Generalized model predictive static programming and its application to 3D impact angle constrained guidance of air-to-surface missiles

A new `generalized model predictive static programming (G-MPSP)' technique is presented in this paper in the continuous time framework for rapidly solving a class of finite-horizon nonlinear optimal control problems with hard terminal constraints. A key feature of the technique is backward propagation of a small-dimensional weight matrix dynamics, using which the control history gets updated. This feature, as well as the fact that it leads to a static optimization problem, are the reasons for its high computational efficiency. It has been shown that under Euler integration, it is equivalent to the existing model predictive static programming technique, which operates on a discrete-time approximation of the problem. Performance of the proposed technique is demonstrated by solving a challenging three-dimensional impact angle constrained missile guidance problem. The problem demands that the missile must meet constraints on both azimuth and elevation angles in addition to achieving near zero miss distance, while minimizing the lateral acceleration demand throughout its flight path. Both stationary and maneuvering ground targets are considered in the simulation studies. Effectiveness of the proposed guidance has been verified by considering first order autopilot lag as well as various target maneuvers.

Optimal Forwarding in Delay-Tolerant Networks With Multiple Destinations

We study the tradeoff between delivery delay and energy consumption in a delay-tolerant network in which a message (or a file) has to be delivered to each of several destinations by epidemic relaying. In addition to the destinations, there are several other nodes in the network that can assist in relaying the message. We first assume that, at every instant, all the nodes know the number of relays carrying the message and the number of destinations that have received the message. We formulate the problem as a controlled continuous-time Markov chain and derive the optimal closed-loop control (i.e., forwarding policy). However, in practice, the intermittent connectivity in the network implies that the nodes may not have the required perfect knowledge of the system state. To address this issue, we obtain an ordinary differential equation (ODE) (i.e., a deterministic fluid) approximation for the optimally controlled Markov chain. This fluid approximation also yields an asymptotically optimal open-loop policy. Finally, we evaluate the performance of the deterministic policy over finite networks. Numerical results show that this policy performs close to the optimal closed-loop policy.

Phase diagram of the half-filled ionic Hubbard model

We study the phase diagram of the ionic Hubbard model (IHM) at half filling on a Bethe lattice of infinite connectivity using dynamical mean-field theory (DMFT), with two impurity solvers, namely, iterated perturbation theory (IPT) and continuous time quantum Monte Carlo (CTQMC). The physics of the IHM is governed by the competition between the staggered ionic potential Delta and the on-site Hubbard U. We find that for a finite Delta and at zero temperature, long-range antiferromagnetic (AFM) order sets in beyond a threshold U = U-AF via a first-order phase transition. For U smaller than U-AF the system is a correlated band insulator. Both methods show a clear evidence for a quantum transition to a half-metal (HM) phase just after the AFM order is turned on, followed by the formation of an AFM insulator on further increasing U. We show that the results obtained within both methods have good qualitative and quantitative consistency in the intermediate-to-strong-coupling regime at zero temperature as well as at finite temperature. On increasing the temperature, the AFM order is lost via a first-order phase transition at a transition temperature T-AF(U,Delta) or, equivalently, on decreasing U below U-AF(T,Delta)], within both methods, for weak to intermediate values of U/t. In the strongly correlated regime, where the effective low-energy Hamiltonian is the Heisenberg model, IPT is unable to capture the thermal (Neel) transition from the AFM phase to the paramagnetic phase, but the CTQMC does. At a finite temperature T, DMFT + CTQMC shows a second phase transition (not seen within DMFT + IPT) on increasing U beyond U-AF. At U-N > U-AF, when the Neel temperature T-N for the effective Heisenberg model becomes lower than T, the AFM order is lost via a second-order transition. For U >> Delta, T-N similar to t(2)/U(1 - x(2)), where x = 2 Delta/U and thus T-N increases with increase in Delta/U. In the three-dimensional parameter space of (U/t, T/t, and Delta/t), as T increases, the surface of first-order transition at U-AF(T,Delta) and that of the second-order transition at U-N(T,Delta) approach each other, shrinking the range over which the AFM order is stable. There is a line of tricritical points that separates the surfaces of first- and second-order phase transitions.

