Stabilization Of Linear Multivariable Systems By Output Feedback Using Genetic Algorithms

Static output feedback stabilization is one of the most important problems in dynamics systems control. This problem is that of finding a constant feedback, if it exists, to stabilize a linear dynamic system. This thesis presents two new approaches to this problem - genetic algorithm and pseudo-inverse method. These approaches show some improvement over the existing methods. A number of examples are presented to illustrate the proposed methods.The first approach proposed in the thesis is the genetic algorithm, which is a well studied algorithm and has been applied in many fields of engineering. It generally outperforms other traditional methods in the case of hard problems, especially the so called NP-problems, which the output stabilization is believed to belong to. In this thesis, the basic genetic algorithm is modified and adopted for improving the probability of finding solutions to the stabilization problem. Traditional generic algorithms assign fixed probabilities to the genetic operators and make heavy use of the crossover. In this thesis, the operators' probabilities are adapted based on two quantities, i.e. diversity of the chromosome population and fitness of the population. Each operator's probability is adjusted using a fuzzy logic paradigm, which takes the diversity and fitness as inputs and produces the change in the operators' probabilities. This adaptation mechanism increases the chances of getting better chromosomes. The traditional fitness measure is not suitable for the stabilization problem, and therefore we define an instability index which is better and more effective for evaluating the chromosome fitness. In general, the proposed genetic algorithm has been found to be effective in solving the stabilization problem.The second approach, namely the pseudo-inverse method, is based on a Jacobian matrix that is derived from a set of nonlinear equations relating the coefficients of the systems characteristic polynomial to the output feedback elements. In order to change the characteristic polynomial vector to its initial to its desired vector needed for stabilization, we define a time dependent cycloid...