An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index

The shifted Legendre orthogonal polynomials are used for the numerical solution of a new formulation for the multi-dimensional fractional optimal control problem (M-DFOCP) with a quadratic performance index. The fractional derivatives are described in the Caputo sense. The Lagrange multiplier method for the constrained extremum and the operational matrix of fractional integrals are used together with the help of the properties of the shifted Legendre orthonormal polynomials. The method reduces the M-DFOCP to a simpler problem that consists of solving a system of algebraic equations. For confirming the efficiency and accuracy of the proposed scheme, some test problems are implemented with their approximate solutions.

Stochastic Population Projection for Germany - based on the Quadratic Spline approach to modelling age specific fertility rates

This contribution builds upon a former paper by the authors (Lipps and Betz 2004), in which a stochastic population projection for East- and West Germany is performed. Aim was to forecast relevant population parameters and their distribution in a consistent way. We now present some modifications, which have been modelled since. First, population parameters for the entire German population are modelled. In order to overcome the modelling problem of the structural break in the East during reunification, we show that the adaptation process of the relevant figures by the East can be considered to be completed by now. As a consequence, German parameters can be modelled just by using the West German historic patterns, with the start-off population of entire Germany. Second, a new model to simulate age specific fertility rates is presented, based on a quadratic spline approach. This offers a higher flexibility to model various age specific fertility curves. The simulation results are compared with the scenario based official forecasts for Germany in 2050. Exemplary for some population parameters (e.g. dependency ratio), it can be shown that the range spanned by the medium and extreme variants correspond to the s-intervals in the stochastic framework. It seems therefore more appropriate to treat this range as a s-interval covering about two thirds of the true distribution.

A new aggregation method for strategic decision making and its application in assignment theory

A new aggregation method for decision making is presented by using induced aggregation operators and the index of maximum and minimum level. Its main advantage is that it can assess complex reordering processes in the aggregation that represent complex attitudinal characters of the decision maker such as psychological or personal factors. A wide range of properties and particular cases of this new approach are studied. A further generalization by using hybrid averages and immediate weights is also presented. The key issue in this approach against the previous model is that we can use the weighted average and the ordered weighted average in the same formulation. Thus, we are able to consider the subjective attitude and the degree of optimism of the decision maker in the decision process. The paper ends with an application in a decision making problem based on the use of the assignment theory.

Linear-quadratic optimal control of descriptor systems

In recent years the analysis and synthesis of (mechanical) control systems in descriptor form has been established. This general description of dynamical systems is important for many applications in mechanics and mechatronics, in electrical and electronic engineering, and in chemical engineering as well. This contribution deals with linear mechanical descriptor systems and its control design with respect to a quadratic performance criterion. Here, the notion of properness plays an important role whether the standard Riccati approach can be applied as usual or not. Properness and non-properness distinguish between the cases if the descriptor system is exclusively governed by the control input or by its higher-order time-derivatives additionally. In the unusual case of non-proper systems a quite different problem of optimal control design has to be considered. Both cases will be solved completely.

Simulation of Steady-State Nonlinear Heat Transfer Problems Through the Minimization of Quadratic Functionals

In this work it is presented a systematic procedure for constructing the solution of a large class of nonlinear conduction heat transfer problems through the minimization of quadratic functionals like the ones usually employed for linear descriptions. The proposed procedure gives rise to an efficient and easy way for carrying out numerical simulations of nonlinear heat transfer problems by means of finite elements. To illustrate the procedure a particular problem is simulated by means of a finite element approximation.

Reinforcement Learning approaches to Economic Dispatch problem

This paper presents Reinforcement Learning (RL) approaches to Economic Dispatch problem. In this paper, formulation of Economic Dispatch as a multi stage decision making problem is carried out, then two variants of RL algorithms are presented. A third algorithm which takes into consideration the transmission losses is also explained. Efficiency and flexibility of the proposed algorithms are demonstrated through different representative systems: a three generator system with given generation cost table, IEEE 30 bus system with quadratic cost functions, 10 generator system having piecewise quadratic cost functions and a 20 generator system considering transmission losses. A comparison of the computation times of different algorithms is also carried out.

