Non-conventional data representation and control
Creators: name: DINEVA, ADRIENN ALEXANDRA
Publisher: name: Universit� degli Studi di Milano
Year: 2017

description: Non-conventional approaches are prime concerns for most design issues in nonlinear adaptive control and signal processing. During the last decade major advances have been made in the theory of Adaptive Systems. Due to the advantageous features of Soft Computing techniques, such as flexibility and robustness, they have become fundamental tools in many areas. These methods are suitable for solving problems that are highly nonlinear or when only partial, uncertain data is available. In such situations, the application of traditional approaches is often complicated and what is more, can not guarantee the expected performance level. Therefore, my primary aim is to reveal new ways to overcome this difficulty by using Soft Computing, non-conventional and novel data representation techniques. In this Thesis I address novel data representation and control methods that are able to adaptively cope with usually imperfect, noisy or even missing information (for instance, wavelet based multiresolution controllers, anytime control, Situational Control, Robust Fixed Point Transformation (RFPT)-based control). The great majority of the adaptive nonlinear control design are based on Lyapunov?s 2nd or commonly referred to as the ?Direct? method. The major defect of this method that it is mathematically complicated and it works with a large number of arbitrary adaptive control parameters. Moreover, the parameter identification process in certain cases is vulnerable if unknown external perturbations can disturb the system under control, etc. In the recent years the RFPT has been introduced for replacing the Lyapunov technique. Since, in this Thesis my first intention was to deal with the possibilities of the combination of classical model identification and the RFPT-based design in depth. I have proposed a new method that utilize the geometric interpretation provided by the Lyapunov-technique that can be directly used for parameter tuning. I have shown that these useful information can be obtained on the actual parameter estimation error by using the same feedback terms and equations of motion as the original methods. In order to improve the parameter tuning process, I have suggested the application of the Modified Gram-Schmidt Algoritm for the possible combination of the RFPT-based method with the Modified Adaptive Inverse Dynamic Robot Controller (MAIDRC) and the Modified Adaptive Slotine-Li Robot Controller (MADSLRC). Besides, I have presented an even simpler tuning technique in the case of the Modified Adaptive Inverse Dynamics Robot Controller that also applies fixed point transformation-based tuning rule for parameter identification. Afterwards, I have presented a systematic method for the generation of a new family of the Fixed Point Transformations, the so-called ?Sigmoid Generated Fixed Point Transformation (SGFPT)? for the purpose of ?Adaptive Dynamic Control? for nonlinear systems. At first, I have outlined the idea for the ?Single Input - Single Output (SISO)? systems, then I have shown that it can be extended to ?Multiple Input ? Multiple Output (MIMO)? systems. Additionally, I have replaced the tuning method by a simple calculation in order to further simplify and improve the method. I have proposed new advances regarding the SGFPT. Also, I have described a new control strategy based on the combination of the ?adaptive? and ?optimal? control by applying time-sharing strategy in the SGFPT method, that supports error containment by cyclic control of the different variables. Further, I have introduced new improvements on the SGFPT technique by introducing ?Stretched Sigmoid Functions?. The efficiency of the presented control solution has been confirmed by the adaptive control of an underactuated mechanical system. I have investigated the applicability of fuzzy approximation in the SGFPT-type control design and demonstrated the usability via simulation investigations. Furthermore, I have shown a new type of function for the adaptive deformation in the SGFPT. The other important issue that includes the maintenance of unwanted sensor noises that are mainly introduced by feedback into the system under control. Therefore, in the development of a control system the signals of noisy measurements has to be addressed first so that more sophisticated signal pre-processing methods are required. Since, I have concerned the issue of well-adapted techniques for smoothing problems in the time domain and fitting data to parametric models. In a wider sense this means, that research is also needed to determine novel approximations that can be used for smoothing the operation of the adaptive controller. After, I have investigated the Savitzky-Golay (SG) smoothing and differentiation filter. It has been proven that the performance of the classical SG-filter depends on the appropriate setting of the windowlength and the polynomial degree. The main limitations of the performance of this filter are the most conspicuous in processing of signals with high rate of change. In order to overcome this limitation I have developed a new adaptive method to smooth signals based on the Savitzky-Golay algorithm. The provided method ensures high precision noise removal by iterative multi-round smoothing. The signal approximated by linear regression lines and corrections are made in each step. Also, in each round the parameters are dynamically change due to the results of the previous smoothing. For supporting high precision reconstruction I have introduced a new parametric weighting function. Thesis applications and proof of operation have been confirmed by numerical simulations.