An Online Implementable Differential Evolution Tuned Optimal Guidance Law

This paper proposes a novel application of differential evolution to solve a difficult dynamic optimisation or optimal control problem. The miss distance in a missile-target engagement is minimised using differential evolution. The difficulty of solving it by existing conventional techniques in optimal control theory is caused by the nonlinearity of the dynamic constraint equation, inequality constraint on the control input and inequality constraint on another parameter that enters problem indirectly. The optimal control problem of finding the minimum miss distance has an analytical solution subject to several simplifying assumptions. In the approach proposed in this paper, the initial population is generated around the seed value given by this analytical solution. Thereafter, the algorithm progresses to an acceptable final solution within a few generations, satisfying the constraints at every iteration. Since this solution or the control input has to be obtained in real time to be of any use in practice, the feasibility of online implementation is also illustrated.

Optimal dynamic inversion-based semi-active control of benchmark bridge using MR dampers

A new two-stage state feedback control design approach has been developed to monitor the voltage supplied to magnetorheological (MR) dampers for semi-active vibration control of the benchmark highway bridge. The first stage contains a primary controller, which provides the force required to obtain a desired closed-loop response of the system. In the second stage, an optimal dynamic inversion (ODI) approach has been developed to obtain the amount of voltage to be supplied to each of the MR dampers such that it provides the required force prescribed by the primary controller. ODI is formulated by optimization with dynamic inversion, such that an optimal voltage is supplied to each damper in a set. The proposed control design has been simulated for both phase-I and phase-II study of the recently developed benchmark highway bridge problem. The efficiency of the proposed controller is analyzed in terms of the performance indices defined in the benchmark problem definition. Simulation results demonstrate that the proposed approach generally reduces peak response quantities over those obtained from the sample semi-active controller, although some response quantities have been seen to be increasing. Overall, the proposed control approach is quite competitive as compared with the sample semi-active control approach.

Optimal simultaneous maximum a posterioriestimation of states, noise statistics and parameters I. Algorithm

The simultaneous state and parameter estimation problem for a linear discrete-time system with unknown noise statistics is treated as a large-scale optimization problem. The a posterioriprobability density function is maximized directly with respect to the states and parameters subject to the constraint of the system dynamics. The resulting optimization problem is too large for any of the standard non-linear programming techniques and hence an hierarchical optimization approach is proposed. It turns out that the states can be computed at the first levelfor given noise and system parameters. These, in turn, are to be modified at the second level.The states are to be computed from a large system of linear equations and two solution methods are considered for solving these equations, limiting the horizon to a suitable length. The resulting algorithm is a filter-smoother, suitable for off-line as well as on-line state estimation for given noise and system parameters. The second level problem is split up into two, one for modifying the noise statistics and the other for modifying the system parameters. An adaptive relaxation technique is proposed for modifying the noise statistics and a modified Gauss-Newton technique is used to adjust the system parameters.

Optimal simultaneous maximum a posterioriestimation of states, noise statistics and parameters II. Numerical performance

A very general and numerically quite robust algorithm has been proposed by Sastry and Gauvrit (1980) for system identification. The present paper takes it up and examines its performance on a real test example. The example considered is the lateral dynamics of an aircraft. This is used as a vehicle for demonstrating the performance of various aspects of the algorithm in several possible modes.

Knowledge discovery from tree databases using balanced optimal search

This research is a step forward in discovering knowledge from databases of complex structure like tree or graph. Several data mining algorithms are developed based on a novel representation called Balanced Optimal Search for extracting implicit, unknown and potentially useful information like patterns, similarities and various relationships from tree data, which are also proved to be advantageous in analysing big data. This thesis focuses on analysing unordered tree data, which is robust to data inconsistency, irregularity and swift information changes, hence, in the era of big data it becomes a popular and widely used data model.

Optimal Interconnections in the Design of Microprocessors and Digital Systems

This paper recasts the multiple data path assignment problem solved by Torng and Wilhelm by the dynamic programming method [1] into a minimal covering problem following a switching theoretic approach. The concept of bus compatibility for the data transfers is used to obtain the various ways of interconnecting the circuit modules with the minimum number of buses that allow concurrent data transfers. These have been called the feasible solutions of the problem. The minimal cost solutions are obtained by assigning weights to the bus-compatible sets present in the feasible solutions. Minimization of the cost of the solution by increasing the number of buses is also discussed.

Optimal Interconnections in the Design of Microprocessors and Digital Systems

This paper recasts the multiple data path assignment problem solved by Torng and Wilhelm by the dynamic programming method [1] into a minimal covering problem following a switching theoretic approach. The concept of bus compatibility for the data transfers is used to obtain the various ways of interconnecting the circuit modules with the minimum number of buses that allow concurrent data transfers. These have been called the feasible solutions of the problem. The minimal cost solutions are obtained by assigning weights to the bus-compatible sets present in the feasible solutions. Minimization of the cost of the solution by increasing the number of buses is also discussed.

