In this paper, trajectory tracking control of AUV in the horizontal plane is investigated. Due to the disturbances in ocean environment, as well as uncertainty of AUV parameters, a two-layer adaptive and robust control is proposed. The conventional sliding mode control as a robust and nonlinear control technique is one of the most applicable methods for AUVs. Unfortunately, it leads to a chattering that is an undesirable phenomenon for driver and motors circuits of AUV. The bound of the switching part of the control signal in the sliding mode control, which is chosen according to disturbances, is a cause of chattering. The greater the gain of the switching control, the lower the tracking error, and the chattering takes place instead. Therefore, a compromise between chattering and tracking error should be made. Combination of adaptive and sliding mode control, while increasing the robustness against disturbances, is also effective in reducing chattering. Furthermore, disturbance is estimated by an adaptive scheme. Using estimationed data, the control effort is calculated and applied to the control system. As a result, chattering decreases and robustness against disturbance is also maintained. In the proposed method, the control objectives are realized by using an adaptive controller based on the conventional sliding mode control; which is robust against the uncertainty and disturbance caused by ocean waves, assuming that the disturbance and its derivative are bounded by unknown boundary values. This methodology is based on a two-layer adaptive law which is not dependent upon the prior knowledge of disturbance boundary and its derivative. The stability of the proposed adaptive-robust control law is proved by the use of Lyapunov theory and the controller's performance is verified through the simulation results. The proposed controller performance is evaluated, in terms of error and control effort. According to the results of comparison and investigation in various disturbance scenarios, the tracking error in the proposed control is found much less than the conventional sliding mode control. In addition, the amplitude of control effort is greater in conventional sliding mode control and is accompanied by chattering, while no chattering is observed in the proposed adaptive-robust control, when the required amplitude of the control effort is estimated. The study is verified through analytical approach as well as simulations.

SUMMARY: The purpose of this paper is to design a stabilizing controller for a car with n connected trailers. The proposed control algorithm is constructed on the Lyapunov theory. In this paper, the purpose of navigating the system toward the desired point considering the slip phenomenon as a main source of uncertainty is analyzed. First mathematical models are presented. Then, a stabilizing control approach based on the Lyapunov theory is presented. Subsequently, an uncertainty estimator is taken into account to overcome the wheel slip effects. Obtained results show the convergence properties of the proposed control algorithm against the slip phenomenon.

Linear variable parameter systems (LPV) are a very special class of nonlinear systems, which are suitable for controlling dynamic systems with parameter changes. Therefore, in this thesis, the problem of using variable parameter linear systems for controller design and stability analysis is raised. A designed controller must be able to reduce the adverse effects of disturbances in the output, for this purpose, in this research, by creating a compromise between the two functions of \(H_{2}\) and \(H_{\infty }\) and combining them with the anticipatory control of the resistant model, a suitable method can be used to eliminate the effect A disturbance was achieved. The controller designed in this research, while stabilizing the system, in the presence of external disturbance, reduces the effect of external disturbance on the output under the control of the system. In general, the purpose of presenting this research is to provide an effective algorithm for controlling a variable parameter linear system with disturbance using the robust model predictive control method, which method presented in this thesis is based on solving the linear matrix inequality, also the proposed method has the ability to consider It has different restrictions on system states and system output. All the results obtained in different sections, including stability analysis, controller performance analysis, are shown using several validated practical examples and their effectiveness. In this thesis, solving optimization problems in the environment is done, as well as the case solvers. It is used to obtain auxiliary and controlling matrices.

This research focuses on the routing algorithm for mobile robots, considering factors such as time, path length, and energy consumption. Various algorithms have been used to plan trajectory curves, including classical methods, probabilistic algorithms, and meta-heuristic algorithms. The artificial bee colony algorithm was used to generate practical path curves without collisions, which were then used to create the optimal path length. The basic model was a projection of the path curve using random initial paths. Spline interpolation was used to obtain the middle points of the path, making the path smooth. The proposed model has less time and length in all environments and better satisfies linear and rotational speed limitations, indicating potential for improvement.