飞行器的航迹规划问题（关于蚁群算法和多目标粒子群算法）

% MPT Multi-Parametric Toolbox % Version 2.6.2 05-Dec-2006 % % http://control.ee.ethz.ch/~mpt/ % % Authors: Michal Kvasnica, Pascal Grieder, Mato Baotic % kvasnica@control.ee.ethz.ch, grieder@control.ee.ethz.ch, baotic@control.ee.ethz.ch MPT Toolbox installation notes Section 1 ========= !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Note: Remove any previous copies of MPT before installing this version! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! The MPT toolbox consists of the following directories mpt/ - toolbox main directory mpt/@mptctrl - methods of the 'mptctrl' object mpt/@polytope - methods of the 'polytope' object mpt/docs - documentation mpt/examples - sample dynamical systems and other demos mpt/extras - extra functionality mpt/solvers - additional solvers mpt/yalmip - contains source-code distribution of the YALMIP interface In order to use MPT, set a Matlab path to the "mpt/" directory and to all it's subdirectories. If you are using Matlab for Windows, go to the "File - Set Path..." menu, choose "Add with Subfolders..." and pick up the MPT directory. Click on the "Save" button to store the updated path setting. Under Unix, you can either manually edit the file "startup.m", or to use the same procedure described above. You can also add the path manually by running following command on the Matlab prompt: addpath(genpath('/path/to/mpt/')); For more information regarding installation consult following page: http://control.ee.ethz.ch/~mpt/downloads/install.php Note: don't put mpt/@polytope folder to your path manually, it is not necessary and may lead to wrong behavior of the toolbox. Once you install the toolbox, please consult Section 3 on how to set default values of certain parameters. To explore functionality of MPT, try one of the following: mpt_studio help mpt help mpt/polytope mpt_demo1 mpt_demo2 mpt_demo3 mpt_demo4 mpt_demo5 mpt_demo6 runExample MPT toolbox comes with a set of pre-defined examples which the user can go through to get familiar with basic features of the toolbox. The toolbox has been successfully tested with Matlab 6.1(R12) and 6.5(R13) on Windows, Solaris and Linux, along with NAG solver, CPLEX 8.0 and CDDlib 0.93. If you wish to be informed about new releases of the toolbox, subscribe to our mailing list by sending an email to: mpt-request@list.ee.ethz.ch and put the word subscribe to the subject field. To unsubscribe, send an email to the same mail address and specify unsubscribe on the subject field. If you have any questions or comments, or you observe buggy behaviour of the toolbox, please send your reports to mpt@control.ee.ethz.ch Section 2 (Additional software requirements) ============================================ LP and QP solvers: ------------------ The MPT toolbox is a package primary designed to tackle multi-parametric programming problems. It relies on external Linear programming (LP) and Quadratic programming (QP) solvers. Since the LP and QP solvers shipped together with Matlab (linprog and quadprog) are rather slow in terms of computational speed, the toolbox provides a unified interface to other solvers. One of the supported LP solvers is the free CDD package from Komei Fukuda (http://www.cs.mcgill.ca/~fukuda/soft/cdd_home/cdd.html) The CDD is not only a fast and reliable LP solver, it can also solve many problems from computational geometry, e.g. computing convex hulls, extreme points of polytopes, calculating projections, etc. A pre-compiled version of the Matlab interface to CDD is included in this release of the MPT toolbox. The interface is available for Windows, Solaris and Linux. You can download the source code of the interface from: http://control.ee.ethz.ch/~hybrid/cdd.php and compile it on your own for other platforms. Please consult Section 3 on how to make CDD a default LP solver for the MPT toolbox. An another supported possibility is the commercial CPLEX solver from ILOG. The authors provide an interface to call CPLEX directly from Matlab, you can download source codes and pre-compiled libraries for Windows, Solaris and Linux from http://control.ee.ethz.ch/~hybrid/cplexint.php Please note that you need to be in possession of a valid CPLEX license in order to use CPLEX solvers. The free GLPK (GNU Linear Programming Kit) solver is also supported by MPT toolbox. In order to use GLPK in Matlab, you need to download a mex interface written by Nicolo Giorgetti from: http://www-dii.ing.unisi.it/~giorgetti/downloads.php Note that we have experienced several numerical inconsistencies when using GLPK. Semi-definite optimization packages: ------------------------------------ Some routines of the MPT toolbox rely on Linear Matrix Inequalities (LMI) theory. Certain functions therefore require solving a semidefinite optimization problem. The YALMIP interface by Johan Lofberg http://control.ee.ethz.ch/~joloef/yalmip.php is included in this release of MPT toolbox. Since the interface is a wrapper and calls external LMI solver, we strongly recommend to install one of the solvers supported by YALMIP. You can obtain a list of free LMI solvers here: http://control.ee.ethz.ch/~joloef/manual/htmldata/solvers.htm YALMIP supports a large variety of Semi-Definite Programming packages. One of them, namely the SeDuMi solver written by Jos Sturm, comes along with MPT. Source codes as well as binaries for Windows are included directly, you can compile the code for other operating systems by following the instructions in mpt/solvers/SeDuMi105/Install.unix For more information, visit http://fewcal.kub.nl/sturm/software/sedumi.html Solvers for projections: ------------------------ MPT allows to compute orthogonal projections of polytopes. To meet this task, several methods for projections are available in the toolbox. Two such methods - ESP and Fourier-Motzkin Elimination are coded in C and need to be accessible as a mex library. These libraries are already provided in compiled form for Linux and Windows. For other architectures you will need to compile the corresponding library on your own. To do so, follow instructions in mpt/solvers/esp and mpt/solvers/fourier respectively. Section 3 (Setting up default parameters) ======================================== Any routine of the MPT toolbox can be called with user-specified values of certain global parameters. To make usage of MPT toolbox as user-friendly as possible, we provide the option to store default values of the parameters in variable "mptOptions", which is kept in MATLAB's workspace as a global variable (i.e. it stays there unless one types 'clear all'). The variable is created when the toolbox get's initialized through a call to mpt_init. Default LP solver: ------------------ In order to set the default LP solver to be used, open the file "mpt_init" in your editor. Scroll down to the following line: mptOptions.lpsolver = []; Integer value on the right-hand side specifies the default LP solver. Allowed values are: 0 - NAG Foundation LP solver 3 - CDD Criss-Cross method (default) 2 - CPLEX 4 - GLPK 5 - CDD Dual-Simplex method 1 - linprog 6 - QSOpt If the right-hand argument is an empty matrix, the fastest solver available will be used. In the above table, solvers are sorted in the order of preference. Default QP solver: ------------------ To change the default QP solver, locate and modify this line in mpt_init.m: mptOptions.qpsolver = []; Allowed values for the right-hand side argument are the following: 0 - NAG Foundation QP solver 1 - quadprog (default) 2 - CPLEX Again, if you leave this line unchanged, MPT will choose the fastest available solver. Note: If you don't have any QP solver available on your machine, set mptOptions.qpsolver = -1; Then you will still be able to solve multi-parametric problems with linear