Patterns of entrepreneurial career development: An optimal matching analysis approach

Longitudinal studies of entrepreneurial career development are rare, and current knowledge of self-employment patterns and their relationships with individual difference characteristics is limited. In this study, the authors analyzed employment data from a subsample of 514 participants from the German Socio-Economic Panel study (1984–2008). Results of an optimal matching analysis indicated that a continuous self-employment pattern could be distinguished from four alternative employment patterns (change from employment to self-employment, full-time employees, part-time employees, and farmers). Results of a multinomial logistic regression analysis showed that certain socio-demographic characteristics (i.e., age and gender) and personality characteristics (i.e., conscientiousness and risk-taking propensity) were related to the likelihood of following a continuous self-employment pattern compared to the other employment patterns. Implications for future research on entrepreneurial career development are discussed.

Essays on socially optimal phosphorus policies in crop production

Phosphorus is a nutrient needed in crop production. While boosting crop yields it may also accelerate eutrophication in the surface waters receiving the phosphorus runoff. The privately optimal level of phosphorus use is determined by the input and output prices, and the crop response to phosphorus. Socially optimal use also takes into account the impact of phosphorus runoff on water quality. Increased eutrophication decreases the economic value of surface waters by Deteriorating fish stocks, curtailing the potential for recreational activities and by increasing the probabilities of mass algae blooms. In this dissertation, the optimal use of phosphorus is modelled as a dynamic optimization problem. The potentially plant available phosphorus accumulated in soil is treated as a dynamic state variable, the control variable being the annual phosphorus fertilization. For crop response to phosphorus, the state variable is more important than the annual fertilization. The level of this state variable is also a key determinant of the runoff of dissolved, reactive phosphorus. Also the loss of particulate phosphorus due to erosion is considered in the thesis, as well as its mitigation by constructing vegetative buffers. The dynamic model is applied for crop production on clay soils. At the steady state, the analysis focuses on the effects of prices, damage parameterization, discount rate and soil phosphorus carryover capacity on optimal steady state phosphorus use. The economic instruments needed to sustain the social optimum are also analyzed. According to the results the economic incentives should be conditioned on soil phosphorus values directly, rather than on annual phosphorus applications. The results also emphasize the substantial effects the differences in varying discount rates of the farmer and the social planner have on optimal instruments. The thesis analyzes the optimal soil phosphorus paths from its alternative initial levels. It also examines how erosion susceptibility of a parcel affects these optimal paths. The results underline the significance of the prevailing soil phosphorus status on optimal fertilization levels. With very high initial soil phosphorus levels, both the privately and socially optimal phosphorus application levels are close to zero as the state variable is driven towards its steady state. The soil phosphorus processes are slow. Therefore, depleting high phosphorus soils may take decades. The thesis also presents a methodologically interesting phenomenon in problems of maximizing the flow of discounted payoffs. When both the benefits and damages are related to the same state variable, the steady state solution may have an interesting property, under very general conditions: The tail of the payoffs of the privately optimal path as well as the steady state may provide a higher social welfare than the respective tail of the socially optimal path. The result is formalized and an applied to the created framework of optimal phosphorus use.

Optimal irrigation planning in river basin development: The case of the Upper Cauvery river basin

The study deals with the irrigation planning of the Cauvery river basin in peninsular India which is extensively developed in the downstream reaches and has a high potential for development in the upper reaches. A four-reservoir system is modelled on a monthly basis by using a mathematical programming (LP) formulation to find optimum cropping patterns, subject to land, water and downstream release constraints, and applied to the Cauvery basin. Two objectives, maximizing net economic benefits and maximizing irrigated cropped area, considered in the model are analysed in the context of multiobjective planning and the trade-offs discussed.

Active vibration suppression of non-linear beams using optimal dynamic inversion

Euler–Bernoulli beams are distributed parameter systems that are governed by a non-linear partial differential equation (PDE) of motion. This paper presents a vibration control approach for such beams that directly utilizes the non-linear PDE of motion, and hence, it is free from approximation errors (such as model reduction, linearization etc.). Two state feedback controllers are presented based on a newly developed optimal dynamic inversion technique which leads to closed-form solutions for the control variable. In one formulation a continuous controller structure is assumed in the spatial domain, whereas in the other approach it is assumed that the control force is applied through a finite number of discrete actuators located at predefined discrete locations in the spatial domain. An implicit finite difference technique with unconditional stability has been used to solve the PDE with control actions. Numerical simulation studies show that the beam vibration can effectively be decreased using either of the two formulations.

