Geometric control of the cell cycle.

How do cells sense their own size and shape? And how does this information regulate progression of the cell cycle? Our group, in parallel to that of Paul Nurse, have recently demonstrated that fission yeast cells use a novel geometry-sensing mechanism to couple cell length perception with entry into mitosis. These rod-shaped cells measure their own length by using a medially-placed sensor, Cdr2, that reads a protein gradient emanating from cell tips, Pom1, to control entry into mitosis. Budding yeast cells use a similar molecular sensor to delay entry into mitosis in response to defects in bud morphogenesis. Metazoan cells also modulate cell proliferation in response to their own shape by sensing tension. Here I discuss the recent results obtained for the fission yeast system and compare them to the strategies used by these other organisms to perceive their own morphology.

Flatness-based control of a single qubit gate

This work considers the open-loop control problem of steering a two-level quantum system from any initial to any final condition. The model of this system evolves on the state space X = SU(2), having two inputs that correspond to the complex amplitude of a resonant laser field. A symmetry preserving flat output is constructed using a fully geometric construction and quaternion computations. Simulation results of this flatness-based open-loop control are provided.

Dynamic recurrent neural network for system identification and control

A dynamic recurrent neural network (DRNN) that can be viewed as a generalisation of the Hopfield neural network is proposed to identify and control a class of control affine systems. In this approach, the identified network is used in the context of the differential geometric control to synthesise a state feedback that cancels the nonlinear terms of the plant yielding a linear plant which can then be controlled using a standard PID controller.

On the requirements of interpolating polynomials for path motion constraints

In the framework of multibody dynamics, the path motion constraint enforces that a body follows a predefined curve being its rotations with respect to the curve moving frame also prescribed. The kinematic constraint formulation requires the evaluation of the fourth derivative of the curve with respect to its arc length. Regardless of the fact that higher order polynomials lead to unwanted curve oscillations, at least a fifth order polynomials is required to formulate this constraint. From the point of view of geometric control lower order polynomials are preferred. This work shows that for multibody dynamic formulations with dependent coordinates the use of cubic polynomials is possible, being the dynamic response similar to that obtained with higher order polynomials. The stabilization of the equations of motion, always required to control the constraint violations during long analysis periods due to the inherent numerical errors of the integration process, is enough to correct the error introduced by using a lower order polynomial interpolation and thus forfeiting the analytical requirement for higher order polynomials.

Remarks on Lipschitz domains in Carnot groups

In this Note we present the basic features of the theory of Lipschitz maps within Carnot groups as it is developed in [8], and we prove that intrinsic Lipschitz domains in Carnot groups are uniform domains.

Controlador integrado baseado em conceito híbrido e controle geométrico para embarcações posicionadas dinamicamente.

O conceito de controle híbrido é aplicado à operação de alívio entre um FPWSO e um navio aliviador. Ambos os navios mantêm suas posições e aproamentos pelo resultado da ação do seu Sistema de Posicionamento Dinâmico (SPD). O alívio dura cerca de 24 horas para ser concluído. Durante este período, o estado de mar pode se alterar e os calados estão sendo constantemente alterados. Um controlador híbrido é projetado para permitir modificacões dos parâmetros de controle/observação se alguma alteração significante do estado de mar e/ou calado das embarcações ocorrer. O principal objetivo dos controladores é manter o posicionamento relativo entre os navios com o intuito de evitar perigosa proximidade ou excesso de tensão no cabo. Com isto em mente, uma nova estratégia de controle que atue integradamente em ambos os navios é proposta baseda em geometria diferencial. Observadores não lineares baseados em passividade são aplicados para estimar a posição, a velocidade e as forças externas de mares calmos até extremos. O critério para troca do controle/observação é baseado na variação do calado e no estado de mar. O calado é assumido conhecido e o estado de mar é estimado pela frequência de pico do espectro do movimento de primeira ordem dos navios. Um modelo de perturbação é proposto para encontrar o número de controladores do sistema híbrido. A equivalência entre o controle geométrico e o controlador baseado em Multiplicadores de Lagrange é demonstrada. Assumindo algumas hipóteses, a equivalência entre os controladores geométrico e o PD é também apresentada. O desempenho da nova estratégia é avaliada por meio de simulações numéricas e comparada a um controlador PD. Os resultados apresentam muito bom desempenho em função do objetivo proposto. A comparação entre a abordagem geométrica e o controlador PD aponta um desempenho muito parecido entre eles.

Introduction to geodesics in sub-Riemannian geometry

International audience

Composite control of non-linear singularly perturbed systems: a geometric approach

Using a geometric approach, a composite control—the sum of a slow control and a fast control—is derived for a general class of non-linear singularly perturbed systems. A new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset. The slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of ε accuracy.

Composite control of non-linear singularly perturbed systems: a geometric approach

Using a geometric approach, a composite control—the sum of a slow control and a fast control—is derived for a general class of non-linear singularly perturbed systems. A new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset. The slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of ε accuracy.

