Identification and control of smooth fuzzy systems

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During the years, we are witnessing a rapid change in the modeling and control of complex processes, which has necessitated employment of the approximate reasoning capacities of humans in the model identification and closed loop control of the uncertain and imprecision systems. One of the manifest of such intelligent schemes of modeling and control is the utilization of fuzzy logic based schemes, which has been facilitated the employment of computational capacities of the hardware. Although the intelligent methods could empower the designers to reach high speed of computation and safe process control strategies, they are not perfect and bring the imperfections. They made the closed loop behavior of the system not to be continuous neither smooth due to the application of min-max composition in the fuzzy structure. This thesis discusses on the alternative method of fuzzy modelling and control for the nonlinear processes, utilizing the smooth compositions. We introduce the modeling capacity of the smooth fuzzy models and then expand the formulation for the adaptive identification methods for the processes with the objective of incorporation to the model based predictive control schemes. The smooth fuzzy compositions construct an overall nonlinear smooth and continuous model of the system. Hence, in the optimization based manipulations and control algorithms the model will require fewer computations in optimization phase rather than the classical fuzzy min-max based modeling scheme. It also provides an improvement in modeling accuracy and would be attractive for application to the systems with hybrid and switched dynamics with the limited number of discontinuity to obtain a continuous fuzzy model. The smoothness property has also impacted the closed loop behavior of the system largely. Although, the combination of the iterative identification and model predictive control of the nonlinear processes have been directed many works in the academia and industry during the years; however, the smooth fuzzy structure will facilitate the employment of the experimental information of the system to closed loop structure with the minimum level of variations. To guarantee the stability of the scheme, we have considered the possibility of reaching the control horizon beyond the specific level to drag the system states inside the basin of attraction. Moreover, due to the smoothness of the scheme, the convergence of the results in face of uncertainties and disturbances will be faster, in comparison to the counterpart classical fuzzy schemes. It also can be easily tuned for the non-minimum phase and open loop unstable processes. The performance of the theoretical studies has been examined using several simulations to demonstrate the outperform of the proposed schemes to the traditional fuzzy structures.
Smooth fuzzy systems, Smooth compositions, Fuzzy control, Optimal control, Model predictive control (MPC)
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