Actuator placement based on reachable set optimization for expected disturbance

This paper examines the role of the control objective and the control time in determining fuel-optimal actuator placement for structural control. A general theory is developed that can be easily extended to include alternative performance metrics such as energy and timeoptimal control. The performance metric defines a convex admissible control set which leads to a max-min optimization problem expressing optimal location as a function of initial conditions and control time. A solution procedure based on a nested genetic algorithm is presented and applied to an example problem. Results indicate that the optimal placement varies widely as a function of both control time and disturbance location. An approximate fitness function is presented to alleviate the computational burden associated with finding exact solutions. This function is shown to accurately predict the optimal actuator locations for a 6th-order system, and is further demonstrated on a 12th-order system.This work was supported by the US Department of Energy at Sandia National Laboratories under Contract DE-AC04-76DP00789.     

A STRUCTURALLY BASED ANALYTIC MODEL FOR ESTIMATION OF BIOMASS AND FUEL LOADS OF WOODLAND TREES

Abstract Allometric/structural relationships in tree crowns are a consequence of the physical, physiological, and fluid conduction processes of trees, which control the distribution, efficient support, and growth of foliage in the crown. The structural consequences of these processes are used to develop an analytic model based on the concept of branch orders. A set of interrelated equations describe the relationships between structural characteristics, including the distribution of a tree's foliage and the partitioning of the structural components within the crown for the efficient support of that foliage. The foliage biomass distribution in a tree crown and the geometric relationships between the branch orders supporting that distribution are used to define a functional depth that is used to compute an associated functional crown volume. These are computed first for the foliage and then for each of the tree's branch orders. Each functional crown volume is linearly related to its respective biomass component. These consistent linear relationships are demonstrated first with data from pinyon pine and then with data from Utah juniper and Valencia orange trees. The structural changes and associated biomass distribution changes suggest that crown growth is controlled from the outside in, with the resulting structural changes an emergent property of crown adjustment to the annual addition of new foliage. The relationships derived are potentially applicable across a range of additional tree species, in other woody species and applicable over a wide range of locations and conditions.     

Optimal control of the Monod-Iyerusalimskii kinetic system

A special problem of optimal control of a closed three-dimensional kinetic system of ordinary differential equations is studied. This problem is a mathematical model of optimal harvesting, which has the following biological interpretation. From a medium with a continuously growing population, stimulated by a flow of nutritious substances and inhibited by excretory products, a part of the biomass is extracted, continuously or discretely, and thus excluded from the reproductive cycle. The problem is posed to find the control of biomass production such that the total harvest gathered over a fixed time interval [0, T] is maximal. At the final moment T the process is terminated by extracting the remainder of the biomass. Bibliography: 11 titles. Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 80, 1996, pp. 47–58.     

MANAGING INTERACTING POPULATIONS UNDER TIME SCALE SEPARATION

Renewable resource modeling is usually characterized by different time scales where some state variables such as biomass may evolve relatively faster than other state variables such as carrying capacity. A strong form of time scale separation (STSS) means that a slowly changing variable is treated as constant over time. Management rules that assume STSS do not account for a time scale externality and this may induce inefficiencies in resource management. In the current work, we study multispecies resource management under time scale separation by adopting the framework of singular perturbation reduction methods. By extending recent work by Vardas and Xepapadeas [2015] to interacting populations, we study regulation with full internalization of the time scale externality. We further study regulation and noncooperative outcomes under STSS and identify deviations in harvesting and biomass paths among these cases. Deviations indicate the inefficiencies associated with adopting STSS.     

Time-optimal control of concentration changes in the chemostat with one single species

We consider the problem of driving in minimal time a system describing a chemostat model to a target point. This problem finds applications typically in the case where the input substrate concentration changes yielding in a new steady state. One essential feature is that the system takes into account a recirculation of biomass effect. We depict an optimal synthesis and provide an optimal feedback control of the problem by using Pontryagin’s Principle and geometric control theory for a large class of kinetics.     

Predator-prey models in heterogeneous environment: Emergence of functional response

In this work, we are interested in prey-predator models. More precisely, we study the spatial heterogeneity effects on the amount of prey eaten per predator per unit time, when different time scales occur. This amount and its relation with the amount of predators produced via the predation are interesting from an ecological point of view. Indeed, the knowledge of these quantities permits us to quantify the transfer of the biomass in the food chain. Our aim is to show how the spatial heterogeneity acts on these amounts. We consider prey-predator systems in a multi-patch environment. We show that density dependent migrations make emerge new models on the total population level and we exhibit some examples. Furthermore, we show that the aggregation method is a good tool for describing the mechanisms hidden behind complex models.     