Genetic Control of Plant Development by Overriding a Geometric Division Rule

Formative cell divisions are critical for multicellular patterning. In the early plant embryo, such divisions follow from orienting the division plane. A major unanswered question is how division plane orientation is genetically controlled, and in particular whether this relates to cell geometry. We have generated a complete 4D map of early Arabidopsis embryogenesis and used computational analysis to demonstrate that several divisions follow a rule that uses the smallest wall area going through the center of the cell. In other cases, however, cell division clearly deviates from this rule, which invariably leads to asymmetric cell division. By analyzing mutant embryos and through targeted genetic perturbation, we show that response to the hormone auxin triggers a deviation from the ``shortest wall'' rule. Our work demonstrates that a simple default rule couples division orientation to cell geometry in the embryo and that genetic regulation can create patterns by overriding the default rule.

Digital geometric-sequence control technique for bidirectional dual active bridge DC-DC converters used in future electric vehicles

Bidirectional DC-DC converters are widely used in different applications such as energy storage systems, Electric Vehicles (EVs), UPS, etc. In particular, future EVs require bidirectional power flow in order to integrate energy storage units into smart grids. These bidirectional power converters provide Grid to Vehicle (V2G)/ Vehicle to Grid (G2V) power flow capability for future EVs. Generally, there are two control loops used for bidirectional DC-DC converters: The inner current loop and The outer loop. The control of DAB converters used in EVs are proved to be challenging due to the wide range of operating conditions and non-linear behavior of the converter. In this thesis, the precise mathematical model of the converter is derived and non-linear control schemes are proposed for the control system of bidirectional DC-DC converters based on the derived model. The proposed inner current control technique is developed based on a novel Geometric-Sequence Control (GSC) approach. The proposed control technique offers significantly improved performance as compared to one for conventional control approaches. The proposed technique utilizes a simple control algorithm which saves on the computational resources. Therefore, it has higher reliability, which is essential in this application. Although, the proposed control technique is based on the mathematical model of the converter, its robustness against parameter uncertainties is proven. Three different control modes for charging the traction batteries in EVs are investigated in this thesis: the voltage mode control, the current mode control, and the power mode control. The outer loop control is determined by each of the three control modes. The structure of the outer control loop provides the current reference for the inner current loop. Comprehensive computer simulations have been conducted in order to evaluate the performance of the proposed control methods. In addition, the proposed control have been verified on a 3.3 kW experimental prototype. Simulation and experimental results show the superior performance of the proposed control techniques over the conventional ones.

Geometric versus Model Predictive Control based guidance algorithms for fixed-wing UAVs in the presence of very strong wind fields.

The recent years have witnessed increased development of small, autonomous fixed-wing Unmanned Aerial Vehicles (UAVs). In order to unlock widespread applicability of these platforms, they need to be capable of operating under a variety of environmental conditions. Due to their small size, low weight, and low speeds, they require the capability of coping with wind speeds that are approaching or even faster than the nominal airspeed. In this thesis, a nonlinear-geometric guidance strategy is presented, addressing this problem. More broadly, a methodology is proposed for the high-level control of non-holonomic unicycle-like vehicles in the presence of strong flowfields (e.g. winds, underwater currents) which may outreach the maximum vehicle speed. The proposed strategy guarantees convergence to a safe and stable vehicle configuration with respect to the flowfield, while preserving some tracking performance with respect to the target path. As an alternative approach, an algorithm based on Model Predictive Control (MPC) is developed, and a comparison between advantages and disadvantages of both approaches is drawn. Evaluations in simulations and a challenging real-world flight experiment in very windy conditions confirm the feasibility of the proposed guidance approach.

THE VANISHING DISCOUNT APPROACH FOR THE AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This work is concerned with the existence of an optimal control strategy for the long-run average continuous control problem of piecewise-deterministic Markov processes (PDMPs). In Costa and Dufour (2008), sufficient conditions were derived to ensure the existence of an optimal control by using the vanishing discount approach. These conditions were mainly expressed in terms of the relative difference of the alpha-discount value functions. The main goal of this paper is to derive tractable conditions directly related to the primitive data of the PDMP to ensure the existence of an optimal control. The present work can be seen as a continuation of the results derived in Costa and Dufour (2008). Our main assumptions are written in terms of some integro-differential inequalities related to the so-called expected growth condition, and geometric convergence of the post-jump location kernel associated to the PDMP. An example based on the capacity expansion problem is presented, illustrating the possible applications of the results developed in the paper.

Schistosomiasis mansoni in an area of low transmission: I. impact of control measures

This work was undertaken in the municipality of Pedro de Toledo (São Paulo State, Brazil) in 1987, to clarify aspects related to the transmission levels of Schistosoma mansoni in a human population where the snail host is Biomphalaria tenagophila. Since 1980 a control programme has been undertaken in this municipality. Urban and rural populations (4,719 subjects) were submitted to faecal examinations (Kato-Katz method). The overall prevalence rate was 4.8% being higher in males (6.2%) and also in the rural zone (5.8%). The geometric mean of S. mansoni eggs was 35.1 eggs per gramme of faeces (epg). Approximately 80.0% of the carriers presented less than 100 epg and only 20 individuals (9.0%) eliminated more than half of total eggs. The highest index of potencial contamination (IPC) was in the age group of 5 to 20 years (57.6%). Two thirds of the investigated patients (207) were autochthonous of Pedro de Toledo. The geographical distribution of the carriers showed a clear aggregation of the autochthonous cases and a close association between human contact sites and breeding places of B. tenagophila. This study shows that schistosomiasis subjects were not randomly aggregated, the youngsters should be the main target in the prophylaxis, and the efficacy of the control programme.