana [grant number ACIF/2017/021]Sala-Mira, I.; Diez, J.; Ricarte Benedito, B.; Bondía Company, J. (2019). Sliding-mode disturbance observers for an artificial pancreas without meal announcement. Journal of Process Control. 78:68-77. https://doi.org/10.1016/j.jprocont.2019.03.00868777

Insulin Estimation and Prediction A REVIEW OF THE ESTIMATION AND PREDICTION OF SUBCUTANEOUS INSULIN PHARMACOKINETICS IN CLOSED-LOOP GLUCOSE CONTROL

This work was supported by the Spanish Ministry of Economy and Competitiveness (MINECO) through grant DPI2013-46982-C2-1-R and the EU through FEDER funds.Bondía Company, J.; Romero Vivó, S.; Ricarte Benedito, B.; Diez, J. (2018). Insulin Estimation and Prediction A REVIEW OF THE ESTIMATION AND PREDICTION OF SUBCUTANEOUS INSULIN PHARMACOKINETICS IN CLOSED-LOOP GLUCOSE CONTROL. IEEE Control Systems. 38(1):47-66. https://doi.org/10.1109/MCS.2017.2766312S476638

Aplicaciones de las matrices totalmente positivas

[ES] Se dice que una matriz es totalmente positiva (se denota por TP) si el determinante de cada una de sus submatrices cuadradas es mayor o igual que cero, y es estrictamente totalmente positiva (denotada por STP) si todos los determinantes de sus submatrices cuadradas son positivos. En este trabajo vamos a considerar la teoría de la total positividad con considerables consecuencias y aplicaciones en diferentes áreas, como son en Biología, Física, Economía, etc. y también en la propia ciencia matemática.Este trabajo ha sido financiado por el proyecto DGI MTM2013-43678-P.Cantó Colomina, R.; Ricarte Benedito, B.; Urbano Salvador, AM. (2014). Aplicaciones de las matrices totalmente positivas. Compobell, S.L. http://hdl.handle.net/10251/74277

Aplicación del álgebra matricial en el estudio de los sistemas de control de ciertos procesos agroforestales

La finalidad de esta comunicación es presentar nuestro trabajo a la comunidad universitaria. Nuestra línea de investigación general se basa en estudiar la teoría matemática de los sistemas de control, concretamente en analizar las propiedades de los sistemas positivos y cuasi-positivos que se utilizan como herramientas de gestión de explotaciones agrícolas y cinegéticas, respectivamente. Para ello, ha sido necesario profundizar en la teoría matricial subyacente, en la que aparece la estructura de Jordan y la descomposición en valores singulares de matrices no invertibles, así como las factorizaciones de matrices.Este trabajo ha sido financiado por el proyecto DGI MTM2010-18228.Cantó Colomina, R.; Ricarte Benedito, B.; Urbano Salvador, AM. (2013). Aplicación del álgebra matricial en el estudio de los sistemas de control de ciertos procesos agroforestales. Compobell, S.L. http://hdl.handle.net/10251/73766

On the Computation of Output Bounds for Compartmental in-Series Models under Parametric Uncertainty

[EN] In this work, the problem of obtaining tight output bounds for compartmental in-series models under parametric uncertainty is addressed. It is well-known that current methods used to compute a solution envelope may produce a significant overestimation. However, monotonicityanalysis enables us to estimate a tight solution envelope. Our main aim is to get an equivalent model to the initial one, which is usually non-monotone, by means of a suitable combination of equations. In this new model the system monotonicity with respect to the uncertain parameters depends on the elimination rate values of the original model. If the equivalent model is monotone, no overestimation occurs in the computation of the output bounds.This work was partially supported by the Spanish Ministerio de Ciencia e Innovacion through Grant DPI-2010- 20764-C02, and by the Generalitat Valenciana through Grant GV/2012/085.De Pereda Sebastián, D.; Romero Vivó, S.; Ricarte Benedito, B.; Bondía Company, J. (2012). On the Computation of Output Bounds for Compartmental in-Series Models under Parametric Uncertainty. Biomath: International Journal on Mathematical Methods and Models in Biosciences. 1(2):1-6. https://doi.org/10.11145/j.biomath.2012.10.043S161

Real-time estimation of plasma insulin concentration from continuous glucose monitor measurements

Continuous glucose monitors can measure interstitial glucose concentration in real time for closed-loop glucose control systems, known as artificial pancreas. These control systems use an insulin feedback to maintain plasma glucose concentration within a narrow and safe range, and thus to avoid health complications. As it is not possible to measure plasma insulin concentration in real time, insulin models have been used in literature to estimate them. Nevertheless, the significant interand intra-patient variability of insulin absorption jeopardizes the accuracy of these estimations. In order to reduce these limitations, our objective is to perform a real-time estimation of plasma insulin concentration from continuous glucose monitoring (CGM). Hovorka s glucose insulin model has been incorporated in an extended Kalman filter in which different selected time-variant model parameters have been considered as extended states. The observability of the original Hovorka s model and of several extended models has been evaluated by their Lie derivatives. We have evaluated this methodology with an in-silico study with 100 patients with Type 1 diabetes during 25 h. Furthermore, it has been also validated using clinical data from 12 insulin pump patients with Type 1 diabetes who underwent four mixed meal studies. Real-time insulin estimations have been compared to plasma insulin measurements to assess performance showing the validity of the methodology here used in comparison with that formerly used for insulin models. Hence, real-time estimations for plasma insulin concentration based on subcutaneous glucose monitoring can be beneficial for increasing the efficiency of control algorithms for the artificial pancreas.This work was partially supported by the Spanish Ministerio de Ciencia e Innovacion through Grant DPI-2010-20764-C02-01 and Grant DPI-2013-46982-C2-1-R, and the European Union through FEDER fund.De Pereda Sebastián, D.; Romero Vivó, S.; Ricarte Benedito, B.; Rossetti, P.; Ampudia Blasco, FJ.; Bondía Company, J. (2015). Real-time estimation of plasma insulin concentration from continuous glucose monitor measurements. Computer Methods in Biomechanics and Biomedical Engineering. Sep:1-9. https://doi.org/10.1080/10255842.2015.1077234S19Se