Point Constraints Research Articles

Efficient automatic gain control algorithm and architecture for wireless LAN receivers

The performance of a receiver front-end limits the quality and range of the given communication link. An appropriate design based on well-defined system parameters and architecture can make a huge difference in the performance, cost and marketability of the entire system. In particular, there is a need for improved digital automatic gain control (AGC) for use in multi-input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) systems with application to wireless local area networks (WLANs), targeted for the upcoming 802.11n standard [Heejung Yu et al., IEEE 802.11 wireless LANs ETRI proposal specification for IEEE 802.11 TGn, IEEE 802.11 document, doc. No. 11-04-0923-00-000n, August, 2004; H. Yu, T. Jeon, S. Lee, Design of dual-band MIMO-OFDM system for next generation wireless LAN, in: IEEE International Conference on Communications (ICC), May, 2005]. In this paper, we propose an efficient algorithm and implementation of the digital AGC for next generation WLANs. The proposed AGC algorithm has two feedback loops for gain control to improve convergence speed, and at the same time maintains the stability of the AGC circuit. Also, a complete set of parameters for practical implementation is obtained by various experiments with fixed point constraints and accuracy requirements.

Nonlinear Predictive Control With End Point Constraints

The optimal nonlinear predictive control structure with end point constraints is presented, which provides asymptotic tracking of smooth reference trajectories. The controller is based on a finite horizon continuous time minimization of nonlinear predicted tracking errors. A key feature of the control law is that its implementation does not need to perform an online optimization, and asymptotic tracking of smooth reference signal is guaranteed. The proposed control scheme is applied to planning motions problem of a mobile robot. Simulations results are performed to validate the tracking performance of the proposed controller.

A Novel Approach to Calibrating Multifunctional Binocular Stereovision Sensor

We present a novel multifunctional binocular stereovision sensor for various threedimensional (3D) inspection tasks. It not only avoids the so-called correspondence problem of passive stereo vision, but also possesses the uniform mathematical model. We also propose a novel approach to estimating all the sensor parameters with free-position planar reference object. In this technique, the planar pattern can be moved freely by hand. All the camera intrinsic and extrinsic parameters with coefficient of lens radial and tangential distortion are estimated, and sensor parameters are calibrated based on the 3D measurement model and optimized with the feature point constraint algorithm using the same views in the camera calibration stage. The proposed approach greatly reduces the cost of the calibration equipment, and it is flexible and practical for the vision measurement. It shows that this method has high precision by experiment, and the sensor measured relative error of space length excels 0.3%.

Lipschitzianity of optimal trajectories for the Bolza optimal control problem

In this paper we investigate Lipschitz continuity of optimal solutions for the Bolza optimal control problem under Tonelli’s type growth condition. Such regularity being a consequence of normal necessary conditions for optimality, we propose new sufficient conditions for normality of state-constrained nonsmooth maximum principles for absolutely continuous optimal trajectories. Furthermore we show that for unconstrained problems any minimizing sequence of controls can be slightly modified to get a new minimizing sequence with nice boundedness properties. Finally, we provide a sufficient condition for Lipschitzianity of optimal trajectories for Bolza optimal control problems with end point constraints and extend a result from (J. Math. Anal. Appl. 143, 301–316, 1989) on Lipschitzianity of minimizers for a classical problem of the calculus of variations with discontinuous Lagrangian to the nonautonomous case.

Optimization of a Spherical Mechanism for a Minimally Invasive Surgical Robot: Theoretical and Experimental Approaches

With a focus on design methodology for developing a compact and lightweight minimally invasive surgery (MIS) robot manipulator, the goal of this study is progress toward a next-generation surgical robot system that will help surgeons deliver healthcare more effectively. Based on an extensive database of in-vivo surgical measurements, the workspace requirements were clearly defined. The pivot point constraint in MIS makes the spherical manipulator a natural candidate. An experimental evaluation process helped to more clearly understand the application and limitations of the spherical mechanism as an MIS robot manipulator. The best configuration consists of two serial manipulators in order to avoid collision problems. A complete kinematic analysis and optimization incorporating the requirements for MIS was performed to find the optimal link lengths of the manipulator. The results show that for the serial spherical 2-link manipulator used to guide the surgical tool, the optimal link lengths (angles) are (60 degrees, 50 degrees). A prototype 6-DOF surgical robot has been developed and will be the subject of further study.

Finite Element Analysis of Interface Cracks Using Multiple Point Constraints

A finite element technique to analyse closed-mode interface cracks is proposed in this study. Stress boundary conditions for a closed-tip model are transformed into multiple point constraints (MPCs) for nodal displacements. These constraints are imposed upon the finite element solutions to simulate closed-tip stress fields in crack-tip elements. This technique can deal with small as well as large crack-tip contact zones, and no special elements other than the standard quarter-point elements are needed. Since stresses approach infinity at the crack tip in a quarter-point element, dominant terms are used in deriving MPCs for nodal displacements. Fracture parameters are obtained by using the virtual crack extension method, and numerical results are in good agreement with analytical results.

