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1460 results in Control systems and optimization

Page 47 of 73

  • 1 - Introduction to object tracking

  • Subhash Challa, University of Melbourne, Mark R. Morelande, University of Melbourne, Darko Mušicki, Robin J. Evans, University of Melbourne
  • Book:
    Fundamentals of Object Tracking
    Published online:
    07 September 2011
    Print publication:
    28 July 2011, pp 1-21

  • Summary

    Object/target tracking refers to the problem of using sensor measurements to determine the location, path and characteristics of objects of interest. A sensor can be any measuring device, such as radar, sonar, ladar, camera, infrared sensor, microphone, ultrasound or any other sensor that can be used to collect information about objects in the environment. The typical objectives of object tracking are the determination of the number of objects, their identities and their states, such as positions, velocities and in some cases their features. A typical example of object/target tracking is the radar tracking of aircraft. The object tracking problem in this context attempts to determine the number of aircraft in a region under surveillance, their types, such as military, commercial or recreational, their identities, and their speeds and positions, all based on measurements obtained from a radar.

    There are a number of sources of uncertainty in the object tracking problem that render it a highly non-trivial task. For example, object motion is often subject to random disturbances, objects can go undetected by sensors and the number of objects in the field of view of a sensor can change randomly. The sensor measurements are subject to random noises and the number of measurements received by a sensor from one look to the next can vary and be unpredictable. Objects may be close to each other and the measurements received might not distinguish between these objects.

  • 9 - Practical object tracking

  • Subhash Challa, University of Melbourne, Mark R. Morelande, University of Melbourne, Darko Mušicki, Robin J. Evans, University of Melbourne
  • Book:
    Fundamentals of Object Tracking
    Published online:
    07 September 2011
    Print publication:
    28 July 2011, pp 312-343

  • Summary

    Chapters 1 to 8 introduced optimal (and suboptimal) Bayes tracking recursions and associated approximations.

    This chapter covers some points that are important when considering the practical implementation of object tracking. It can be viewed as a collection of separate sections, each section dealing with a specific practical issue. Although object existence is often mentioned in this chapter, with due diligence and prudence the material presented can also apply to, or provide infrastructure for, other algorithms.

    Section 9.2 introduces the linear multi-target method for suboptimal multiobject tracking in clutter. As the name implies, the additional numerical complexity of the linear multi-target method is linear in the number of targets and the number of measurements. This is followed by some practical methods for the clutter measurement density estimation in Section 9.3. Bayes recursion needs to be initialized; in the absence of prior target information, tracks are initialized using available measurements. Some track initialization methods and trade-offs are discussed in Section 9.4. For various reasons, multiple tracks may end following the same sequence of measurements; in Section 9.5 the track merging procedure detects and solves this situation. Finally, Section 9.6 presents some (simulated) surveillance situations and automatic target tracking solutions.

    Introduction

    In complex situations, involving a large number of objects and/or heavy clutter, algorithms based on the optimal multi-object approach (Section 5.5.4) may not be feasible due to its excessive computational requirements. The linear multi-target procedure to efficiently convert single-object trackers into multi-object trackers is detailed in Section 9.2.

  • 5 - Single- and multiple-object tracking in clutter: object-existence-based approach

  • Subhash Challa, University of Melbourne, Mark R. Morelande, University of Melbourne, Darko Mušicki, Robin J. Evans, University of Melbourne
  • Book:
    Fundamentals of Object Tracking
    Published online:
    07 September 2011
    Print publication:
    28 July 2011, pp 133-222

  • Summary

    In many practical situations, the number and existence of objects that are supposed to be tracked are a priori unknown. This information is an important part of the tracking output. In this chapter we include the object existence in the track state. As in previous chapters, the track state pdf propagates between scans as a Markov process, and is updated using the Bayes formula.

