Control of Lateral Vehicle Dynamics and Dynamic Optimization using the Genetic Algorithm Toolbox

The genetic algorithm appears to be a useful tool in a wide spectrum of activities in control engineering. This paper reports on a Genetic Algorithm Toolbox for the widely accepted computer aided control system design package Matlab that enables control engineers to use genetic search methods readily, within the framework of an existing software tool. With the aid of two examples, control of lateral vehicle dynamics and dynamic optimization, it is demonstrated how the Genetic Algorithm Toolbox may be used to apply genetic methods to problems in control system design.

Keywords:

Genetic Algorithms, Distributed Algorithms, Parallel Algorithms, Multiple Population, Non-linear Ranking, Dynamic Optimization, Control Systems, Test Functions, Matlab

Contents

• 1 Introduction
• 2 The Matlab GA Toolbox
• 2.1 Data structures
• 2.2 Toolbox structure
• 2.2.1 Population initialisation
• 2.2.2 Fitness assignment
• 2.2.3 Selection functions
• 2.2.4 Crossover operators
• 2.2.5 Mutation operators
• 2.2.6 Multiple subpopulation support
• 3 Example Applications
• 3.1 Lateral vehicle control
• 3.1.1 The model of lateral control
• 3.1.2 Controller design and simulation
• 3.1.3 Objective function
• 3.1.4 Results of Optimization
• 3.2 Dynamic optimization
• 4 Concluding Remarks
• 5 References

1 Introduction

There has been widespread interest from the control community in applying the Genetic Algorithm (GA) to problems in control systems engineering. Compared to traditional search and optimization procedures, such as calculus-based and enumerative strategies, the GA is robust, global and generally more straightforward to apply in situations where there is little or no a priori knowledge about the process to be controlled. As the GA does not require derivative information or a formal initial estimate of the solution region and because of the stochastic nature of the search mechanism, the GA is capable of searching the entire solution space with more likelihood of finding the global optimum.

Matlab has become a de-facto standard in Computer Aided Control System Design (CACSD) for the control engineer. The complete design cycle from modelling and simulation through controller design is addressed with a wide range of toolboxes, notably the Control System and Optimization Toolboxes, and the Simulink non-linear simulation package along with extensive visualisation and analysis tools. In addition, Matlab has an open and extensible architecture allowing individual users to develop further routines for their own applications. These qualities provide a uniform and familiar environment on which to build genetic algorithm tools for the control engineer.

This paper describes the development and implementation of a Genetic Algorithm Toolbox for Matlab [4] and provides examples of a number of application areas in control systems engineering.

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