Multi-objective optimization in Aspergillus niger fermentation for selective product enhancement

A multi-objective optimization formulation that reflects the multi-substrate optimization in a multi-product fermentation is proposed in this work. This formulation includes the application of epsilon-constraint to generate the trade-off solution for the enhancement of one selective product in a multi-product fermentation, with simultaneous minimization of the other product within a threshold limit. The formulation has been applied to the fed-batch fermentation of Aspergillus niger that produces a number of enzymes during the course of fermentation, and of these, catalase and protease enzyme expression have been chosen as the enzymes of interest. Also, this proposed formulation has been applied in the environment of three control variables, i.e. the feed rates of sucrose, nitrogen source and oxygen and a set of trade-off solutions have been generated to develop the pareto-optimal curve. We have developed and experimentally evaluated the optimal control profiles for multiple substrate feed additions in the fed-batch fermentation of A. niger to maximize catalase expression along with protease expression within a threshold limit and vice versa. An increase of about 70% final catalase and 31% final protease compared to conventional fed-batch cultivation were obtained. Novel methods of oxygen supply through liquid-phase H2O2 addition have been used with a view to overcome limitations of aeration due to high gas-liquid transport resistance. The multi-objective optimization problem involved linearly appearing control variables and the decision space is constrained by state and end point constraints. The proposed multi-objective optimization is solved by differential evolution algorithm, a relatively superior population-based stochastic optimization strategy.

Scene point constraints in camera auto-calibration: an implementational perspective

We present a scheme for incorporating scene constraints into the auto-calibration process for the structure and motion recovery problem. The steps covered by the scheme include projective factorization of the joint image measurement matrix, recovery of the absolute dual quadric, the upgrade from projective structure to its Euclidean counterpart, and incorporation of constraints from orthogonal scene planes into bundle adjustment. The focus of the paper is on the implementation details of all these steps and discussion of the various issues that arose. We have tested the scheme on both synthetic and real image data and found that it is more advantageous to incorporate into camera auto-calibration and bundle adjustment as many scene constraints as are available rather than performing auto-calibration and bundle adjustment alone.

Second-order necessary conditions for differential–difference inclusion problems

We study an optimal control problem given by differential–difference inclusions with end point constraints. An approach concerning second-order optimality conditions is proposed.

Reduced order output feedback control design for PDE systems using proper orthogonal decomposition and nonlinear semidefinite programming

The design of an optimal (output feedback) reduced order control (ROC) law for a dynamic control system is an important example of a difficult and in general non-convex (nonlinear) optimal control problem. In this paper we present a novel numerical strategy to the solution of the ROC design problem if the control system is described by partial differential equations (PDE). The discretization of the ROC problem with PDE constraints leads to a large scale (non-convex) nonlinear semidefinite program (NSDP). For reducing the size of the high dimensional control system, first, we apply a proper orthogonal decomposition (POD) method to the discretized PDE. The POD approach leads to a low dimensional model of the control system. Thereafter, we solve the corresponding small-sized NSDP by a fully iterative interior point constraint trust region (IPCTR) algorithm. IPCTR is designed to take advantage of the special structure of the NSDP. Finally, the solution is a ROC for the low dimensional approximation of the control system. In our numerical examples we demonstrate that the reduced order controller computed from the small scaled problem can be used to control the large scale approximation of the PDE system.

An alternative method of curve interpolation

Given a point data set that contains several fairly unevenly distributed random points, this paper presents a new paradigm of curve interpolation to fit a curve to the data with end tangent vector constraints. The method uses a base curve, which is subjected to constrained shape manipulations to achieve interpolation, while maintaining end point and end tangent constraints. The algorithm is not sensitive to the distribution or to the randomness of the data, as long as the points represent fairly simple shapes, as in reverse engineering of properly segmented points, or in shape design using simple segments. The method is iterative in nature and allows various forms of adjustments to achieve good results.

Preliminary Design of Earth-Mars Cyclers Using Solar Sails

Motivated by the concept of using cycler trajectories for Mars return missions, an optimal Earth-Mars cycler is designed for spacecraft that use solar sails. The design is preliminary in the sense that the trajectories are assumed to be coplanar and the orbits of Earth and Mars are assumed to be circular. The optimality criterion is the vehicle's hyperbolic excess speed V ∞ with respect to Mars. This trajectory optimization problem is formulated using the framework of optimal periodic control with interior point constraints that include jump discontinuities that arise as a result of gravity assists. The problem is numerically solved using the concept of pseudospectral knots (PSK) by way of a general-purpose dynamic optimization software. Feasibility of the PSK-derived trajectories is demonstrated using numerical propagation. Results show that solar sails can be used to reduce significantly V ∞ at Mars. For example, it is shown that a sail with a lightness number of 0.17 can achieve a V ∞ with respect to Mars of 2.5 km/s at every synodic encounter.

