Stochastic Approximation Algorithms for Constrained Optimization via Simulation

We develop four algorithms for simulation-based optimization under multiple inequality constraints. Both the cost and the constraint functions are considered to be long-run averages of certain state-dependent single-stage functions. We pose the problem in the simulation optimization framework by using the Lagrange multiplier method. Two of our algorithms estimate only the gradient of the Lagrangian, while the other two estimate both the gradient and the Hessian of it. In the process, we also develop various new estimators for the gradient and Hessian. All our algorithms use two simulations each. Two of these algorithms are based on the smoothed functional (SF) technique, while the other two are based on the simultaneous perturbation stochastic approximation (SPSA) method. We prove the convergence of our algorithms and show numerical experiments on a setting involving an open Jackson network. The Newton-based SF algorithm is seen to show the best overall performance.

Reliable Routing in Sensor Networks

In sensor networks, routing algorithms should be designed such that packet losses due to wireless links are reduced.In this paper, we present a ”potential”-based routing scheme to find routes with high packet delivery ratios. The basic idea is to define a scalar potential value at each node in the network and forward data to the neighbour with the highest potential.For a simple 2-relay network, we propose a potential function that takes into account wireless channel state. Markov-chain based analysis provides analytical expressions for packet delivery ratio. Considerable improvement can be observed compared to a channel-state-oblivious policy. This motivates us to define a channel-state-dependent potential function in a general network context. Simulations show that for a relatively slowly changing wireless network, our approach can provide up to 20% better performance than the commonly- used shortest-hop-count-based routing.

An analytical model for an IEEE~802.11 WLAN using DCF with two types of VoIP calls

In this paper we develop and numerically explore the modeling heuristic of using saturation attempt probabilities as state dependent attempt probabilities in an IEEE 802.11e infrastructure network carrying packet telephone calls and TCP controlled file downloads, using enhanced distributed channel access (EDCA). We build upon the fixed point analysis and performance insights. When there are a certain number of nodes of each class contending for the channel (i.e., have nonempty queues), then their attempt probabilities are taken to be those obtained from saturation analysis for that number of nodes. Then we model the system queue dynamics at the network nodes. With the proposed heuristic, the system evolution at channel slot boundaries becomes a Markov renewal process, and regenerative analysis yields the desired performance measures. The results obtained from this approach match well with ns2 simulations. We find that, with the default IEEE 802.11e EDCA parameters for AC 1 and AC 3, the voice call capacity decreases if even one file download is initiated by some station. Subsequently, reducing the voice calls increases the file download capacity almost linearly (by 1/3 Mbps per voice call for the 11 Mbps PHY)

Formation flying of small satellites using suboptimal MPSP guidance

Using the recently developed model predictive static programming (MPSP), a suboptimal guidance logic is presented in this paper for formation flying of small satellites. Due to the inherent nature of the problem formulation, MPSP does not require the system dynamics to be linearized. The proposed guidance scheme is valid both for high eccentricity chief satellite orbits as well as large separation distance between chief and deputy satellites. Moreover, since MPSP poses the desired conditions as a set of `hard constraints', the final accuracy level achieved is very high. The proposed guidance scheme has been tested successfully for a variety of initial conditions and for a variety of formation commands as well. Comparison with standard Linear Quadratic Regulator (LQR) solution (which serves as a guess solution for MPSP) and another nonlinear controller, State Dependent Riccati Equation (SDRE) reveals that MPSP guidance achieves the objective with higher accuracy and with lesser amount of control usage as well.

Intercepting maneuvering target with specified impact angle by modified SDRE technique

A guidance law derived by modifying state dependent Riccati equation technique, to enable the imposition of a predetermined terminal intercept angle to a maneuvering target, is presented in this paper. The interceptor is assumed to have no knowledge about the type of maneuver the target is executing. The problem is cast in a non-cooperative game theoretic form. The guidance law obtained is dependent on the LOS angular rotational rate and on the impact angle error. Theoretical conditions which guarantee existence of solutions under this method have been derived. It is shown that imposing the impact angle constraint calls for an increase in the gains of the guidance law considerably, subsequently requiring a higher maneuverability advantage of the interceptor. The performance of the proposed guidance law is studied using a non-linear two dimensional simulation of the relative kinematics, assuming first order dynamics for the interceptor and target.