Event-triggered Sampling and Reconstruction of Sparse Real-valued Trigonometric Polynomials

We propose data acquisition from continuous-time signals belonging to the class of real-valued trigonometric polynomials using an event-triggered sampling paradigm. The sampling schemes proposed are: level crossing (LC), close to extrema LC, and extrema sampling. Analysis of robustness of these schemes to jitter, and bandpass additive gaussian noise is presented. In general these sampling schemes will result in non-uniformly spaced sample instants. We address the issue of signal reconstruction from the acquired data-set by imposing structure of sparsity on the signal model to circumvent the problem of gap and density constraints. The recovery performance is contrasted amongst the various schemes and with random sampling scheme. In the proposed approach, both sampling and reconstruction are non-linear operations, and in contrast to random sampling methodologies proposed in compressive sensing these techniques may be implemented in practice with low-power circuitry.

A mean-reverting stochastic model for the political business cycle

In this article, we look at the political business cycle problem through the lens of uncertainty. The feedback control used by us is the famous NKPC with stochasticity and wage rigidities. We extend the New Keynesian Phillips Curve model to the continuous time stochastic set up with an Ornstein-Uhlenbeck process. We minimize relevant expected quadratic cost by solving the corresponding Hamilton-Jacobi-Bellman equation. The basic intuition of the classical model is qualitatively carried forward in our set up but uncertainty also plays an important role in determining the optimal trajectory of the voter support function. The internal variability of the system acts as a base shifter for the support function in the risk neutral case. The role of uncertainty is even more prominent in the risk averse case where all the shape parameters are directly dependent on variability. Thus, in this case variability controls both the rates of change as well as the base shift parameters. To gain more insight we have also studied the model when the coefficients are time invariant and studied numerical solutions. The close relationship between the unemployment rate and the support function for the incumbent party is highlighted. The role of uncertainty in creating sampling fluctuation in this set up, possibly towards apparently anomalous results, is also explored.

Exact Phase Retrieval in Principal Shift-Invariant Spaces

We address the problem of phase retrieval from Fourier transform magnitude spectrum for continuous-time signals that lie in a shift-invariant space spanned by integer shifts of a generator kernel. The phase retrieval problem for such signals is formulated as one of reconstructing the combining coefficients in the shift-invariant basis expansion. We develop sufficient conditions on the coefficients and the bases to guarantee exact phase retrieval, by which we mean reconstruction up to a global phase factor. We present a new class of discrete-domain signals that are not necessarily minimum-phase, but allow for exact phase retrieval from their Fourier magnitude spectra. We also establish Hilbert transform relations between log-magnitude and phase spectra for this class of discrete signals. It turns out that the corresponding continuous-domain counterparts need not satisfy a Hilbert transform relation; notwithstanding, the continuous-domain signals can be reconstructed from their Fourier magnitude spectra. We validate the reconstruction guarantees through simulations for some important classes of signals such as bandlimited signals and piecewise-smooth signals. We also present an application of the proposed phase retrieval technique for artifact-free signal reconstruction in frequency-domain optical-coherence tomography (FDOCT).

Models and algorithms for detection and tracking of coordinated groups

In this paper, we describe models and algorithms for detection and tracking of group and individual targets. We develop two novel group dynamical models, within a continuous time setting, that aim to mimic behavioural properties of groups. We also describe two possible ways of modeling interactions between closely using Markov Random Field (MRF) and repulsive forces. These can be combined together with a group structure transition model to create realistic evolving group models. We use a Markov Chain Monte Carlo (MCMC)-Particles Algorithm to perform sequential inference. Computer simulations demonstrate the ability of the algorithm to detect and track targets within groups, as well as infer the correct group structure over time. ©2008 IEEE.

Consumption and portfolio rules whit stochastic hyperbolic discounting

We extend the classic Merton (1969, 1971) problem that investigates the joint consumption-savings and portfolio-selection problem under capital risk by assuming sophisticated but time-inconsistent agents. We introduce stochastic hyperbolic preferences as in Harris and Laibson (2013) and find closed-form solutions for Merton's optimal consumption and portfolio selection problem in continuous time. We find that the portfolio rule remains identical to the time-consistent solution with power utility and no borrowing constraints. However,the marginal propensity to consume out of wealth is unambiguously greater than the time-consistent, exponential case and,importantly, it is also more responsive to changes in risk. These results suggest that hyperbolic discounting with sophisticated agents offers promise for contributing to explaining important aspects of asset market data.