Second-order necessary conditions for discrete inclusions with end point constraints

Second-order necessary conditions for discrete inclusions with end point constraints

Inequality path constraints in optimal control: a finite iteration ε-convergent scheme based on pointwise discretization

This paper presents a new result in the analysis and implementation of path constraints in optimal control problems (OCPs). The scheme uses the well-known concept of discretizing path constraints on a finite number of points, yielding a set of interior-time point constraints replacing the original path constraints. The approach replaces the original OCP by a sequence of OCPs which is shown to converge in a finite number of steps to the solution of the original path constrained problem with ε-accuracy. Numerical results, verifying the theoretical analysis, are presented. The method is shown to be effective and promising for future applications, particularly in control vector parameterization implementations.

Design and implementation of synchronization and AGC for OFDM-based WLAN receivers

An efficient implementation of several tasks at the receiver becomes crucial in OFDM-based high-speed WLAN systems, such as automatic gain control, time and frequency synchronization, and offset tracking. This paper deals with fixed point constraints and accuracy requirements for implementation of those algorithms. Also, a complete set of thresholds for the practical implementation of time and frequency synchronization sub-blocks is obtained. Moreover, a technique to mitigate the remaining frequency offset after coarse acquisition is proposed, yielding a good trade-off between performance and complexity. Finally, we propose the implementation of a simple and effective automatic gain control procedure.

Necessary optimality conditions for impulsive control problems

In this article, we present first and second order necessary conditions of optimality for impulsive control problems recently obtained by the authors. Two kind of results are discussed: first order necessary conditions of optimaiity for the free time optimal control problem with state and control constraints and second order necessary conditions for fixed time optimal control problems with state end point and control constraints. The main feature of these conditions is their nondegeneracy. A discussion of these results in the context of the state-of-the-art providing a historical perspective and insight for future perspectives is also included.

Methodologies of discrete patches filling in reverse engineering and rapid prototyping

In the process of part or product design, reverse engineering is an important method for constructing CAD models from a physical part that already exists. In industrial applications, a user may need to reconstruct CAD models for parts where data point capture is incomplete, such as where digitized points are captured from a damaged physical part or from certain geometric features that are difficult for a coordinate measuring machine to characterize. The sets of data points consist of some regions without data. To fill these regions whose boundaries are hole loops with the desired shape, this paper presents two methods: (1) discrete Coons patches and (2) discrete Gaussian curvatures. The first method adapts an existing discrete Coons patches algorithm to fill n-sided discrete points constraints. Based on discrete Gaussian curvatures, the second method adopts an angle deficit algorithm for discrete Gaussian curvatures approximation. For rapid prototyping, an automated STL file generation algorithm is also presented in this paper.

Stieltjes Truncated Moment Problem with Point Constraints

AbstractThe truncated Hamburger and Stieltjes moment problems [1] were solved elsewhere (see [3] and references therein) using the methods of the extension theory of Hermitian operators and, in particular, the results on extensions of nonnegative operators and matrices. Moreover, applying methods of the extension theory we found a purely algebraic algorithm for the solution of both problems. Here we solve the corresponding moment problems with point constraints.

Constrained deformation of freeform surfaces using surface features for interactive design

There is an increasing demand in conceptual design for more intuitive methods for creating and modifying freeform curves and surfaces in CAD modeling systems. The methods should be based not only on the change of the mathematical parameters but also on the user's specified constraints and shapes. This paper presents a new surface representation model for freeform surface deformation representation. The model is a combination of two functions: a displacement function and a function for representing an existing NURBS surface called a parent surface. Based on the surface model, the authors develop several novel deformation methods which are named SingleDef (Single-point constraint based deformation method), MultiDef (Multiple-points constraints based deformation method), CurDef (Curve constraints based deformation method) and FeatDef (Feature constraint based deformation method). The techniques for freeform surface deformation allow conceptual designers to modify a parent surface by directly applying point constraints, curve constraint or a surface constraint to the parent surface. The deformation methods are implemented in an experimental CAD system. The results show that designers can easily and intuitively control the surface shape.

An improved CSPC equation of state for pure fluids

The three-parameter Cubic Simplified Perturbed Hard-Chain (CSPHC) equation of state (EOS) developed by Wang and Guo (1993) is improved by applying the classical critical point constraints, modifyin...