Deriving optimal fishing effort for managing Australia's Moreton Bay multispecies trawl fishery with aggregated effort data

Deriving an estimate of optimal fishing effort or even an approximate estimate is very valuable for managing fisheries with multiple target species. The most challenging task associated with this is allocating effort to individual species when only the total effort is recorded. Spatial information on the distribution of each species within a fishery can be used to justify the allocations, but often such information is not available. To determine the long-term overall effort required to achieve maximum sustainable yield (MSY) and maximum economic yield (MEY), we consider three methods for allocating effort: (i) optimal allocation, which optimally allocates effort among target species; (ii) fixed proportions, which chooses proportions based on past catch data; and (iii) economic allocation, which splits effort based on the expected catch value of each species. Determining the overall fishing effort required to achieve these management objectives is a maximizing problem subject to constraints due to economic and social considerations. We illustrated the approaches using a case study of the Moreton Bay Prawn Trawl Fishery in Queensland (Australia). The results were consistent across the three methods. Importantly, our analysis demonstrated the optimal total effort was very sensitive to daily fishing costs—the effort ranged from 9500–11 500 to 6000–7000, 4000 and 2500 boat-days, using daily cost estimates of $0, $500, $750, and $950, respectively. The zero daily cost corresponds to the MSY, while a daily cost of $750 most closely represents the actual present fishing cost. Given the recent debate on which costs should be factored into the analyses for deriving MEY, our findings highlight the importance of including an appropriate cost function for practical management advice. The approaches developed here could be applied to other multispecies fisheries where only aggregated fishing effort data are recorded, as the literature on this type of modelling is sparse.

Growth analysis and biomass partitioning of Cyperus iria in response to rice planting density and nitrogen rate

Cyperus iria is a weed of rice with widespread occurrence throughout the world. Because of concerns about excessive and injudicious use of herbicides, cultural weed management approaches that are safe and economical are needed. Developing such approaches will require a better understanding of weed biology and ecology, as well as of weed response to increases in crop density and nutrition. Knowledge of the effects of nitrogen (N) fertilizer on crop-weed competitive interactions could also help in the development of integrated weed management strategies. The present study was conducted in a screenhouse to determine the effects of rice planting density (0, 5, 10, and 20 plants pot−1) and N rate (0, 50, 100, and 150 kg ha−1) on the growth of C. iria. Tiller number per plant decreased by 73–88%, leaf number by 85–94%, leaf area by 85–98%, leaf biomass by 92–99%, and inflorescence biomass by 96–99% when weed plants were grown at 20 rice plants pot−1 (i.e., 400 plants m−2) compared with weed plants grown alone. All of these parameters increased when N rates were increased. On average, weed biomass increased by 118–389% and rice biomass by 121–275% with application of 50–150 kg N ha−1, compared to control. Addition of N favored weed biomass production relative to rice biomass. Increased N rates reduced the root-to-shoot weight ratio of C. iria. Rice interference reduced weed growth and biomass and completely suppressed C. iria when no N was applied at high planting densities (i.e., 20 plants pot−1). The weed showed phenotypic plasticity in response to N application, and the addition of N increased the competitive ability of the weed over rice at densities of 5 and 10 rice plants pot−1 compared with 20 plants pot−1. The results of the present study suggest that high rice density (i.e., 400 plants m−2) can help suppress C. iria growth even at high N rates (150 kg ha−1).

Problems and Algorithms for Sequence Segmentations

The analysis of sequential data is required in many diverse areas such as telecommunications, stock market analysis, and bioinformatics. A basic problem related to the analysis of sequential data is the sequence segmentation problem. A sequence segmentation is a partition of the sequence into a number of non-overlapping segments that cover all data points, such that each segment is as homogeneous as possible. This problem can be solved optimally using a standard dynamic programming algorithm. In the first part of the thesis, we present a new approximation algorithm for the sequence segmentation problem. This algorithm has smaller running time than the optimal dynamic programming algorithm, while it has bounded approximation ratio. The basic idea is to divide the input sequence into subsequences, solve the problem optimally in each subsequence, and then appropriately combine the solutions to the subproblems into one final solution. In the second part of the thesis, we study alternative segmentation models that are devised to better fit the data. More specifically, we focus on clustered segmentations and segmentations with rearrangements. While in the standard segmentation of a multidimensional sequence all dimensions share the same segment boundaries, in a clustered segmentation the multidimensional sequence is segmented in such a way that dimensions are allowed to form clusters. Each cluster of dimensions is then segmented separately. We formally define the problem of clustered segmentations and we experimentally show that segmenting sequences using this segmentation model, leads to solutions with smaller error for the same model cost. Segmentation with rearrangements is a novel variation to the segmentation problem: in addition to partitioning the sequence we also seek to apply a limited amount of reordering, so that the overall representation error is minimized. We formulate the problem of segmentation with rearrangements and we show that it is an NP-hard problem to solve or even to approximate. We devise effective algorithms for the proposed problem, combining ideas from dynamic programming and outlier detection algorithms in sequences. In the final part of the thesis, we discuss the problem of aggregating results of segmentation algorithms on the same set of data points. In this case, we are interested in producing a partitioning of the data that agrees as much as possible with the input partitions. We show that this problem can be solved optimally in polynomial time using dynamic programming. Furthermore, we show that not all data points are candidates for segment boundaries in the optimal solution.