Temporal and spatial variations of energy consumption in rural China

Presented in this paper is an overview of energy consumption in rural China in view of temporal and spatial variations. Characterized by steadily decreased proportion of biomass use and increased percentage of coal and electricity use, coal and biomass are still the major energy sources in rural areas, accounting for nearly 80% of the total rural energy consumption. Moreover, the energy consumption varies significantly across provinces both in total sum and by fuel types due to diversities of geographic features, economic development levels and local energy source availability. Three statistical groups are clustered associated with quantitative change and structural change, exhibiting evident transition from noncommercial energy pattern to commercial energy pattern. Much more work need to be done to cope with the forthcoming dramatic changes associated with booming rural economy and newly released policy from the points of both energy security and environmental pressure in China.     

A Structural Analysis of Performance Deviations: A Time Series Perspective

A time series modelling approach is suggested to analyze the set of performance deviations which are generated by the institution's control system. The purpose of the time series analysis is to provide decision makers with information regarding the structure underlying the set of performance deviations. This structural analysis is intended to facilitate the selection and implementation of appropriate control actions. The basic control system's elements needed to generate information amenable to a time series analysis are specified. A simple case is presented to illustrate the time series method suggested.     

Regenerative pull (Kanban) production control policies

A production system consists of a set of parallel robotic cells manufacturing parts for several distinct work stations. The stations order parts from these cells and withdraw parts from their buffers only at the rate and at the time of consumption. The desired decision vector provides for the instantaneous number of cells assigned to produce parts for each work station. Two novel tractable and optimal regenerative pull (‘Kanban’) control policies are formulated: one policy minimizes the weighted starvation penalty, while the other maximizes the weighted throughputs per unit time. Following these regenerative policies the production schedules are re-evaluated at each decision epoch to mitigate the effects of processing time variability.Several important properties regarding the inherent interaction between the structure of the optimal policy, the performance of the system and the desired allocation of productive capabilities among the manufacturing resources are examplified. It is shown that the optimal policy attempts to marginally assign as much of the cells capacity as possible to certain critical part types. Substantial changes in the structure of the optimal policy, resulting either from incrementing the number of cells or from increasing their capacity, are also identified. More generally, attention is drawn to the qualitative behavior of the optimal pull control policy in certain manufacturing systems with stochastic processing rates.     

On asymptotic optimization of a class of nonlinear stochastic hybrid systems

We consider the problem of control for continuous time stochastic hybrid systems in finite time horizon. The systems considered are nonlinear: the state evolution is a nonlinear function of both the control and the state. The control parameters change at discrete times according to an underlying controlled Markov chain which has finite state and action spaces. The objective is to design a controller which would minimize an expected nonlinear cost of the state trajectory. We show using an averaging procedure, that the above minimization problem can be approximated by the solution of some deterministic optimal control problem. This paper generalizes our previous results obtained for systems whose state evolution is linear in the control.This work is supported by the Australian Research Council. All correspondence should be directed to the first author.     

Propuesta de fórmula empírica para el factor de pérdidas

Noise transmitted by the sidewalls of buildings is essential to study the overall airborne sound insulation. For the determination of the lateral transmissions we must determine a parameter known as vibration reduction index. To obtain the value of the vibration reduction index to know the acoustic behaviour of the whole constructive, it is necessary to know the velocity level difference and the structural reverberation time. The indeterminations in the velocity level difference, or in the structural reverberation time will add diversions in the global determination of the isolation of the whole constructive.In the Standard UNE EN 12354-1:2000 there are empirical expressions for obtained the structural reverberation time. In the Standard UNE-EN ISO 10848-1:2007 there is a detailed procedure to determine experimentally the velocity level difference and the structural reverberation time, and to know the sidewalls transmissions.In this work, it is compared the structural reverberation time obtained by empirical expression and the structural reverberation time obtained experimentally, applying the normalized procedure. Based on this comparison we readjusted the empirical equations with a fundamental parameter; the loss factor. It is observed that the estimates do not reflect reality if we consider the same loss factor for all the structural elements, as it is allowed in the predictions of UNE EN 12354.     

Effects of time delays on the stability of collocated and noncollocated point control of discrete dynamic structural systems

The effects of time delays on collocated as well as noncollocated point control of discrete dynamic systems have been examined. Controllers of proportional-integral-derivative (PID) type have been considered. Analytical estimates of time delays to maintain/obtain stability for small gains have been given. Several new results dealing with the effect of time delays on collocated and noncollocated control designs are obtained. It is shown that undamped structural systems cannot be stabilized with pure velocity (or integral) feedback without time delays while using a controller which is not collocated with the sensor when the mass matrix is diagonal. However, with the appropriate choice of time delays for certain classes of commonly occurring structural systems, stable noncollocated control can be achieved. Analytical results providing the upper bound on the controller's gain necessary for stability have been presented. The theoretical results obtained are illustrated and verified with numerical examples.     

具有捕食食饵种群的Chemostat模型的一致持续生存

本文主要讨论了单营养食物链的Chemostat模型的渐进性态,给出了该系统一致持续生存和绝灭的充分条件.     