Asymptotic Hyperstability of a Class of Linear Systems under Impulsive Controls Subject to an Integral Popovian Constraint

This paper is focused on the study of the important property of the asymptotic hyperstability of a class of continuous-time dynamic systems. The presence of a parallel connection of a strictly stable subsystem to an asymptotically hyperstable one in the feed-forward loop is allowed while it has also admitted the generation of a finite or infinite number of impulsive control actions which can be combined with a general form of nonimpulsive controls. The asymptotic hyperstability property is guaranteed under a set of sufficiency-type conditions for the impulsive controls.

An observer-based vaccination control law for an SEIR epidemic model based on feedback linearization techniques for nonlinear systems

This paper presents a vaccination strategy for fighting against the propagation of epidemic diseases. The disease propagation is described by an SEIR (susceptible plus infected plus infectious plus removed populations) epidemic model. The model takes into account the total population amounts as a refrain for the illness transmission since its increase makes the contacts among susceptible and infected more difficult. The vaccination strategy is based on a continuous-time nonlinear control law synthesised via an exact feedback input-output linearization approach. An observer is incorporated into the control scheme to provide online estimates for the susceptible and infected populations in the case when their values are not available from online measurement but they are necessary to implement the control law. The vaccination control is generated based on the information provided by the observer. The control objective is to asymptotically eradicate the infection from the population so that the removed-by-immunity population asymptotically tracks the whole one without precise knowledge of the partial populations. The model positivity, the eradication of the infection under feedback vaccination laws and the stability properties as well as the asymptotic convergence of the estimation errors to zero as time tends to infinity are investigated.

Random propagation in complex systems : nonlinear matrix recursions and epidemic spread

This dissertation studies long-term behavior of random Riccati recursions and mathematical epidemic model. Riccati recursions are derived from Kalman filtering. The error covariance matrix of Kalman filtering satisfies Riccati recursions. Convergence condition of time-invariant Riccati recursions are well-studied by researchers. We focus on time-varying case, and assume that regressor matrix is random and identical and independently distributed according to given distribution whose probability distribution function is continuous, supported on whole space, and decaying faster than any polynomial. We study the geometric convergence of the probability distribution. We also study the global dynamics of the epidemic spread over complex networks for various models. For instance, in the discrete-time Markov chain model, each node is either healthy or infected at any given time. In this setting, the number of the state increases exponentially as the size of the network increases. The Markov chain has a unique stationary distribution where all the nodes are healthy with probability 1. Since the probability distribution of Markov chain defined on finite state converges to the stationary distribution, this Markov chain model concludes that epidemic disease dies out after long enough time. To analyze the Markov chain model, we study nonlinear epidemic model whose state at any given time is the vector obtained from the marginal probability of infection of each node in the network at that time. Convergence to the origin in the epidemic map implies the extinction of epidemics. The nonlinear model is upper-bounded by linearizing the model at the origin. As a result, the origin is the globally stable unique fixed point of the nonlinear model if the linear upper bound is stable. The nonlinear model has a second fixed point when the linear upper bound is unstable. We work on stability analysis of the second fixed point for both discrete-time and continuous-time models. Returning back to the Markov chain model, we claim that the stability of linear upper bound for nonlinear model is strongly related with the extinction time of the Markov chain. We show that stable linear upper bound is sufficient condition of fast extinction and the probability of survival is bounded by nonlinear epidemic map.

A pré-história e reencontro com o tempo em Sem tecto, entre ruínas de Augusto Abelaira

O presente trabalho consiste em um estudo crítico do romance Sem tecto, entre ruínas, de Augusto Abelaira. Inicialmente é feita a análise sobre as possíveis consequências de uma apreensão descontínua e material do tempo, seus efeitos nas relações entre o protagonista e seu mundo, que se apresentam sob a forma de tédio e paralisia. Para a crítica proposta foram retomados conceitos descontinuidade e homogeneidade apresentados pelo filósofo Henri Bergson, além da noção de desligamento e desejo demonstrados pela sociologia de Zigmunt Bauman. O próximo alvo contemplado na pesquisa é a presença da memória e da lembrança indicados sob o ponto de vista contínuo do tempo, também analisados à luz da filosofia de Bergson, além do pensamento de Gilles Deleuze. A partir desse caminho investigativo é possível pensar a condição do protagonista como um confronto de si, uma experiência do tempo que traz uma revelação mediante a condição de ser tarde demais

Circulação e fluxo de material particulado em suspensão no principal canal de acesso à baía de Sepetiba

