In this paper, an adaptive type-2 fuzzy controller is proposed to control the load frequency of a two-area power system based on descending gradient training and error back-propagation. The dynamics of the system are completely uncertain. The multilayer perceptron (MLP) artificial neural network structure is used to extract Jacobian and estimate the system model, and then, the estimated model is applied to the controller, online. A proportional–derivative (PD) controller is added to the type-2 fuzzy controller, which increases the stability and robustness of the system against disturbances. The adaptation, being real-time and independency of the system parameters are new features of the proposed controller. Carrying out simulations on New England 39-bus power system, the performance of the proposed controller is compared with the conventional PI, PID and internal model control based on PID (IMC-PID) controllers. Simulation results indicate that our proposed controller method outperforms the conventional controllers in terms of transient response and stability.

A key research topic in the field of robotics is the formation control of a group of robots in trajectory tracking problems. Using organized robots has many advantages over using them individually, such as efficient use of resources, increased reliability due to cooperation, and better resistance against defects. To achieve this, a controller is proposed that steers the leader robot and subsequent follower robots asymptotically to a reference trajectory. The basic controller is feedback linearization. To ensure stability against perturbations, a compensator based on type-3 fuzzy logic systems (T3-FLSs) and a data-driven control strategy is designed. The approach involves employing a finite number of open-loop data and using the model-based predictive controller (MPC) approach to acquire sufficient criteria for stability. An infinite-horizon function is minimized online, which allows the data-based control policy to be considered the optimal control method. The gains of the constrained data-based control signal are computed at each time step to enhance accuracy. Applying the data-based state feedback controller to the system yields positive and stable state trajectories with appropriate transient responses. The suggested data-driven compensator is guaranteed to handle constraints. A practical example is simulated to evaluate the proposed strategy.