The work contains an original comparison of selected algorithms using artificial neural network models, such as RBF neural networks, and classic algorithms, approaches that are based on structured programming in the image identification task. The existing studies exploring methods for the problem of classifying musical notation used in this work are still scarce. The research of neural network based and the classical method of image recognition was carried out on the basis of the effectiveness of recognizing the notes presented on the treble staff. In order to carry out the research, the density of the data distribution was modeled by means of the probabilistic principal component analysis, and a simple regression was performed with the use of a radial neural network. The methods of image acquisition and analysis are presented. The obtained results were successively tested in terms of selected quality criteria. The development of this research may contribute to supporting the learning of musical notation by both beginners and blind people. The further development of the experiments can provide a convenient reading of the musical notation with the help of a classification system. The research is also an introduction of new algorithms to further tests and projects in the field of music notation classification.

In this paper a new method concerning the problem of pole-free perfect control for discrete-time LTI nonsquare systems is presented. It is shown that application of σ-inverse of parameter matrix into the process of designing the above-mentioned control strategy can be useful for nonsquare systems, i.e. systems comprising different numbers of input and output variables. Thus, the special selected so-called degrees of freedom of σ-inverse contribute to more robust pole-free perfect control. Notwithstanding, the proposed approach can only be used for second-order systems, thus giving rise to develop the research effort for more complex systems in the future. Simulation examples made in Matlab environment confirm the big potential of a new analytical pole-free perfect control solution corresponding to the well-known pole placement problem.

In this paper, a new study concerning the usage of artificial neural networks in the control application is given. It is shown, that the data gathered during proper operation of a given control plant can be used in the learning process to fully embrace the control pattern. Interestingly, the instances driven by neural networks have the ability to outperform the original analytically driven scenarios. Three different control schemes, namely perfect, linear-quadratic, and generalized predictive controllers were used in the theoretical study. In addition, the nonlinear recurrent neural network-based generalized predictive controller with the radial basis function-originated predictor was obtained to exemplify the main results of the paper regarding the real-world application.

The application of the switching control framework to the perfect control algorithm is presented in this paper. Employing the nonunique matrix inverses, the different closed-loop properties are obtained and further enhanced with possible switching methodology implementation. Simulation examples performed in the MATLAB/Simulink environment clearly show that the new framework can lead to benefits in terms of the control energy, speed, and robustness of the perfect control law. The possibility of transferring the new obtained results to the symmetrical nonlinear plants seems to be immediate.

In this paper a criterion for minimizing the control energy of discrete-time perfect control systems is presented. It is shown, that there is an analytical formula which allows to estimate the control cost of said algorithm. Following the recently presented issues concerning the minimum-energy perfect control the new formula which monitors the system properties better than the old one is shown here. Simulation examples made in Matlab/Simulink environment confirm useful behavior of the new proposed criterion in the minimum-energy perfect control tasks.

In this paper an innovative study concerning the perfect control algorithm is presented. This particular control strategy has already been developed for continuous- and discrete-time transfer-function-originated plants, as well as discrete-time state-space-related systems, however the approach devoted to continuous-time state-space objects is still an unexplored research area. With the application of the time-dependent system correction joined with nonunique matrix inverses, a new maximum-speed and maximum-accuracy control paradigm is established within this research. Simulation cases performed in the Matlab/Simulink environment show, that the new results can successfully be applied in the field of control theory and practice.