Nonlinear Differential Games-Based Impact-Angle-Constrained Guidance Law

The problem of intercepting a maneuvering target at a prespecified impact angle is posed in nonlinear zero-sum differential games framework. A feedback form solution is proposed by extending state-dependent Riccati equation method to nonlinear zero-sum differential games. An analytic solution is obtained for the state-dependent Riccati equation corresponding to the impact-angle-constrained guidance problem. The impact-angle-constrained guidance law is derived using the states line-of-sight rate and projected terminal impact angle error. Local asymptotic stability conditions for the closed-loop system corresponding to these states are studied. Time-to-go estimation is not explicitly required to derive and implement the proposed guidance law. Performance of the proposed guidance law is validated using two-dimensional simulation of the relative nonlinear kinematics as well as a thrust-driven realistic interceptor model.

Nonlinear control of an air-breathing engine including its validation with vehicle guidance

An implementable nonlinear control design approach is presented for a supersonic air-breathing ramjet engine. The primary objective is to ensure that the thrust generated by the engine tracks the commanded thrust without violating the operational constraints. An important constraint is to manage the shock wave location in the intake so that it neither gets detached nor gets too much inside the intake. Both the objectives are achieved by regulating the fuel flow to the combustion chamber and by varying the throat area of the nozzle simultaneously. The design approach accounts for the nonlinear cross-coupling effects and nullifies those. Also, an extended Kalman filter has been used to filter out the sensor and process noises as well as to make the states available for feedback. Furthermore, independent control design has been carried out for the actuators. To test the performance of the engine for a realistic flight trajectory, a representative trajectory is generated through a trajectory optimization process, which is augmented with a newly-developed finite-time state dependent Riccati equation technique for nullifying the perturbations online. Satisfactory overall performance has been obtained during both climb and cruise phases. (C) 2015 Elsevier Masson SAS. All rights reserved.

Octopamine neurons mediate flight-induced modulation of visual processing in Drosophila melanogaster

Activity-dependent modulation of sensory systems has been documented in many organisms, and is likely to be essential for appropriate processing of information during different behavioral states. However, the mechanisms underlying these phenomena, and often their functional consequences, remain poorly characterized. I investigated the role of octopamine neurons in the flight-dependent modulation observed in visual interneurons in the fruit fly Drosophila melanogaster. The vertical system (VS) cells exhibit a boost in their response to visual motion during flight compared to quiescence. Pharmacological application of octopamine evokes responses in quiescent flies that mimic those observed during flight, and octopamine neurons that project to the optic lobes increase in activity during flight. Using genetic tools to manipulate the activity of octopamine neurons, I find that they are both necessary and sufficient for the flight-induced visual boost. This work provides the first evidence that endogenous release of octopamine is involved in state-dependent modulation of visual interneurons in flies. Further, I investigated the role of a single pair of octopamine neurons that project to the optic lobes, and found no evidence that chemical synaptic transmission via these neurons is necessary for the flight boost. However, I found some evidence that activation of these neurons may contribute to the flight boost. Wind stimuli alone are sufficient to generate transient increases in the VS cell response to motion vision, but result in no increase in baseline membrane potential. These results suggest that the flight boost originates not from a central command signal during flight, but from mechanosensory stimuli relayed via the octopamine system. Lastly, in an attempt to understand the functional consequences of the flight boost observed in visual interneurons, we measured the effect of inactivating octopamine neurons in freely flying flies. We found that flies whose octopamine neurons we silenced accelerate less than wild-type flies, consistent with the hypothesis that the flight boost we observe in VS cells is indicative of a gain control mechanism mediated by octopamine neurons. Together, this work serves as the basis for a mechanistic and functional understanding of octopaminergic modulation of vision in flying flies.

Delayed control of a Moore-Greitzer axial compressor model

Several feedback control laws have appeared in the literature concerning the stabilization of the nonlinear Moore-Greitzer axial compression model. Motivated by magnitude and rate limitations imposed by the physical implementation of the control law, Larsen et al. studied a dynamic implementation of the S-controller suggested by Sepulchre and Kokotović. They showed the potential benefit of implementing the S-controller through a first-order lag: while the location of the closed-loop equilibrium achieved with the static control law was sensitive to poorly known parameters, the dynamic implementation resulted in a small limit cycle at a very desirable location, insensitive to parameter variations. In this paper, we investigate the more general case when the control is applied with a time delay. This can be seen as an extension of the model with a first-order lag. The delay can either be a result of system constraints or be deliberately implemented to achieve better system behavior. The resulting closed-loop system is a set of parameter-dependent delay differential equations. Numerical bifurcation analysis is used to study this model and investigate whether the positive results obtained for the first-order model persist, even for larger values of the delay.