Design, Development and Realization of Quadratic Volterra Filters for Selected Applications

The basic concepts of digital signal processing are taught to the students in engineering and science. The focus of the course is on linear, time invariant systems. The question as to what happens when the system is governed by a quadratic or cubic equation remains unanswered in the vast majority of literature on signal processing. Light has been shed on this problem when John V Mathews and Giovanni L Sicuranza published the book Polynomial Signal Processing. This book opened up an unseen vista of polynomial systems for signal and image processing. The book presented the theory and implementations of both adaptive and non-adaptive FIR and IIR quadratic systems which offer improved performance than conventional linear systems. The theory of quadratic systems presents a pristine and virgin area of research that offers computationally intensive work. Once the area of research is selected, the next issue is the choice of the software tool to carry out the work. Conventional languages like C and C++ are easily eliminated as they are not interpreted and lack good quality plotting libraries. MATLAB is proved to be very slow and so do SCILAB and Octave. The search for a language for scientific computing that was as fast as C, but with a good quality plotting library, ended up in Python, a distant relative of LISP. It proved to be ideal for scientific computing. An account of the use of Python, its scientific computing package scipy and the plotting library pylab is given in the appendix Initially, work is focused on designing predictors that exploit the polynomial nonlinearities inherent in speech generation mechanisms. Soon, the work got diverted into medical image processing which offered more potential to exploit by the use of quadratic methods. The major focus in this area is on quadratic edge detection methods for retinal images and fingerprints as well as de-noising raw MRI signals

Asymmetrically fair rules for an indivisible good problem with a budget constraint

We study a particular restitution problem where there is an indivisible good (land or property) over which two agents have rights: the dispossessed agent and the owner. A third party, possibly the government, seeks to resolve the situation by assigning rights to one and compensate the other. There is also a maximum amount of money available for the compensation. We characterize a family of asymmetrically fair rules that are immune to strategic behavior, guarantee minimal welfare levels for the agents, and satisfy the budget constraint.

Performance of asynchronous channel assignment scheme in non-uniform and dynamic topology WLANs

Dense deployments of wireless local area networks (WLANs) are fast becoming a permanent feature of all developed cities around the world. While this increases capacity and coverage, the problem of increased interference, which is exacerbated by the limited number of channels available, can severely degrade the performance of WLANs if an effective channel assignment scheme is not employed. In an earlier work, an asynchronous, distributed and dynamic channel assignment scheme has been proposed that (1) is simple to implement, (2) does not require any knowledge of the throughput function, and (3) allows asynchronous channel switching by each access point (AP). In this paper, we present extensive performance evaluation of this scheme when it is deployed in the more practical non-uniform and dynamic topology scenarios. Specifically, we investigate its effectiveness (1) when APs are deployed in a nonuniform fashion resulting in some APs suffering from higher levels of interference than others and (2) when APs are effectively switched `on/off' due to the availability/lack of traffic at different times, which creates a dynamically changing network topology. Simulation results based on actual WLAN topologies show that robust performance gains over other channel assignment schemes can still be achieved even in these realistic scenarios.

An asynchronous channel assignment scheme: performance evaluation

Due to its popularity, dense deployments of wireless local area networks (WLANs) are becoming a common feature of many cities around the world. However, with only a limited number of channels available, the problem of increased interference can severely degrade the performance of WLANs if an effective channel assignment scheme is not employed. In an earlier work, we proposed an improved asynchronous distributed and dynamic channel assignment scheme that (1) is simple to implement, (2) does not require any knowledge of the throughput function, and (3) allows asynchronous channel switching by each access point (AP). In this paper, we present extensive performance evaluation of the proposed scheme in practical scenarios found in densely populated WLAN deployments. Specifically, we investigate the convergence behaviour of the scheme and how its performance gains vary with different number of available channels and in different deployment densities. We also prove that our scheme is guaranteed to converge in a single iteration when the number of channels is greater than the number of neighbouring APs.