Entre 06/08/11 e 25/02/12 foram obtidas séries temporais contínuas de intensidade e direção das correntes e intensidade do eco ao longo de toda a coluna dágua, e medições, de temperatura e pressão, próximas ao fundo, na região adjacente ao canal de acesso à baía de Sepetiba (230'16.5"S e 4359'29.4"W, profundidade local de aproximadamente 25 m) através da utilização de um perfilador acústico ADCP (Acoustic Doppler Current Profiler), modelo WorkHorse BroadBand Sentinel (600 kHz, Teledyne-RDI). A partir dos dados adquiridos, observou-se a existência de correntes intensas próximo ao fundo (até 1,02 m/s), principalmente durante os períodos de enchente sob condições de sizígia, que são fortemente influenciadas pela orientação do canal de navegação. A análise das séries temporais das componentes da velocidade mostraram, em conformidade ao relatado por alguns autores, que esta é uma baía cuja circulação é fortemente influenciada pela dinâmica da maré sendo M2, M4, M6 e M8 as principais componentes harmônicas que atuam no sistema. Além disso, observou-se significativa assimetria da maré, sendo os períodos de enchente consideravelmente mais curtos e associados às correntes mais intensas, o que permite concluir que no setor investigado da baía de Sepetiba há dominância de enchente. Outra característica interessante da área de estudo relaciona-se à observação de que ventos intensos de S-SO são responsáveis pelo empilhamento de água no interior da baía, sendo que altura do nível da superfície da água apresenta relação direta com as variações da pressão atmosférica local. Em diversos períodos, quando há atuação de ventos de E-NE é possível encontrar Água Central do Atlântico Sul (ACAS) no interior da baía de Sepetiba, desde a sua entrada principal até as adjacências da ilha Guaíba. Além disso, foram identificadas diversas oscilações de baixa frequência que puderam ser associadas à variação da pressão atmosférica. Oscilações de alta frequência foram associadas à dinâmica da maré, a co-oscilações da maré e ao vento. Em relação à concentração de Material Particulado em Suspensão (MPS), durante os períodos de sizígia foram registradas as maiores concentrações material particulado na coluna dágua. Durante os períodos de sizígia, o fluxo de MPS é mais pronunciado do que durante as quadraturas, sendo que, independente do período da maré, o fluxo cumulativo de material particulado em suspensão é dirigido para o interior da baía de Sepetiba. Considerando o alinhamento dos vetores de velocidade em conformidade a direção preferencial do canal de navegação, tem-se que o fluxo cumulativo de MPS varia entre dirigido para SE na região próxima ao fundo, a dirigido para NE próximo ao topo da coluna dágua, o que sugere a deflexão do movimento das correntes em consequência do atrito. Ao longo de um dia, o fluxo do material particulado é mais pronunciado durante as enchentes, quando há aumento das tensões cisalhantes que atuam sobre o leito da baía redisponibilizando para a coluna dágua o material que estava depositado no fundo.

Interannual variability of siliceous phytoplankton fluxes and relationships with hydrography in the northeastern subarctic Pacific, 1982-1986 [abstract and figures]

EXTRACT (SEE PDF FOR FULL ABSTRACT): Time-series flux variabilities of biogenic opal particles were measured during 1982-1986 at pelagic Station PAPA (50° N, 145° W) located just south of the Gulf of Alaska, eastern North Pacific. PARFLUX sediment traps with two week sampling increments were deployed at 1000 m and 3800 m in 4200 m deep water, yielding nearly continuous time-series flux records for four years. The flux data allowed us to examine interannual and seasonal variabilities of siliceous phytoplankton production as well as environmental signals retained within the siliceous shells, which can be used to reconstruct environments.

Changes in mass balance of South Cascade Glacier, North Cascades, 1959 to 1994

EXTRACT (SEE PDF FOR FULL ABSTRACT): Annual, winter, and summer mass balance measurements at South Cascade Glacier in the North Cascade Mountains of Washington State constitute a continuous time series 36 years long, from 1959 to 1994. ... The long-term trends at South Cascade Glacier are decreased winter accumulation and increased summer ablation, neither of which is conducive to glacier growth, so the trend in the Pacific Northwest is clearly away from an ice-age type of climate at the current time. The data also demonstrate that a glaciologically significant long-term change in snow precipitation can occur rapidly, in as short an interval as 1 year, much more rapidly than changes in temperature.