Structural Stability of Discontinuous Galerkin Schemes

The goal of this work is to determine classes of traveling solitary wave solutions for a differential approximation of a discontinuous Galerkin finite difference scheme by means of an hyperbolic ansatz. It is shown that spurious solitary waves can occur in finite-difference solutions of nonlinear wave equation. The occurence of such a spurious solitary wave, which exhibits a very long life time, results in a non-vanishing numerical error for arbitrary time in unbounded numerical domain. Such a behavior is referred here to have a structural instability of the scheme, since the space of solutions spanned by the numerical scheme encompasses types of solutions (solitary waves in the present case) that are not solutions of the original continuous equations. This paper extends our previous work about classical schemes to discontinuous Galerkin schemes (David and Sagaut in Chaos Solitons Fractals 41(4):2193?C2199, 2009; Chaos Solitons Fractals 41(2):655?C660, 2009).     

Optimal Control Problems of Phase Relaxation Models

This work is concerned with optimal control problems with convex cost criterion governed by the relaxed Stefan problem with or without memory. The existence of an optimal control is proved and necessary conditions for a given function to be an optimal control are found. Moreover, an asymptotic analysis is performed as the time relaxation parameter tends to zero.     

Direct solution of a Riccati equation arising in a stochastic control problem with control and observation on the boundary

The optimal control of a class of stochastic parabolic systems is studied. This class includes systems with noise depending on spatial derivatives of the state, Neumann boundary control, and Dirichlet boundary observation, and extends a class of stochastic systems with distributed control studied by Da Prato [3] and Da Prato and Ichikawa [4]. The work is based on the direct study of the Riccati equation arising in the optimal control problem over finite time horizon. The problem over infinite time horizon and the corresponding algebraic Riccati equation are also considered.     

State space theory of linear time-invariant systems with delays in state,control, and observation variables,II

We study a coupled mathematical system which provides a good model for important families of linear time-invariant hereditary systems: delay-differential equations, integrodifferential equations, Volterra-Stieltjes integral equations, functional differential equations of retarded and neutral types, etc. Appropriate states are constructed and associated semigroups and abstract differential equations are obtained. We emphasize the structural operator approach as in Delfour and Manitius. Control operators are added to the coupled mathematical system allowing delays in the control variables. Again structural operators are introduced to define the state and obtain abstract differential equations without delays in the control variable as in the work of Vinter and Kwong. Finally observation operators are added which allow for delays in the observation variable. Again a new state and a state equations are constructed in such a way that no delay appear in the new observation operator as in the recent work of D. Salamon.     

Polynomial time algorithms for two special classes of the proportionate multiprocessor open shop

This paper describes a complex scheduling problem taken from a hospital diagnostic testing center that schedules hundreds of patients in an open shop environment consisting of multiple facilities and multiple processors. This scheduling problem, known as the multiprocessor open shop (MPOS) problem, is strongly NP-hard with few published results. Realizing that in many MPOS environments processing times are stage-dependent, not both job and stage-dependent, this paper examines a new class of problems for the MPOS—proportionate ones. This paper exploits the structural nature of the proportionate MPOS and defines new terms. Despite the enormous complexity of the MPOS problem, this work demonstrates that polynomial time algorithms exist for two special cases. Since other applications of this problem exist in service and manufacturing environments, solving the proportionate MPOS problem is not only significant in the theory of optimization, but also in many real-world applications.     

Time series modeling of Army Mission Command communication networks: an event-driven analysis

We examine the communication time series of a fully-networked Army coalition command and control organization. The network comprised two echelons of command, at the Division and Brigade levels, over a 2-week military scenario exercise involving a Mission Command staff communicating over email and phone. We used time series analysis to predict the communications record based on an external work variable of the number of important scenario events occurring across time. After taking into account structural features of the time series—decreasing communications over time, a network crash, and the transition between weeks—we examined the remaining variability in email and phone communication. We found that the exercise scenario events were not a significant predictor of the Divisional communications, which were best fit by an auto-regressive model of order 1, meaning that the best predictor of the volume of communications at a given time point was the volume of communications on the immediately preceding time point. The occurrence of scenario events, however, did predict the Brigade communication time series, which were well fit by a lag dependent variable model. These results demonstrate that Brigade communications responded to and could be predicted by battlefield events, whereas the Division communications were only predicted by their own past values. These results highlight the importance of modeling environmental work events to predict organizational communication time series and suggest that network communications are perhaps increasingly dependent upon battlefield events for lower echelons of command closer to the tactical edge.     

Modeling the effect of time delay on the conservation of forestry biomass

In this paper, we have studied the effect of time delay on conservation of forestry biomass by proposing a non-linear mathematical model. In the modeling process, it is assumed that the density of forestry biomass depletes due to the presence of human population and it is being conserved by applying some technological efforts. The analysis of model shows that the density of forestry biomass may be conserved if the technological effort is applied within the appropriate time. A longer delay in applying technological effort for its conservation destabilizes the system. The direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by applying the normal form theory and the center manifold theorem. Numerical simulations are given to illustrate the mathematical results.