    Object existence is particularly important in the cluttered environment, when the origin of each measurement is a priori unknown. This chapter reveals the close relationship (generalization/specialization) of a number of object-existence-based target tracking filters, which have a common derivation and common update cycle.

    Some of the algorithms mentioned here also appear in other chapters of this book. These include probabilistic data association (PDA) (Section 4.3), integrated PDA (IPDA) (Sections 5.4.4 and 6.4.4) and joint IPDA (JIPDA) (Section 6.4.5). The derivations of this chapter follow a different track, and the results are more general as they also cater for non-homogeneous clutter.

    Introduction

    Object tracking aims to estimate the states of a (usually moving) unknown number of objects, using measurements received from sensors, and based on assumptions and models of the objects and measurements.

    The object tracking algorithms presented in this chapter are based on the following assumptions, unless stated otherwise:

    • Object:

    • – There are zero or more objects in the surveillance area. The number and the position of the objects are a priori unknown.

    • […]

Quasilinear Control
  • Performance Analysis and Design of Feedback Systems with Nonlinear Sensors and Actuators
  • ShiNung Ching, Yongsoon Eun, Cevat Gokcek, Pierre T. Kabamba, Semyon M. Meerkov
  • Published online:
    01 June 2011
    Print publication:
    06 December 2010
  • This is a textbook and reference for readers interested in quasilinear control (QLC). QLC is a set of methods for performance analysis and design of linear plant or nonlinear instrumentation (LPNI) systems. The approach of QLC is based on the method of stochastic linearization, which reduces the nonlinearities of actuators and sensors to quasilinear gains. Unlike the usual - Jacobian linearization - stochastic linearization is global. Using this approximation, QLC extends most of the linear control theory techniques to LPNI systems. A bisection algorithm for solving these equations is provided. In addition, QLC includes new problems, specific for the LPNI scenario. Examples include Instrumented LQR/LQG, in which the controller is designed simultaneously with the actuator and sensor, and partial and complete performance recovery, in which the degradation of linear performance is either contained by selecting the right instrumentation or completely eliminated by the controller boosting.

Complex-Valued Matrix Derivatives
  • With Applications in Signal Processing and Communications
  • Are Hjørungnes
  • Published online:
    03 May 2011
    Print publication:
    24 February 2011
  • In this complete introduction to the theory of finding derivatives of scalar-, vector- and matrix-valued functions with respect to complex matrix variables, Hjørungnes describes an essential set of mathematical tools for solving research problems where unknown parameters are contained in complex-valued matrices. The first book examining complex-valued matrix derivatives from an engineering perspective, it uses numerous practical examples from signal processing and communications to demonstrate how these tools can be used to analyze and optimize the performance of engineering systems. Covering un-patterned and certain patterned matrices, this self-contained and easy-to-follow reference deals with applications in a range of areas including wireless communications, control theory, adaptive filtering, resource management and digital signal processing. Over 80 end-of-chapter exercises are provided, with a complete solutions manual available online.

  • 7 - Direct Search Methods for Nonlinear Optimization

  • Ashok D. Belegundu, Pennsylvania State University, Tirupathi R. Chandrupatla, Rowan University, New Jersey
  • Book:
    Optimization Concepts and Applications in Engineering
    Published online:
    28 May 2018
    Print publication:
    28 March 2011, pp 294-337

  • Summary

    Introduction

    Multivariable minimization can be approached using gradient and Hessian information, or using the function evaluations only. We have discussed the gradient- or derivative-based methods in earlier chapters. We present here several algorithms that do not involve derivatives. We refer to these methods as direct methods. These methods are referred to in the literature as zero order methods or minimization methods without derivatives. Direct methods are generally robust. A degree of randomness can be introduced in order to achieve global optimization. Direct methods lend themselves valuable when gradient information is not readily available or when the evaluation of the gradient is cumbersome and prone to errors. We present here the algorithms of cyclic coordinates, method of Hooke and Jeeves [1961], method of Rosenbrock [1960], simplex method of Nelder and Mead [1965], Powell's [1964] method of conjugate directions. The concepts of simulated annealing, genetic, and differential evolution algorithms are also discussed. Box's complex method for constrained problems is also included. All these algorithms are implemented in complete computer programs.

