Juan Carlos Martínez-García

MIMO systems properties preservation under SPR substitutions

The preservation of some control-oriented positive real properties (passivity, positivity, bounded realness, as well as input-output behavior) in multi-input multi-output transfer functions is studied, when performing substitutions (of the complex Laplace variable s) by a particular class of rational strictly positive real (SPR) functions, the so-called SPR functions of zero relative degree (SPR0 functions). We also consider here the preservation of stability properties of a class of unforced linear time-invariant systems with memoryless (possibly time-varying nonlinear) input depending on the system output.

Gene regulatory network underlying the immortalization of epithelial cells

BackgroundTumorigenic transformation of human epithelial cells in vitro has been described experimentally as the potential result of spontaneous immortalization. This process is characterized by a series of cell–state transitions, in which normal epithelial cells acquire first a senescent state which is later surpassed to attain a mesenchymal stem–like phenotype with a potentially tumorigenic behavior. In this paper we aim to provide a system–level mechanistic explanation to the emergence of these cell types, and to the time–ordered transition patterns that are common to neoplasias of epithelial origin. To this end, we first integrate published functional and well–curated molecular data of the components and interactions that have been found to be involved in such cell states and transitions into a network of 41 molecular components. We then reduce this initial network by removing simple mediators (i.e., linear pathways), and formalize the resulting regulatory core into logical rules that govern the dynamics of each of the network components as a function of the states of its regulators.ResultsComputational dynamic analysis shows that our proposed Gene Regulatory Network model recovers exactly three attractors, each of them defined by a specific gene expression profile that corresponds to the epithelial, senescent, and mesenchymal stem–like cellular phenotypes, respectively. We show that although a mesenchymal stem–like state can be attained even under unperturbed physiological conditions, the likelihood of converging to this state is increased when pro–inflammatory conditions are simulated, providing a systems–level mechanistic explanation for the carcinogenic role of chronic inflammatory conditions observed in the clinic. We also found that the regulatory core yields an epigenetic landscape that restricts temporal patterns of progression between the steady states, such that recovered patterns resemble the time–ordered transitions observed during the spontaneous immortalization of epithelial cells, both in vivo and in vitro.ConclusionOur study strongly suggests that the in vitro tumorigenic transformation of epithelial cells, which strongly correlates with the patterns observed during the pathological progression of epithelial carcinogenesis in vivo, emerges from underlying regulatory networks involved in epithelial trans–differentiation during development.

Bounded control based on saturation functions of nonlinear under-actuated mechanical systems: The cart-pendulum system case

We are concerned in this paper by bounded control of nonlinear underactuated dynamical systems. We focus our exposition on a feedback-based stabilization bounded control action shaped by saturation functions. A simple stabilizing controller for the well-known cart-pendulum system is then designed in this paper. Our control strategy describes in lumped linear time-invariant terms the concerned underactuated nonlinear system as a cascade nonlinear dynamical system consisted of a simple chain of four integrators with a high-order smooth nonlinear perturbation, and assumes initialization of the resulting underactuated system in the upperhalf plane. Our proposed feedback-based regulation design procedure involves the simultaneous combination of two control actions: one bounded linear and one bounded quasilinear. Control boundedness is provided in both involved control actions by specific saturation functions. The first bounded control action brings the non-actuated coordinate near to the upright position and keep it inside of a well-characterized small vicinity, whereas the second bounded control action asymptotically brings the whole state of the dynamical system to the origin. The necessary closed-loop stability analysis uses standard linear stability arguments as well as the traditional well-known Lyapunov method and the LaSalles theorem. Our proposed control law ensures global stability of the closed-loop system in the upper half plane, while avoiding the necessity of solving either partial differential equations, nonlinear differential equations or fixed-point controllers. We illustrate the effectiveness of the proposed control strategy via numerical simulations.

PD Control for Vibration Attenuation in a Physical Pendulum with Moving Mass

This paper proposes a Proportional Derivative controller plus gravity compensation to damp out the oscillations of a frictionless physical pendulum with moving mass. A mass slides along the pendulum main axis and operates as an active vibration-damping element. The Lyapunov method together with the LaSalles theorem allows concluding closed-loop asymptotic stability. The proposed approach only uses measurements of the moving mass position and velocity and it does not require synchronization of the pendulum and moving mass movements. Numerical simulations assess the performance of the closed-loop system.

Characterizing families of positive real matrices by matrix substitutions on scalar rational functions

This paper concerns the characterization of positive real matrices generated by substitutions (of the Laplace variable s) in scalar rational transfer function by matrix positive real functions. Our main results are restricted to both strongly strictly positive real matrices arid strictly bounded real matrices. As a way to illustrate our main results, we also include here a partial extension of both the Kalman-Yakubovich-Popov lemma (for strongly strictly positive real systems of zero relative degree) and the circle criterion (for strictly positive real systems of zero relative degree).

Lyapunov-Based PD Linear Control of the Oscillatory Behavior of a Nonlinear Mechanical System: The Inverted Physical Pendulum with Moving Mass Case

This paper concerns active vibration damping of a frictionless physical inverted pendulum with a radially moving mass. The motion of the inverted pendulum is restricted to an admissible set. The proposed Proportional Derivative linear controller damps the inverted pendulum (which is anchored by a torsion spring to keep it in a stable upright position), exerting a force on the radially moving mass. The controller design procedure, which follows a traditional Lyapunov-based approach, tailors the energy behavior of the system described in Euler-Lagrange terms.

Tuning of Two-Degrees-of-Freedom PID Controllers via the Multiobjective Genetic Algorithm NSGA-II

In this paper a procedure is used to tuner two degrees of freedom controllers (PID-ISA) raised as a multiobjective optimization problem (MOP), applying the multiobjective genetic algorithm NSGA-II (MOGA NSGA-II). The objective functions are deployed considering, setpoint response, load disturbances, measurement noises and robustness to model uncertainty

Preservation of solvability conditions in Riccati equations when applying SPR0 substitutions

We are concerned by algebraic Riccati equations associated to robust control problems. We tackle the preservation of solvability conditions of algebraic Riccati equations when applying substitutions of the Laplace variable s by some class of strictly positive real functions in the corresponding single-input and single-output transfer functions. In particular, we study the preservation of solvability conditions associated to the existence of stabilizing solutions of algebraic Riccati equations characterized by an H/sup /spl infin//-norm constraint on a particular linear time-invariant system. We illustrate our results with the study of the closed-loop stability of a family of linear time-invariant systems, affected by time-varying uncertainty, controlled via robust sliding mode control.

Fixed Poles and Disturbance Rejecting Feedback Synthesis

Abstract The aim of this paper is to give an algebraic characterization of the family of static state feedbacks which decouple the disturbance, in a linear time invariant system, and which give rise to the minimal set of closed-loop fixed poles, while insuring the maximum of free degrees in terms of pole placement.

Medical Systems Biology

The aim of this volume is to encourage the use of systems-level methodologies to contribute to the improvement of human-health . We intend to motivate biomedical researchers to complement their current theoretical and empirical practice with up-to-date systems biology conceptual approaches. Our perspective is based on the deep understanding of the key biomolecular regulatory mechanisms that underlie health, as well as the emergence and progression of human-disease . We strongly believe that the contemporary systems biology perspective opens the door to the effective development of novel methodologies to the improvement of prevention . This requires a deeper and integrative understanding of the involved underlying systems-level mechanisms. In order to explain our proposal in a simple way, in this chapter we privilege the conceptual exposition of our chosen framework over formal considerations. The formal exposition of our proposal will be expanded and discussed later in the next chapters.