Optimal feedback control rules sensitive to controlled endogenous risk-aversion

The objective of this paper is to correct and improve the results obtained by Van der Ploeg (1984a, 1984b) and utilized in the theoretical literature related to feedback stochastic optimal control sensitive to constant exogenous risk-aversion (see, Jacobson, 1973, Karp, 1987 and Whittle, 1981, 1989, 1990, among others) or to the classic context of risk-neutral decision-makers (see, Chow, 1973, 1976a, 1976b, 1977, 1978, 1981, 1993). More realistic and attractive, this new approach is placed in the context of a time-varying endogenous risk-aversion which is under the control of the decision-maker. It has strong qualitative implications on the agent's optimal policy during the entire planning horizon.

Feedback control of DnaA-mediated replication initiation by replisome-associated HdaA protein in Caulobacter.

Chromosome replication in Caulobacter crescentus is tightly regulated to ensure that initiation occurs at the right time and only once during the cell cycle. The timing of replication initiation is controlled by both CtrA and DnaA. CtrA binds to and silences the origin. Upon the clearance of CtrA from the cell, the DnaA protein accumulates and allows loading of the replisome at the origin. Here, we identify an additional layer of replication initiation control that is mediated by the HdaA protein. In Escherichia coli, the Hda protein inactivates DnaA after replication initiation. We show that the Caulobacter HdaA homologue is necessary to restrict the initiation of DNA replication to only once per cell cycle and that it dynamically colocalizes with the replisome throughout the cell cycle. Moreover, the transcription of hdaA is directly activated by DnaA, providing a robust feedback regulatory mechanism that adjusts the levels of HdaA to inactivate DnaA.

Feedback control of unstable cellular solidification fronts

We present a feedback control scheme to stabilize unstable cellular patterns during the directional solidification of a binary alloy. The scheme is based on local heating of cell tips which protrude ahead of the mean position of all tips in the array. The feasibility of this scheme is demonstrated using phase-field simulations and, experimentally, using a real-time image processing algorithm, to track cell tips, coupled with a movable laser spot array device to heat the tips locally. We demonstrate, both numerically and experimentally, that spacings well below the threshold for a period-doubling instability can be stabilized. As predicted by the numerical calculations, cellular arrays become stable with uniform spacing through the feedback control which is maintained with minimal heating.

Spontaneous cell polarization: Feedback control of Cdc42 GTPase breaks cellular symmetry.

Spontaneous polarization without spatial cues, or symmetry breaking, is a fundamental problem of spatial organization in biological systems. This question has been extensively studied using yeast models, which revealed the central role of the small GTPase switch Cdc42. Active Cdc42-GTP forms a coherent patch at the cell cortex, thought to result from amplification of a small initial stochastic inhomogeneity through positive feedback mechanisms, which induces cell polarization. Here, I review and discuss the mechanisms of Cdc42 activity self-amplification and dynamic turnover. A robust Cdc42 patch is formed through the combined effects of Cdc42 activity promoting its own activation and active Cdc42-GTP displaying reduced membrane detachment and lateral diffusion compared to inactive Cdc42-GDP. I argue the role of the actin cytoskeleton in symmetry breaking is not primarily to transport Cdc42 to the active site. Finally, negative feedback and competition mechanisms serve to control the number of polarization sites.

Parameter-dependent Lyapunov functions for state-derivative feedback control in polytopic linear systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Observer-based state-feedback versus H-infinity output feedback control solved by LMI approach for applications in smart structures

This paper aims with the use of linear matrix inequalities approach (LMIs) for application in active vibration control problems in smart strutures. A robust controller for active damping in a panel was designed with piezoelectrical actuators in optimal locations for illustration of the main proposal. It was considered, in the simulations of the closed-loop, a model identified by eigensystem realization algorithm (ERA) and reduced by modal decomposition. We tested two differents techniques to solve the problem. The first one uses LMI approach by state-feedback based in an observer design, considering several simultaneous constraints as: a decay rate, limited input on the actuators, bounded output peak (output energy) and robustness to parametic uncertainties. The results demonstrated the vibration attenuation in the structure by controlling only the first modes and the increased damping in the bandwidth of interest. However, it is possible to occur spillover effects, because the design has not been done considering the dynamic uncertainties related with high frequencies modes. In this sense, the second technique uses the classical H. output feedback control, also solved by LMI approach, considering robustness to residual dynamic to overcome the problem found in the first test. The results are compared and discussed. The responses shown the robust performance of the system and the good reduction of the vibration level, without increase mass.