Improved BCS-type pairing for the relativistic mean-field theory

A density-dependent delta interaction (DDDI) is proposed in the formalism of BCS-type pairing correlations for exotic nuclei whose Fermi surfaces are close to the threshold of the unbound state. It provides the possibility to pick up those states whose wave functions are concentrated in the nuclear region by making the pairing matrix elements state dependent. On this basis, the energy level distributions, occupations, and ground-state properties are self-consistently studied in the RMF theory with deformation. Calculations are performed for the Sr isotopic chain. A good description of the total energy per nucleon, deformations, two-neutron separation energies and isotope shift from the proton drip line to the neutron drip line is found. Especially, by comparing the single-particle structure from the DDDI pairing interaction with that from the constant pairing interaction for a very neutron-rich nucleus it is demonstrated that the DDDI pairing method improves the treatment of the pairing in the continuum.

Simulating a typhoon storm surge in the East Sea of China using a coupled model

A coupled numerical model with a 2' x 2' resolution grid has been developed and used to simulate five typical typhoon storm surges (5612, 7413, 7910, 8114, and 9711) in the East Sea of China. Three main driving forces have been considered in this coupled model: wave radiation stress, combined wave-current bottom shear stress and wave-state-dependent surface wind stress. This model has then been compared with in situ measurements of the storm set-up. The effect of different driving force components on the total storm surge has also been investigated. This study has found that the coupled model with high resolution is capable of simulating the five typical typhoons better than the uncoupled models, and that the wave-dependent surface wind stress plays an important role in typhoon storm surge-wave coupling in this area and can increase the storm set-up by 1 m. The study of the five typhoon cases has shown that the general coupling effects could increase storm set-up by 20-32%. Thus, it is suggested that to predict typhoon storm surges in the East Sea of China, a storm surge-wave coupled model be adopted. (C) 2008 National Natural Science Foundation of China and Chinese Academy of Sciences. Published by Elsevier Limited and Science in China Press. All rights reserved.

Neural Control of Interlimb Coordination and Gait Timing in Bipeds and Quadrupeds

1) A large body of behavioral data conceming animal and human gaits and gait transitions is simulated as emergent properties of a central pattern generator (CPG) model. The CPG model incorporates neurons obeying Hodgkin-Huxley type dynamics that interact via an on-center off-surround anatomy whose excitatory signals operate on a faster time scale than their inhibitory signals. A descending cornmand or arousal signal called a GO signal activates the gaits and controL their transitions. The GO signal and the CPG model are compared with neural data from globus pallidus and spinal cord, among other brain structures. 2) Data from human bimanual finger coordination tasks are simulated in which anti-phase oscillations at low frequencies spontaneously switch to in-phase oscillations at high frequencies, in-phase oscillations can be performed both at low and high frequencies, phase fluctuations occur at the anti-phase in-phase transition, and a "seagull effect" of larger errors occurs at intermediate phases. When driven by environmental patterns with intermediate phase relationships, the model's output exhibits a tendency to slip toward purely in-phase and anti-phase relationships as observed in humans subjects. 3) Quadruped vertebrate gaits, including the amble, the walk, all three pairwise gaits (trot, pace, and gallop) and the pronk are simulated. Rapid gait transitions are simulated in the order--walk, trot, pace, and gallop--that occurs in the cat, along with the observed increase in oscillation frequency. 4) Precise control of quadruped gait switching is achieved in the model by using GO-dependent modulation of the model's inhibitory interactions. This generates a different functional connectivity in a single CPG at different arousal levels. Such task-specific modulation of functional connectivity in neural pattern generators has been experimentally reported in invertebrates. Phase-dependent modulation of reflex gain has been observed in cats. A role for state-dependent modulation is herein predicted to occur in vertebrates for precise control of phase transitions from one gait to another. 5) The primary human gaits (the walk and the run) and elephant gaits (the amble and the walk) are sirnulated. Although these two gaits are qualitatively different, they both have the same limb order and may exhibit oscillation frequencies that overlap. The CPG model simulates the walk and the run by generating oscillations which exhibit the same phase relationships. but qualitatively different waveform shapes, at different GO signal levels. The fraction of each cycle that activity is above threshold quantitatively distinguishes the two gaits, much as the duty cycles of the feet are longer in the walk than in the run. 6) A key model properly concerns the ability of a single model CPG, that obeys a fixed set of opponent processing equations to generate both in-phase and anti-phase oscillations at different arousal levels. Phase transitions from either in-phase to anti-phase oscillations, or from anti-phase to in-phase oscillations, can occur in different parameter ranges, as the GO signal increases.

