Perturbation analysis of singular linear systems with index one ∗

A new perturbation result for singular but consistent linear systems with coefficient matrix of index one is presented. However, if the system is inconsistent, we also derive a perturbation bound of the generalized linear least squares solution. Our treatment extends a classical perturbation result in numerical linear algebra.     

Optimal control with a bounded energy input derivative for a class of distributed systems†

An optimal control problem, for a class of distributed parameter systems, with a constraint on the input derivative, is posed. The constraint is a bound on the L ₂ norm of the input derivative. Existence of optimal controls is proved, and a non-linear integro-differential equation is derived to serve as a necessary and sufficient condition for the optimal controls to satisfy. Also, a computational scheme, for optimal controls, is suggested.     

Computerized energy management systems—why and how

This paper discusses why computerized energy management systems have displaced the time clocks and mechanical controllers, and how these new systems perform. A brief review of the development of computerized energy management systems and how they compare with hard-wired digital controllers is presented first. Then the energy management needs of a facility are discussed. Various factors include size of operation, type of equipment and process, and geographical location. Four levels of energy management functions and the corresponding systems are identified. These are: (i) Level 1 system — basic energy management, (ii) Level 2 system — advanced energy management, (iii) Level 3 system — total energy management, and (iv) Level 4 system — total engineering applications. The hardware used in these systems range from simple demand controllers to minicomputers.The evaluation criteria for energy management systems (EMS) are discussed. A classification of EMS hardware and features is presented. This also includes discussion on the plant size and type, computer facility, number of control points and features.     

On the abs algorithms for perturbed linear systems ∗

One of the most important problems in numerical analysis and numerical optimization is to solve a linear system of equations. Sometimes it should be repeated when one of the equations is replaced by a new one. In this paper as a result of theoretical analysis, an algorithm model and a particular algorithm which are based on the ABS class are proposed. After the original linear system has been solved by the ABS class, the algorithms proposed here can efficiently solve the new system which is obtained from the original system by replacing one of its equations by using information obtained in the previous computation. These algorithms can be used continually when some equations of the original system are replaced by new equations successively with less computation effort.     

A hybrid Wi-Fi P2P with bluetooth low energy for optimizing smart device’s communication property

Peer-to-Peer Networking and Applications - Recently, due to the popularity of smart devices, a need for various types of wireless communication has been tremendously increasing and several types of...     

On the stability problem for distributed parameter energy systems†

In this paper asymptotic stability of the non-trivial or operating equilibrium state of a distributed parameter energy system is considered. Sufficient conditions are obtained by the method of comparison functions. This enables one to obtain bounds on the maximum value of the state variables. The criteria derived depend on the eigenvalues of the linearized system as well as on a bound for the feedback control law.     

Minimal controllability for systems with delays†

In this paper we consider the problem of minimal controllability for a general class of linear spectrally controllable systems. We show that the smallest number of controls that are necessary in order that spectral controllability may hold depends only upon the matrices of the uncontrolled system and that it is equal to the smallest number of outputs necessary for the dual problem of ‘spectral observability’; moreover, any spectrally controllable system can be made minimally controllable by acting upon the control matrix only, and any spectrally observable system can be made minimally observable by acting upon the output matrix only. In the sequel this result is explained in the cases of the delayed systems and of some kind of generalized systems.     

Control of switched systems with actuator saturation

1 Introduction Switched systems are composed of a set of subsystems and a switching rule designating which subsystem to be actuated at each moment. Switched systems are commonly found in various engineering practice, such as in auto- motive engine control systems, chemical process control, robotic manufacture, multiple-model systems and so on. In the past decade, many literatures have been devoted to the study of switched systems. Stability is an important issue in the analysis and synthesis o…     

Linear systems with non-stationary random inputs†

This paper concerns the response correlation matrix of a linear time variable system with stationary or non-stationary stochastic inputs modulated by linear homogeneous operators. By adapting Lanczos' ‘selected points’ method an algorithm is introduced to compute the state covariance matrix of systems with deterministic initial state. Certain computational features of response correlation matrices of systems with random initial state and random inputs are also outlined. Limited numerical studies indicate that the proposed method is efficient to treat uni-dimensional and small-order multi-dimensional systems. Mean square response comparisons with some of the previously studied systems indicate good agreement and the saving in machine time appears to be substantial.     

Convergence of two-stage iterative methods for singular symmetric positive semidefinite systems ∗

Convergence of two-stage iterative methods for singular symmetric positive semidefinite (spsd) systems is studied. The main tool we used to derive the iterative methods and to analyze their convergence is the extended diagonally compensated reduction     

On simultaneous control of the energy and actuated variables of underactuated mechanical systems – example of the acrobot with counterweight

The energy-based control approach aiming to control both the total mechanical energy and actuated variables of underactuated mechanical systems has generated renewed interest in recent years. Different from the reports of successful applications of this approach, we investigate whether there exists an underactuated mechanical system for which we fail to control both the total mechanical energy and actuated variable(s) to some given desired values by studying a CWA (Counter-Weighted Acrobot), which is a modified Acrobot with its first link having a counterweight and only its second link being actuated. By analyzing globally the solution of the closed-loop system consisting of the CWA and the controller designed via the energy-based control approach, we show that unless the CWA is linearly controllable at the up–up equilibrium, where links 1 and 2 are in the upright position, the controller fails to achieve the goal of controlling the energy to the potential energy at the equilibrium and controlling the actuated joint variable to zero. We also provide corresponding results for the up–down, down–up, and down–down equilibriums of the CWA, where up and down denote that the link is in the upright and downward positions, respectively. We present numerical simulation results to validate the theoretical results.     