A simple feedback control for a chaotic oscillator with limited power supply

We proposed a simple feedback control method to suppress chaotic behavior in oscillators with limited power supply. The small-amplitude controlling signal is applied directly to the power supply system, so as to alter the characteristic curve of the driving motor. Numerical results are presented showing the method efficiency for a wide range of control parameters. Moreover, we have found that, for some parameters, this kind of control may introduce coexisting periodic attractors with complex basins of attraction and, therefore, serious problems with predictability of the final state the system will asymptote to. (c) 2006 Elsevier Ltd. All rights reserved.

On control and synchronization in chaotic and hyperchaotic systems via linear feedback control

This paper presents the control and synchronization of chaos by designing linear feedback controllers. The linear feedback control problem for nonlinear systems has been formulated under optimal control theory viewpoint. Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation thus guaranteeing both stability and optimality. The formulated theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations were provided in order to show the effectiveness of this method for the control of the chaotic Rossler system and synchronization of the hyperchaotic Rossler system. (C) 2007 Elsevier B.V. All rights reserved.

H ∞ state feedback control of discrete-time Markov jump linear systems through linear matrix inequalities

This paper addresses the H ∞ state-feedback control design problem of discretetime Markov jump linear systems. First, under the assumption that the Markov parameter is measured, the main contribution is on the LMI characterization of all linear feedback controllers such that the closed loop output remains bounded by a given norm level. This results allows the robust controller design to deal with convex bounded parameter uncertainty, probability uncertainty and cluster availability of the Markov mode. For partly unknown transition probabilities, the proposed design problem is proved to be less conservative than one available in the current literature. An example is solved for illustration and comparisons. © 2011 IFAC.

A TSG101/MDM2 regulatory loop modulates MDM2 degradation and MDM2/p53 feedback control

The p53 tumor suppressor protein and the MDM2 oncoprotein form a feedback-control loop that up-regulates cellular MDM2 production, blocks p53 activity, and promotes p53 decay. tsg101 was discovered as a gene whose deficiency results in neoplastic transformation of NIH 3T3 cells and the ability to generate metastatic tumors in nude mice. Its protein product contains a domain, Ubc, characteristic of the catalytic domain of ubiquitin conjugase (E2) enzymes but lacking an active-site cysteine crucial for ubiquitin conjugase activity. Here we report that TSG101 participates with MDM2 in an autoregulatory loop that modulates the cellular levels of both proteins, and also of p53, by affecting protein decay. We show that the Ubc domain of TSG101 interferes with ubiquitination of MDM2, that TSG101 inhibits MDM2 decay and elevates its steady-state level, and that these events are associated with down-regulation of p53 protein. Conversely, pulse–chase and Western blot experiments in wild-type and mutant fibroblasts indicate that elevation of MDM2 by overexpression of wild-type p53, by amplification of the endogenous MDM2 gene, or by transfection of MDM2-expressing constructs promotes TSG101 loss, which we show occurs by 26S proteasome-dependent decay. Our results identify TSG101 as both a regulator of, and target of, MDM2/p53 circuitry.

Feedback Control and Diurnal Regulation of Gibberellin 20-Oxidase Transcript Levels in Potato1

Tuber formation in potato (Solanum tuberosum) is promoted by short photoperiods and is inhibited by gibberellins (GAs). Endogenous levels of GA1 were shown to decrease in stolons and leaves of potato plants induced to tuberize, which suggests that photoperiodic regulation of GA biosynthesis may play a role in tuber induction. We report the isolation of three potato cDNA clones (StGA20ox1–3) encoding GA 20-oxidase, a key regulatory enzyme in the GA-biosynthetic pathway. Using northern analysis, we detected a differential pattern of tissue-specific expression of the mRNAs corresponding to these clones. StGA20ox mRNAs were also very abundant in leaves of the potato ga1 mutant, which is blocked in the 13-hydroxylation step, and were strongly down-regulated by gibberellic acid, suggesting a feedback regulation of these genes. In plants grown in short-day (inductive) conditions, levels of the StGA20ox transcripts in leaves fluctuated during a 24-h period, with a peak of accumulation observed about 4 h after the lights were turned off. Interruption of the night with a 30-min “night break” of light (noninductive conditions) did not have a marked effect on the levels of accumulation of the three GA 20-oxidase mRNAs during the day, but it induced a second peak of expression of StGA20ox1 and StGA20ox3 transcripts late in the night. This observation, together with the finding that StGA20ox1 mRNA is expressed at high levels in leaves, suggests that night-break induction of this gene might play a role in the control of tuberization by regulating endogenous levels of GAs in response to daylength conditions.