Co-regulation of nuclear respiratory factor-1 by NFkappaB and CREB links LPS-induced inflammation to mitochondrial biogenesis.

The nuclear respiratory factor-1 (NRF1) gene is activated by lipopolysaccharide (LPS), which might reflect TLR4-mediated mitigation of cellular inflammatory damage via initiation of mitochondrial biogenesis. To test this hypothesis, we examined NRF1 promoter regulation by NFκB, and identified interspecies-conserved κB-responsive promoter and intronic elements in the NRF1 locus. In mice, activation of Nrf1 and its downstream target, Tfam, by Escherichia coli was contingent on NFκB, and in LPS-treated hepatocytes, NFκB served as an NRF1 enhancer element in conjunction with NFκB promoter binding. Unexpectedly, optimal NRF1 promoter activity after LPS also required binding by the energy-state-dependent transcription factor CREB. EMSA and ChIP assays confirmed p65 and CREB binding to the NRF1 promoter and p65 binding to intron 1. Functionality for both transcription factors was validated by gene-knockdown studies. LPS regulation of NRF1 led to mtDNA-encoded gene expression and expansion of mtDNA copy number. In cells expressing plasmid constructs containing the NRF-1 promoter and GFP, LPS-dependent reporter activity was abolished by cis-acting κB-element mutations, and nuclear accumulation of NFκB and CREB demonstrated dependence on mitochondrial H(2)O(2). These findings indicate that TLR4-dependent NFκB and CREB activation co-regulate the NRF1 promoter with NFκB intronic enhancement and redox-regulated nuclear translocation, leading to downstream target-gene expression, and identify NRF-1 as an early-phase component of the host antibacterial defenses.

Transient receptor potential melastatin 8 (TRPM8) channel involvement in the regulation of vascular tone

The transient receptor potential melastatin 8 (TRPM8) channel has been characterized as a cold and menthol receptor expressed in a subpopulation of sensory neurons but was recently identified in other tissues, including the respiratory tract, urinary system, and vasculature. Thus TRPM8 may play multiple functional roles, likely to be in a tissue- and activation state-dependent manner. We examined the TRPM8 channel presence in large arteries from rats and the functional consequences of their activation. We also aimed to examine whether these channels contribute to control of conscious human skin blood flow. TRPM8 mRNA and protein were detected in rat tail, femoral and mesenteric arteries, and thoracic aorta. This was confirmed in single isolated vascular myocytes by immunocytochemistry. Isometric contraction studies on endothelium-denuded relaxed rat vessels found small contractions on application of the TRPM8-specific agonist menthol (300 microM). However, both menthol and another agonist icilin (50 microM) caused relaxation of vessels precontracted with KCl (60 mM) or the alpha-adrenoceptor agonist phenylephrine (2 microM) and a reduction in sympathetic nerve-mediated contraction. These effects were antagonized by bromoenol lactone treatment, suggesting the involvement of Ca(2+)-independent phospholipase A(2) activation in TRPM8-mediated vasodilatation. In thoracic aorta with intact endothelium, menthol-induced inhibition of KCl-induced contraction was enhanced. This was unaltered by preincubation with either N(omega)-nitro-l-arginine methyl ester (l-NAME; 100 nM), a nitric oxide synthase inhibitor, or the ACh receptor antagonist atropine (1 microM). Application of menthol (3% solution, topical application) to skin caused increased blood flow in conscious humans, as measured by laser Doppler fluximetry. Vasodilatation was markedly reduced or abolished by prior application of l-NAME (passive application, 10 mM) or atropine (iontophoretic application, 100 nM, 30 s at 70 microA). We conclude that TRPM8 channels are present in rat artery vascular smooth muscle and on activation cause vasoconstriction or vasodilatation, dependent on previous vasomotor tone. TRPM8 channels may also contribute to human cutaneous vasculature control, likely with the involvement of additional neuronal mechanisms.

Joint measurements on qubits and cloning of observables

Cloning of observables, unlike standard cloning of states, aims at copying the information encoded in the statistics of a class of observables rather then on quantum states themselves. In such a process the emphasis is on the quantum operation (evolution plus measurement) necessary to retrieve the original information. We analyze, for qubit systems, the cloning of a class generated by two noncommuting observables, elucidating the relationship between such a process and joint measurements. This helps in establishing an optimality criterion for cloning of observables. We see that, even if the cloning machine is designed to act on the whole class generated by two noncommuting observables, the same optimal performances of a joint measurement can be attained. Finally, the connection with state dependent cloning is enlightened.