Remarks on the paper “Optimal control of a class of linear multivariable systems with integral quadratic energy constraint ”

An optimal periodic control problem for a system described by differential equations is considered. Control units are assumed to generate control actions with the square-integrable derivative. The above problem is approximated by a sequence of discretized problems containing trigonometric polynomials, which approximate the state and control variables, and the functions in the criterion and differential equations. The conditions for a sequence of optimal solutions to discretized problems, which are to be a generalized minimizing sequence for the basic problem, are given. Extensions to more general problem formulations are presented. The possibility of application is illustrated by the example of an optimal periodic control problem for a chemical reactor.     

The energy cost of women walking and running in shoes and boots∗

The purpose of this study was to determine the difference in energy cost for women walking and running in shoes versus heavier boots. Seven subjects wore athletic shoes (mean weight = 514 ± 50g) and leather military boots (mean weight = 1371 ± 104g) at three walking speeds (4·0, 5·6 and 7·3km/hour) and two running speeds (8middot;9 and 10·5 km/hour). During each walking and running trial oxygen uptake ([Vdot]O₂ ml kg^?1 min^?1) was measured. The [Vdot]O₂ for women wearing boots were significantly higher (P < 0·05) than for shoes for both walking and running, with the exception of the slowest walking speed. The average increment in energy cost was 1·0% per 100-g increase in weight per pair of footwear. These results are similar to those reported for men from other studies which found increments in energy cost of 0·7 to 0·9% per 100-g increase in weight of footwear.     

Fast convergence pirkn-type pc methods with adams-type predictors ∗

This paper discusses predictor–corrector iteration schemes (PC iteration schemes) based on direct collocatio–based Runge–Kutt–Nyström corrector methods (RKN corrector methods) for solving nonstiff initial-value problems (IVPs) for systems of special second-order differential equations y′′(t) = f(y(t)) Our approach is to regard the well-known parallel-iterated RKN methods (PIRKN methods) as PC iteration processes in which the simple, low-order last step value predictors are replaced with the high-order Adams-type predictors. Moreover, the param-eters of the new direct collocation-based RKN corrector methods are chosen in such a way that the convergence rate of the considered PC iteration processes is optimized. In this way, we obtain parallel PC methods with fast convergence and high-accurate predictions. Application of the resulting parallel PC methods to a few widely-used test problems reveals that the sequential costs are very much reduced when compared with the parallel and sequential explicit RKN methods from the literature.     

Ant colony optimization inspired resource discovery in P2P Grid systems

It is a challenge for the traditional centralized or hierarchical Grid architecture to manage the large-scale and dynamic resources, while providing scalability. The Peer-to-Peer (P2P) model offers a prospect of dynamicity, scalability, and availability of a large pool of resources. By integrating the P2P philosophy and techniques into a Grid architecture, P2P Grid system is emerging as a promising platform for executing large-scale, resource intensive applications. There are two typical resource discovery approaches for a large-scale P2P system. The first one is an unstructured approach which propagates the query messages to all nodes to locate the required resources. The method does not scale well because each individual query generates a large amount of traffic and the network quickly becomes overwhelmed by the messages. The second one is a structured approach which places resources at specified locations to make subsequent queries easier to satisfy. However, the method does not support multi-attribute range queries and may not work well in the network which has an extremely transient population. This paper proposes and designs a large-scale P2P Grid system which employs an Ant Colony Optimization (ACO) algorithm to locate the required resources. The ACO method avoids a large-scale flat flooding and supports multi-attribute range query. Multiple ants can be employed to improve the parallelism of the method. A simulator is developed to evaluate the proposed resource discovery mechanism. Comprehensive simulation results validate the effectiveness of the proposed method compared with the traditional unstructured and structured approaches.

Synthesis of systems with dominant complex roots†

Systems with three (or more) free parameters are considered. Pre-determined locations are assigned to one pair of complex roots, and their existence is guaranteed by assigning two degrees of freedom (two parameters) to constrain them to the desired location. The constraints are used to construct a reduced characteristic equation from which the assigned parameters have been eliminated. The polynomial thus obtained defines the locations of all roots except the specified complex pair, and (for the case of three parameters) a root locus study permits choice of a value of the third parameter such that the root pattern is compatible with a dominance requirement for the specified complex pair     

Stability of time-delay systems with sampled feedback†

Implementation of a feedback control which approximates the optimal control for a linear delay system is considered. Sufficient conditions for asymptotic stability of the resulting sampled-data feedback system are determined.