Research On The Control System Design Based On Chaos Optimization Theory

Chaos occurs in many nonlinear systems. Ergodic, stochastic and regular properties are the characteristics of chaos, which means it can track any state in a certain scope without repetition according to its regularity. Due to its significant characteristics, chaos has been applied to optimization problem to avoid trapping into local minimum and this is the so-called "Chaos optimization". Usually, the design of many controllers, such as PID, neural network and fuzzy neural network controller, can be transferred into parameter or structure optimization problems. How to perform the novel chaos optimization method effectively in control system is a great challenge and the work in this dissertation is just to solve the problem. In the paper, the main innovatory researches are studied to realize optimal design of controllers, including PID controller parameters, structure and parameters of neural networks control system, and fuzzy rules and parameters of fuzzy neural network controller.The main contribution of this dissertation is as follows:1. The calculation methods of Lyapunov exponent on continuous and discrete-time nonlinear dynamic systems are discussed. The Lyapunov exponent of logistic map and its doubling period bifurcation to chaos are quantitatively analyzed. Ergodicity and stochastic probability are especially studied when logistic map is in chaos state.2. The dissertation provides basic theories of chaos optimization by quantificational analyzing the ergodicity and statistic properties of chaos series generated by logistic map. A method is proposed for parameters tuning of normalized PID controller with chaos variables. The PID controller is globally optimized with chaos ergodic searching. For stable or unstable plants the stabilities of the close-loop system are discussed. The advantages of chaos optimization are not only time-decreasing of optimization but guarantee of stability. Simulations prove the effectiveness of our method.3. We propose a new chaos optimization algorithm for feed-forward neural network weights tuning. This algorithm solves local minimum problem easily occurred in other learning algorithms and gives globallyoptimal solutions to neural network parameters. In order to improve the speed of chaos optimization and make local search more efficiently, a local fine search method and a new chaos-BP hybrid-learning algorithm are put forward. Simulations show that the two algorithms can effectively avoid the shortcoming of weak partial chaos optimization and relatively slow speed.4. The structure of neural network is an important factor that affects generalization ability of neural network. The optimization method is proposed for three-layer feed-forward neural network structure and parameters by means of chaos ergodic and randomicity. Chaos variables are applied to search for neural network structure and parameters. In the course of searching, node numbers of hidden layer and all weights of neural network are in chaos state. All neural network structures are variable. A globally optimal or approximate globally optimal neural network structure is found from dynamic neural networks according to a new performance standard. Simulation shows feed-forward neural network using the method has high approximation precision ad good generalization capability. The self-adaptive control system of feed-forward neural network is constructed based on chaos optimization. Two schemes are proposed in hardware design in order to solve the real-time performing problem in neural network applications. By using master/slave computer control model, a self-adaptive control system for ZWP-II inverted pendulum is designed based on chaos optimization.5. A new fuzzy-neural network (FNN) controller, constructed with cascade of simple fuzzy logical and feed-forward neural network. Is introduced. Controller parameters are optimized by means of combination of global and partial chaos searching. The optimization method is proposed for a FNN structure...