The contributions to the field of control systems from the late nineteenth and early twentieth centuries described the main concepts on modeling, analysis and control design of dynamic linear systems based on linear algebra and differential calculus. However, at the mid 40s emerged a new interest on nonlinear systems. That interest contributed to the develop of theoretical tools for analysis and design on nonlinear systems. The main fact of the rapid development of this new field was the space race between United States and the Soviet Union. As well, other industries such as automotive or chemical also were a claim for the development of new nonlinear control techniques.
Nowadays, there are different methodologies that are used in analysis and design of nonlinear control systems. However, there is no generalized theory as in linear control systems. Therefore, there are different research topics focus on the study of nonlinear processes and working on the improvement of existing tools in real environments.
First, the phd document presents an extend state of art in nonlinear modeling and identification. A particular emphasis in modeling techniques and identification based on Takagi-Sugeno (TS) fuzzy models, since that models will be the starting point in the proposed approach.
Furthermore, state of art presented introduces the design of fuzzy controllers defined as Parallel Distributed Compensators (PDC), its application to predictive control and the mathematical foundation recast the design problem of PDC in terms of Linear Matrix Inequalities (LMIs).
The main drawback, introduced in the state of art, is the resolution of the optimization problem when TS models are used as predictors, since this models must be solved iteratively. Therefore, this thesis proposes two new design methods that can overcome this constraint in the optimization stage.
The first approach is based on obtaining a new predictor defined as FLAP (Large Fuzzy Ahead Prediction). This predictor is obtained using experimental data and identification techniques. The main feature of FLAP predictors is the possibility of obtaining the future state vector in a prediction horizon from the state vector and the future control actions. Therefore, this new predictor do not need to be iterated in the optimization stage.
Afterwards, a PDC fuzzy controller can be designed based on the predictor FLAP. All the problem design is solved in terms of LMIs. The controller design stage is particularly sensitive because of the need to include the minimization of a quadratic cost index and the conditions of closed-loop stability.
The last approach is based on the Bellman optimality principle, where the main idea is to divide the original design problem into a set of simpler optimization problems, which can be assumed as different stages of decision from the the dynamic programming point. The iterative algorithm that solves the design problem has been called Forward-Backward and provide a predictive fuzzy controller that ensures the stability and minimizing the quadratic index of the closed-loop system.