RBF-ARX Model-Based Complex Systems Modeling,Optimization And Control

The RBF-ARX model is a global nonlinear time serious model which can be locally linearized at each state-dependent working point. Using radial basis function (RBF) networks to approximate the functional coefficients of a state-dependent AutoRegressive model with eXogenous variable (SD-ARX) yields the RBF-ARX model. Therefore, it incorporates the advantages of SD-ARX models in nonlinear dynamics description and the RBF network in function approximation.The parameters of the RBF-ARX model are identified offline by a structured nonlinear parameter optimization method which can avoid the potential problems of online parameter estimation. The parameter search space is divided into the linear weight subspace and the nonlinear parameter space, and therefore the computational convergence speed and the modeling accuracy are improved. Besides, compared with the single RBF network model it does not need too many RBF centers, because the model’s complexity is dispersed into the lags of the autoregressive parts.The main research works and achievements are summarized as follows.(1) On the basis of a large amount of existing research results, this dissertation presents the multi-input multi-output (MIMO) RBF-ARX model together with its parameter optimization method. Based-on the MIMO RBF-ARX model, a predictive control strategy is designed to control the multivariable nonlinear system.The state-space form of the MIMO RBF-ARX model can be easily obtained, thus it is convenient to apply the RBF-ARX model to the industry control field. In this dissertation, the MIMO RBF-ARX modeling method is for the first time applied to a fast multivariable control plant (the quadrotor helicopter); a hybrid model based-on the RBF-ARX model is presented for the first time to characterize a slow control process (the ship’s trajectory tracking process). In the two real control applications, the RBF-ARX model-based modeling method, optimization method and controller design approaches are discussed deeply.(2) The referenced quadrotor in this dissertation is a fast system (sampling period:0.1s) and has a unique configuration which is different from the classic quadrotor in cross configuration. It is a typical complex multi-input and multi-output control system with strong coupling and uncertain nonlinearities. Firstly, the physical model-based LQR control strategy is introduced. Secondly, the working space of the quadrotor is divided into16working areas averagely, then16linear ARX models are identified in each area and the ARX model-set-based LQR gain scheduling controller is designed. At last, a global RBF-ARX model-based LQR control strategy is proposed to realize the attitude control of the quadrotor.(3) Ship tracking control process is a typical slow complex under-actuated system with1input and2outputs (sampling period:Is). A single input single output RBF-ARX model is built to describe the nonlinear relation between the ship heading angle deviation and the ship ruder. Then a single input dual outputs state space model combined with the relationship between the heading angle deviation and the cross track errors is proposed to represent the tracking dynamic behavior. Based on the hybrid state space model a model predictive controller is designed to steer the ship tracking a predefined reference trajectory with a constant velocity.(4) A navigation strategy together with a multistep forecast strategy is designed for the ship tracking predictive controller, which could suppress the overshot at the switching points of the curve trajectory, and reduce the cross track error during the curve tracking segments.(5) For improving the long-term prediction performance of the hybrid model, an RBF-ARX model-based critical stable hybrid model was proposed. It is verified by comparing the turning test trajectory that the dynamic behavior of the new hybrid model is much better.(6) A pure single input dual outputs RBF-ARX model was built for more detailed representation of a ship’s dynamic tracking behavior. The modeling results showed that the pure RBF-ARX model has a better modeling accuracy not only in the one-step-ahead prediction but also in a finite horizon long-term prediction.(7) Apart from the modeling, external natural force will also result in the large offset of the cross track. For overcoming the influence introduced by the irresistible natural force, a novel RBF-ARX model-based predictive controller with output compensation was proposed. The real-time control result of the straight-line tracking verified the effectiveness of the compensation strategy.The two successful applications verified the effectiveness and the superiority of the multivariable RBF-ARX model-based modeling and control method in handling multivariable nonlinear systems modeling and control problem, not only for the slow control processes but also for some fast systems. It is also verified that the multivariable RBF-ARX model-based modeling, optimization and control method is a general, reliable, convenient and advanced method, which has the significance in both the industry field and national defense.