Shooting, finite difference, or harmonic balance techniques in conjunction with a damped Newton method are widely employed for the numerical calculation of limit cycles of (free-running, autonomous) oscillators. In some cases, however, nonconvergence occurs when the initial estimate of the solution is not close enough to the exact one. Generally, the higher the quality factor of the oscillator the tighter are the constraints for the initial estimate. A 2-D homotopy method is presented in this paper that overcomes this problem. The resulting linear set of equations is underdetermined, leading to a nullspace of rank two. This underdetermined system is solved in a least squares sense for which a rigorous mathematical basis can be derived. An efficient algorithm for solving the least squares problem is derived where sparse matrix techniques can be used. As continuation methods are only employed for obtaining a sufficient initial guess of the limit cycle, a coarse grid discretization is sufficient to make the method runtime efficient.

The numerical calculation of the limit cycle of oscillators with resonators exhibiting a high quality factor such as quartz crystals is a difficult task in the time domain. Time domain integration formulas introduce numerical damping which leads asympotically to erroneous limit cycles or spurious oscillations. The numerical problems for solving the underlying differential algebraic equations are studied in detail. Based on these results a class of novel integration formulas is derived and the results are compared with the well-known Harmonic Balance (HB) technique. The discretized system is sparser than that of the HB method, therefore easier to solve and slower run time.

In code division multiple access (CDMA) systems a significant degradation in detection performance due to multiuser interference can be avoided by the utilization of interference cancellation methods. Further enhancement can be obtained by optimizing the power allocation of the users. The resulting constrained single-objective optimization problem is solved here by means of particle swarm optimization (PSO). It is shown that the maximum number of users for a CDMA system can be increased significantly if an optimized power profile is employed. Furthermore, an extensive study of PSO control parameter settings using three different neighborhood topologies is performed on the basis of the power allocation problem, and two constraint-handling techniques are evaluated. Results from the parameter study are compared with examinations from the literature. It is shown that thevon-Neumannneighborhood topology performs consistently better thangbestandlbest. However, strong interaction effects and conflicting recommendations for parameter settings are found that emphasize the need for adaptive approaches.

PI cascade controllers are often used in control applications due to their simplicity. Because of uncertain and varying system parameters, a robust control is needed. However, known methods to generate robust controllers often lead to complicated control structures. Unfortunately, there are no analytical solutions to generate robust controllers with a fixed simple structure like the PI cascade. Therefore, easy-to-use optimization algorithms are needed. In this paper it is shown that for a practical approach using recommended parameter settings from literature both Differential Evolution and Particle Swarm Optimization can be used for the optimization of a PI cascade control. A performance comparison shows similar results, so both of them are useful to field engineers who apply optimization algorithms to real-world problems and are often inexperienced concerning optimization.

To avoid the effort associated with choosing control parameter settings, an adaptive approach for parameter setting of a multi-objective particle swarm optimization algorithm is presented in this work. The adaptive parameter control relies on methods from design of experiments which are able to detect significant performance variations of parameter settings. Furthermore, interaction effects of different parameters can be discovered. The adaptive control is applied to the parameters which are incorporated in the update equations of PSO, so the movement of particles is adapted based on feedback about successes during the search. The adaptive approach is evaluated using 13 test functions and several performance measures.

Control parameter settings influence the convergence probability and convergence speed of evolutionary algorithms but it is often not obvious how to choose them. In this work an adaptive approach for setting the control parameters of a multi-objective differential evolution algorithm is presented. The adaptive approach is based on methods from design of experiments, so it is able to detect significant performance differences of individual parameters as well as interaction effects between parameters. It is evaluated based on 13 test functions and several performance measures.

Widely separated time-scales occur in many radio-frequency (RF) circuits, making the analysis with standard numerical methods difficult and costly. Low and high frequency signals are often superimposed enforcing very small time-steps over a long time-period in the computation of the numerical solution. Hence, classical numerical techniques result into long runtimes. In this paper we present a general method of embedding the underlying system of ordinary differential-algebraic equations (DAEs) in a system of partial differential equations (PDEs), such that a restriction of the solution of the PDEs onto a suitable path yields the desired solution of the DAEs. This allows to treat contributions with different frequencies separately in different dimensions, each dimension representing a time-scale. Along the coordinates the solution of the PDEs is typically very smooth, making numerical techniques for the solution of PDEs highly efficient. Here, theoretical results as well as new numerical methods are presented

This poster shows the work-in-progress results of an effective method for predicting the residual battery energy in WSN nodes including the battery behavior. This method uses a hybrid approach consisting of a deterministic part by counting credit points for any operation of the sensor node and a model-based State-of-Charge (SoC) estimation based on battery voltage and temperature. It is applied for Li-Ion accumulators on modified Tmote Sky motes. For demonstration purposes the method is used for cluster head selection in a cluster-based topology formation algorithm to ensure equal distribution of the cluster head role among the network nodes based on the residual energy.

Differential evolution (DE) is a rather new evolutionary optimization algorithm that has been shown to be fast and simple for unconstrained single-objective optimization problems. In this work DE is employed for the constrained optimization test suite of the special session on constrained real parameter optimization at CEC06. Constraints are handled using a modified selection procedure that does not require additional parameters. For the control parameters of the DE algorithm the best found settings from another examination were used so that almost no parameter tuning was necessary. Most of the test functions are successfully and reliably optimized. Difficulties arise mainly from a high number of equality constraints.

Particle Swarm Optimization (PSO) is an optimization method that is derived from the behavior of social groups like bird flocks or fish schools. In this work PSO is used for the optimization of the constrained test suite of the special session on constrained real parameter optimization at CEC06. Constraint-handling is done by modifying the procedure for determining personal and neighborhood best particles. No additional parameters are needed for the handling of constraints. Numerical results are presented, and statements are given about which types of functions have been successfully optimized and which features present difficulties.

