In this thesis, by combining two nonlinear control approach of sliding mode and backstepping, a backstepping sliding mode combined controller is proposed for a class of nonlinear systems with parameter uncertainty and external disturbances. To compensate uncertainties and incoming disturbances to the system, a sliding mode controller is used. Using the backstepping approach as a very powerful design tool for nonlinear systems, makes the designed controller more robust against incoming disturbances to the system. The combination of these two nonlinear methods not only does not significantly increase the complexity of the design, but also firstly benefits from the simplicity of designing the backstepping approach, and secondly, it benefits from various advantages sliding mode controller. The use of developed sliding mode controllers such as terminal sliding mode to increase the convergence of states to equilibrium points, dynamic sliding mode to reduce the chattering in the input control signal, as well as the fractional order sliding mode to increase the degree of freedom of the controller, are suitable options that are used from these controllers in combination with the backstepping method to increase the performance of the controller. Asymptotic stability of the closed loop system will be proven by Lyapunov stability theorem. Finally, in order to confirm the theoretical results, the combined controller has been applied to the two systems of micro electromechanical gyroscope and a ducted fan engine and the results are compared with the sliding mode controller. The simulation results performed with MATLAB software show that designed backstepping sliding mode controller has better performance than the sliding mode controller, and more importantly, it has more robustness against to external disturbances and parameter variations. In this thesis, to further upgrade the controller, fuzzy logic method, adaptive method, high gain observer and disturbance observer in some designs have been used.

In this thesis, using nonlinear optimal control based on state dependent differential-differential equation (SDDRE) for a class of nonlinear time-varying and time-invariance systems, finite-time regulator and tracking SDDRE is designed. Using the approximate solution method based on the Lyapunov equation, the differential Riccati Equation (DRE) is solved. In the absence of necessary conditions to design controller, solutions will be provided to overcome this problem. Although the SDRE control method is an optimal method, but it does not have a high robustness against external disturbances and uncertainties. In order to improve the performance of the SDDRE controller in the presence of external disturbances, its combination with the theory of sliding mode control (SMC) is used so that two variable structure control based on SDDRE has been suggested. In the first design, instead of using sliding surface, a sliding sector is used. The sliding sector has been designed using DRE. In addition, using Lyapunov stability theory, the finite-time stability of this controller has been proven. In the second design, an integral surface as the sliding surface is considered. After that, discontinues control law is extracted from this surface such that the control law is combined with SDDRE method and the resulted robust optimal sliding mode control (ROSMC). In the next step, by Lyapunov stability theory, the stability of this controller is proven. To verify the theoretical results, all three proposed controllers taking into account different scenarios, are applied to two real systems with nonlinear dynamics and the extracted results are compared with each other.
Simulation and coding is done in software environment MATLAB. The simulation results show that all three controller methods in the tracking and regulator problems have high performances. Two proposed combination methods compared to the SDDRE controller have optimal performances and are less sensitive or more robust to external disturbances.

In recent years, wind power has played a significant role in energy generation of micro-grids (MGs). However, randomness nature of wind speed leading to uncertainty in wind power forecast, imposes some problems such as overestimating wind power on optimized scheduling of MG. In this thesis, we propose an adaptive probabilistic concept of confidence interval (APCCI) to address these problems. The main purpose of the proposed APCCI is to modify the risk we endure to schedule wind power with other distributed energy resources (DERs) in order to degrade the unnecessary rigors and upgrade the other ones. The forecasting method which is used in this thesis is artificial neural network (ANN). In order to increase the accuracy of forecasting, wavelet decomposition (WD) is applied to the wind power time series then the results are sent to ANN. After that, dependable levels for the predicted wind power based on APCCI are obtained. An energy storage system (ESS) is utilized not only to decrease the impact of forecasting errors on the MG but also to increase the flexibility of the planning. A comprehensive formulation with operational constraints is employed to model the optimization problem. An economic dispatch based non-dominated sorting genetic algorithm II (EDNSGA-II) is proposed and applied to solve the multi-objective optimization problem. The optimization algorithm produces some alternatives which consist of different combination of objectives (cost and emission). TOPSIS method is utilized to make a compromised decision between the alternatives. Eventually, the proposed algorithm is applied to a typical MG which consists of micro turbine (MT), fuel cell (FC), photo voltaic (PV), wind turbine (WT) and energy storage system (ESS). Evaluation of the results show that the proposed APCCI works well and can adapt the level of confidence interval in various situations. Moreover, the results confirm the superiority of WNN over ANN. The results also show that the proposed EDNSGA-II is more efficient in comparison with the well-known NSGA-II.

In this thesis, based on the theory of fractional calculus and integer order sliding mode control, a new robust controller called fractional order sliding mode controller (FOSMC) is proposed for a class of nonlinear systems. In general, in FOSMC algorithm, an arbitrary linear manifold based on the fractional order operators of the state variables is considered as a sliding surface, which can guarantee the asymptotic stability and desired performance of the closed-loop control system. Then, control law is formulated based on the Lyapanov stability theory to guarantee the sliding condition.
In the following, in order to develop the convergence with a robustness feature and also to possess more degrees of freedom, a fractional order terminal sliding mode controller (FOTSMC) is proposed. The finite time stability of the close loop system is guaranteed for terminal sliding mode controller design. FOMCON toolbox of MATLAB has been used to simulate fractional order cntrollers.
Finally, in order to verify the theoretical result, the proposed controllers is applied to the Antilock Braking and coupled tanks Systems. Two different scenarios are considered for simulation. Simulation results demonstrate that the proposed fractional order sliding mode and fractional order terminal sliding mode controllers not only achieve better control performance with smaller chattering than with integer order sliding mode controller, but also is robust to external disturbances and parameter variations.