    Cyclic Coordinate Search

    In this method, the search is conducted along each of the coordinate directions for finding the minimum. If ei is the unit vector along the coordinate direction i, we determine the value αi minimizing f(α) = f(x + αei), where αi is a real number. A move is made to the new point x + αiei at the end of the search along the direction i.

  • 4 - Linear Programming

  • Ashok D. Belegundu, Pennsylvania State University, Tirupathi R. Chandrupatla, Rowan University, New Jersey
  • Book:
    Optimization Concepts and Applications in Engineering
    Published online:
    28 May 2018
    Print publication:
    28 March 2011, pp 131-188

  • Summary

    Introduction

    Linear programming (LP) is the term used for defining a wide range of optimization problems, in which the objective function to be minimized or maximized is linear in the unknown variables and the constraints are a combination of linear equalities and inequalities. LP problems occur in many real-life economic situations where profits are to be maximized or costs minimized with constraint limits on resources. While the simplex method introduced in the following can be used for hand solution of LP problems, computer use becomes necessary even for a small number of variables. Problems involving diet decisions, transportation, production and manufacturing, product mix, engineering limit analysis in design, airline scheduling, and so on, are solved using computers. Linear programming also has applications in nonlinear programming (NLP). Successive linearization of a nonlinear problem leads to a sequence of LP problems that can be solved efficiently.

    Practical understanding and geometric concepts of LP problems including computer solutions with EXCEL SOLVER and MATLAB, and output interpretation are presented in Sections 4.1–4.5. Thus, even if the focus is on nonlinear programming, the student is urged to understand these sections. Subsequently, algorithms based on Simplex (Tableau-, Revised-, Dual-) and Interior methods, and Sensitivity Analysis, are presented.

  • 11 - Optimization Applications for Transportation, Assignment, and Network Problems

  • Ashok D. Belegundu, Pennsylvania State University, Tirupathi R. Chandrupatla, Rowan University, New Jersey
  • Book:
    Optimization Concepts and Applications in Engineering
    Published online:
    28 May 2018
    Print publication:
    28 March 2011, pp 400-423

  • Summary

    Introduction

    Transportation, assignment, and network problems are of great significance in engineering industry, agriculture, global economy, and commerce. These problems can be solved by the conventional simplex method of linear programming. However, because of their simpler structures, they are more efficiently solved by special methods. In most cases, the calculations involved are simple additions and subtractions and the methods are effective and robust. Many problems in totally different situations may be closely related to these models and the methods may be used for their solution. We consider the transportation, assignment, and network flow problems with a view to develop the formulation of the problems, the solution algorithms, and their implementation in simple computer codes.

    Transportation Problem

    There are m supply points where quantities s1, s2,…, sm, respectively, are produced or stocked. There are n delivery points or destinations where respective quantities of d1, d2,…, dn, are in demand. Cost is incurred on an item shipped from origination point i to the destination j. The problem is to determine the amounts (≥ 0) originating at i and delivered at j so that the supply and demand constraints are satisfied and the total cost is a minimum.

  • 10 - Dynamic Programming

  • Ashok D. Belegundu, Pennsylvania State University, Tirupathi R. Chandrupatla, Rowan University, New Jersey
  • Book:
    Optimization Concepts and Applications in Engineering
    Published online:
    28 May 2018
    Print publication:
    28 March 2011, pp 385-399

  • Summary

    Introduction

    Dynamic programming evolved out of the extensive work of Richard Bellman in the 1950s. The method is generally applicable to problems that break up into stages and exhibit the Markovian property. A process exhibits the Markovian property if the decisions for optimal return at a stage in the process depend only on the current state of the system and the subsequent decisions. A variety of problems in engineering, economics, agriculture and science exhibit this property. Dynamic programming is the method of choice in many computer science problems, such as the Longest Common Subsequence problem that is used frequently by biologists to determine the longest common subsequence in a pair of DNA sequences; it is also the method of choice to determine the difference between two files.