Effectiveness of asynchronous channel assignment scheme in heterogeneous WLANs

Due to their popularity, dense deployments of wireless local area networks (WLANs) are becoming a common feature of many cities around the world. However, with only a limited number of channels available, the problem of increased interference can severely degrade the performance of WLANs if an effective channel assignment scheme is not employed. Previous studies on channel assignment in WLANs almost always assume that all access points (AP) employ the same channel assignment scheme which is clearly unrealistic. On the other hand, to the best of our knowledge, the interaction between different channel assignment schemes has also not been studied before. Therefore, in this paper, we investigate the effectiveness of our earlier proposed asynchronous channel assignment scheme in these heterogeneous WLANs scenarios. Simulation results show that our proposed scheme is still able to provide robust performance gains even in these scenarios.

An improved distributed dynamic channel assignment scheme for dense WLANs

The popularity of wireless local area networks (WLANs) has resulted in their dense deployment in many cities around the world. The increased interference among different WLANs severely degrades the throughput achievable. This problem has been further exacerbated by the limited number of frequency channels available. An improved distributed and dynamic channel assignment scheme that is simple to implement and does not depend on the knowledge of the throughput function is proposed in this work. It also allows each access point (AP) to asynchronously switch to the new best channel. Simulation results show that our proposed scheme converges much faster than similar previously reported work, with a reduction in convergence time and channel switches as much as 77.3% and 52.3% respectively. When it is employed in dynamic environments, the throughput improves by up to 12.7%.

Integrable quadratic Hamiltonians on the Euclidean group of motions

In this paper, we discuss the problem of globally computing sub-Riemannian curves on the Euclidean group of motions SE(3). In particular, we derive a global result for special sub-Riemannian curves whose Hamiltonian satisfies a particular condition. In this paper, sub-Riemannian curves are defined in the context of a constrained optimal control problem. The maximum principle is then applied to this problem to yield an appropriate left-invariant quadratic Hamiltonian. A number of integrable quadratic Hamiltonians are identified. We then proceed to derive convenient expressions for sub-Riemannian curves in SE(3) that correspond to particular extremal curves. These equations are then used to compute sub-Riemannian curves that could potentially be used for motion planning of underwater vehicles.

A new approach for the solution of the optimal set-point tracking problem for nonlinear systems

In this paper, a discrete time dynamic integrated system optimisation and parameter estimation algorithm is applied to the solution of the nonlinear tracking optimal control problem. A version of the algorithm with a linear-quadratic model-based problem is developed and implemented in software. The algorithm implemented is tested with simulation examples.

Rapid protein domain assignment from amino acid sequence using predicted secondary structure

The elucidation of the domain content of a given protein sequence in the absence of determined structure or significant sequence homology to known domains is an important problem in structural biology. Here we address how successfully the delineation of continuous domains can be accomplished in the absence of sequence homology using simple baseline methods, an existing prediction algorithm (Domain Guess by Size), and a newly developed method (DomSSEA). The study was undertaken with a view to measuring the usefulness of these prediction methods in terms of their application to fully automatic domain assignment. Thus, the sensitivity of each domain assignment method was measured by calculating the number of correctly assigned top scoring predictions. We have implemented a new continuous domain identification method using the alignment of predicted secondary structures of target sequences against observed secondary structures of chains with known domain boundaries as assigned by Class Architecture Topology Homology (CATH). Taking top predictions only, the success rate of the method in correctly assigning domain number to the representative chain set is 73.3%. The top prediction for domain number and location of domain boundaries was correct for 24% of the multidomain set (±20 residues). These results have been put into context in relation to the results obtained from the other prediction methods assessed