The performance of evolutionary algorithms is strongly dependent on the setting of control parameters. Not only the convergence speed is influenced, but also if the optimum of a function is reached at all. For differential evolution premature convergence or even stagnation can occur due to certain parameter settings. In this paper a parameter study for differential evolution is conducted. As basis for the examination a real-world problem is employed that consists of optimizing the power allocation for a CDMA (code division multiple access) system. For the CDMA system interference cancellation methods are applied as the detection performance is significantly degraded by multi-user interference. The convergence of the interference cancellation method establishes a constraint for the single-objective optimization problem. Optimization results for both parallel and successive interference cancellation are given. The findings of the parameter study are compared with results from literature, and recommendations concerning settings of DE control parameters are given.

Shooting, finite difference or Harmonic Balance techniques in conjunction with Newton's method are widely employed for the numerical calculation of limit cycles of oscillators. The resulting set of nonlinear equations are normally solved by damped Newton's method. In some cases however divergence occurs when the initial estimate of the solution is not close enough to the exact one. A two-dimensional homotopy method is presented in this paper which overcomes this problem. The resulting linear set of equations employing Newton's method is under-determined and is solved in a least squares sense for which a rigorous mathematical basis can be derived.

In this paper we study efficient numerical methods for obtaining consistent initial conditions for systems of differential-algebraic equations (DAEs) with higher index arising, for example, from electronic circuits. We show that the class of Gear's backward differentiation formulas, unlike other multi-step techniques, are a useful means for obtaining consistent initial conditions when carefully implemented. Because the method employs sparse matrix techniques, it is efficient even for large circuits, The numerical experiments suggest that the method works reliably even for index-3 DAEs.

Commonly used scheduling algorithms in high-level synthesis only accept one process at a time and are not capable of sharing resources across process boundaries. This results in the usage of at least one resource per operation type and process. A new method is proposed in order to overcome these restrictions and to share high-cost or limited resources within a process group. This allows the use of less than one resource per operation type and process, while keeping the mutual independence of the involved processes. The method represents an extension of general scheduling algorithms and is not tied to a specific algorithm. It is applied to the time constrained force-directed scheduling algorithm. For this the scope of the scheduling is extended to the processes of the whole system and a two-part modification is applied to the original procedure. A multi-process example illustrates the resource sharing capabilities of the extension.

When simulating analog and microwave circuits, the steady-state behavior is of primary interest. One method for simulating the steady-state is the harmonic balance technique (HB). HB is characterized by the use of trigonometric basis functions. The resulting nonlinear equations are solved by Newton's method (NR). The linear systems arising from NR are very large, indefinite but sparse. They can be solved by direct, stationary or Krylov subspace methods. This paper deals with the solution of linear systems arising from NE using preconditioned Krylov subspace methods (CGS, BiCGSTAB, BiCGSTAB(2), TFQMR).

This paper describes an architecture based on a new full search block-matching algorithm called vector-characterization algorithm (VCA). A single-chip realization in form of a 1.0 /spl mu/m CMOS standard cell design shows that the architecture is suitable for HDTV applications.

This paper describes a new VLSI realization of the International Data Encryption Algorithm IDEA. The presented VLSI architecture is compared with the VINCI chip, the first silicon realization of the IDEA. Principal design aspects are also discussed. Although the VINCI circuit can be used for real-time encryption in high-speed networks such as ATM, there are requirements for VLSI circuits with faster encryption ability. Further, the implemented test during the normal operation in the VINCI chip cannot detect all possible errors. The proposed new implementation is motivated by the requirement for higher data rates and a new solution for the on-line test problem, which is a main task in implementing cryptographic algorithms. First design results show that the resulting circuit can achieve an encryption rate of about 355 Mb/s. This is achieved by the implementation of one round in a 0.8 /spl mu/m CMOS technology. The architecture includes a concurrent self-test based on a mod-3 residue code self-checking system which allows the detection of permanent and temporary single- and multiple-bit errors in the IDEA datapath and hence the secure prevention of faulty encrypted or decrypted data.

A macromodel for nonlinear devices exhibiting hysteresis is presented. Although this model is based on existing ideas of ferromagnetic hysteresis, it can be applied to all hysteresis phenomena by choosing suitable parameters. It exhibits all main features of hysteresis, such as initial curve, saturation, minor loops, coercivity and remanence. Using standard elements of the widespread simulator SPICE, the macromodel is applicable to all commonly used circuit simulators.>

This paper presents a new strategy for automatic test pattern generation for synchronous sequential circuits. It is known that it is difficult and time-consuming to detect stuck-at faults in sequential circuits. A sequence of test patterns is often required to detect a target fault in sequential circuits using conventional sequential test pattern generators. In order to reduce CPU time and the number of test patterns and to improve fault coverage, we propose a new strategy for sequential test pattern generation using the clock isolation, which can enhance the performance of the conventional test pattern generator. Furthermore the test pattern can be generated efficiently using a new testability measure, a sixteen-valued logic, complete multiple-path sensitisation and a modified algorithm of conventional sequential test pattern generation.>

A modular circuit is defined as a combination of a certain number of k-modules, which are embedded in a carrier network. The modules may represent subcircuits of varying complexity down to single devices. Such modular circuits lend themselves to a description by a system of modular equations. MEDUSA is a user-oriented simulator which utilizes system modularity during the simulation process itself, i.e., for solving the underlying equations. This approach enables the consistent numerical solution of both the basic equations of several bipolar devices and the network equations for a circuit environment. Hence, MEDUSA in its present state is a merged device-circuit simulator meeting simultaneously the requirements of device and circuit design.