    When applicable, advantages of dynamic programming over other methods lie in being able to handle discrete variables, constraints, and uncertainty at each subproblem level as opposed to considering all aspects simultaneously in an entire decision model, and in sensitivity analysis. However, computer implementation via dynamic programming does require some problem-dedicated code writing.

    Dynamic programming relies on the principle of optimality enunciated by Bellman. The principle defines an optimal policy.

  • 5 - Constrained Minimization

  • Ashok D. Belegundu, Pennsylvania State University, Tirupathi R. Chandrupatla, Rowan University, New Jersey
  • Book:
    Optimization Concepts and Applications in Engineering
    Published online:
    28 May 2018
    Print publication:
    28 March 2011, pp 189-260

  • Summary

    Introduction

    The majority of engineering problems involve constrained minimization – that is, the task is to minimize a function subject to constraints. A very common instance of a constrained optimization problem arises in finding the minimum weight design of a structure subject to constraints on stress and deflection. Important concepts pertaining to linear constrained problems were discussed in Sections 4.1–4.5 in Chapter 4 including active or binding constraints, Lagrange multipliers, computer solutions, and geometric concepts. These concepts are also relevant to nonlinear problems. The numerical techniques presented here directly tackle the nonlinear constraints, most of which call an LP solver within the iterative loop. In contrast, penalty function techniques transform the constrained problem into a sequence of unconstrained problems as discussed in Chapter 6. In this chapter, we first present graphical solution for two variable problems and solution using EXCEL SOLVER and MATLAB. Subsequently, formulating problems in “standard NLP” form is discussed followed by optimality conditions, geometric concepts, and convexity. Four gradient-based numerical methods applicable to problems with differentiable functions are presented in detail:

  • Rosen's Gradient Projection method for nonlinear objective and linear constraints

  • Zoutendijk's Method of Feasible Directions

  • The Generalized Reduced Gradient method

  • Sequential Quadratic Programming method

    • Each of these methods is accompanied by a computer program in the disk at the end of the book. The reader can learn the theory and application of optimization with the help of the software.

  • 9 - Integer and Discrete Programming

  • Ashok D. Belegundu, Pennsylvania State University, Tirupathi R. Chandrupatla, Rowan University, New Jersey
  • Book:
    Optimization Concepts and Applications in Engineering
    Published online:
    28 May 2018
    Print publication:
    28 March 2011, pp 359-384

  • Summary

    Introduction

    There are many problems where the variables are not divisible as fractions. Some examples are the number of operators that can be assigned to jobs, the number of airplanes that can be purchased, the number of plants operating, and so on. These problems form an important class called integer programming problems. Further, several decision problems involve binary variables that take the values 0 or 1. If some variables must be integers and others allowed to take fractional values, the problem is of the mixed integer type. Discrete programming problems are those problems where the variables are to be chosen from a discrete set of available sizes, such as available shaft sizes and beam sections, engine capacities, pump capacities.

    In integer programming problems, treating the variable as continuous and rounding off the optimum solution to the nearest integer is easily justified if the involved quantities are large. Consider the example of the number of barrels of crude processed where the solution results in 234566.4 barrels. This can be rounded to 234566 barrels or even 234570 without significantly altering the characteristics of the solution. When the variable values are small, such as the number of aircraft in a fleet, rounding is no longer intuitive and may not even yield a feasible solution. In problems with binary variables, rounding makes no sense as the choice between 0 or 1 is a choice between two entirely different decisions. The following two variable example provides some characteristics of integer requirements.

Page 47 of 73