Real-world applications of nonlinear systems tracking control are always challenging due to the existence of uncertainties and disturbances. To design a robust optimal tracking controller for uncertain nonlinear systems with disturbances and actuator saturation, this paper investigates the prescribed performance robust optimal tracking control problem. A prescribed performance mechanism is constructed to convert the dynamics of tracking error into transformed error dynamics, which keeps the system’s operating states within specific bounds, ensuring tracking with predefined error constraints. For the optimal tracking controller design, an optimal index is established to optimize the performance of tracking control, and a robust optimal index is established to optimize the disturbance effect on the tracking error. To achieve robust optimal tracking control that minimizes both optimal and robust optimal indexes, a Stackelberg game is constructed, which provides a hierarchical game structure for the optimal controller and the worst disturbance. The robust optimal controller is approximated online using reinforcement learning techniques. An actor-critic-identifier algorithm is designed to approximate the optimal value function, optimal controller, and drifted system parameters. Lyapunov theory is utilized to analyze the closed-loop system’s stability. To demonstrate the effectiveness of the proposed robust optimal control method, two numerical simulations and a hardware experiment on a quadcopter system are conducted. The experiment results demonstrate that our method successfully achieves prescribed performance tracking control when actuators are saturated and disturbances are present.

This paper proposes a hierarchical safe reinforcement learning with prescribed performance control (HSRL-PPC) scheme to address the challenges of interconnected leader-follower systems operating in complex environments. The framework consists of two levels: at the higher level, the leader agent detects and avoids moving obstacles while planning optimal paths; at the lower level, the follower agent tracks the leader within strict prescribed performance bounds. We formulate the optimal prescribed performance safe control problem and solve it using the Hamilton-Jacobi-Bellman (HJB) equation. Due to system nonlinearity and obstacle complexity, we approximate the leader’s optimal value function using a state-following neural network that efficiently extrapolates training data to neighboring states, while employing a regular critic neural network for the follower’s value function approximation. Lyapunov stability analysis demonstrates the closed-loop system’s theoretical guarantees. Experimental results from two simulation examples and hardware tests with a quadcopter-vehicle system validate the effectiveness of the proposed approach in achieving safe navigation and precise tracking performance in dynamic environments. Note to Practitioners—Challenges exist in unpredictable obstacles and agent limitations for the interconnected leader-follower system. To provide a safe, efficient, and reliable control scheme, hierarchical safe reinforcement learning with prescribed performance control is proposed in this paper. The hierarchical structure is utilized to coordinate the leader and follower agents in the interconnected system, where the leader agent plans the optimal path and avoids obstacles, and the follower agent tracks the leader within prescribed performance bounds. Based on the proposed hierarchical structure, engineers can design efficient and safe control schemes for interconnected leader-follower systems with moving obstacles. In future work, we will address the problem of external disturbances and uncertainties in the interconnected leader-follower system.

Insulator segmentation is a critical step for automatic insulator fault diagnosis in high voltage transmission systems. Existing methods fail to segment insulators when they have a low contrast with the surroundings. Considering the unique shape and texture characteristics of insulators, a texture-and-shape based active contour model is proposed for insulator segmentation. The segmentation is achieved by evolving a curve iteratively by the texture features and shape priors. In the texture-driven curve evolution, a semi-local region descriptor is used to extract the texture features of insulators and a new convex energy functional is defined based on the extracted features with the topology-preserving term. The topology-preserving term keeps the curve's topology unchanged as the curve topology is determined by the shape template. In the shape-driven curve evolution, the shape context descriptor is used to align the shape template with the current curve. The semantic transformation between the shape template and the current curve is obtained by Procrustes analysis and then adopted to update the current curve to resemble the shape prior. The proposed method is applied to a set of images, and the experimental results confirm the efficacy and effectiveness of the proposed method for segmenting insulators in cluttered backgrounds.

Human-unmanned aerial vehicle (UAV) collaboration requires control frameworks that are both efficient and safe. This article introduces a stochastic fixed-time inverse optimal control (FxT-IOC) approach designed for such systems. The proposed framework constructs IOC, enabling the extraction of human operator intent. It features a FxT adaptive learning mechanism that guarantees parameter convergence within a predetermined time, irrespective of initial conditions. Crucially, the design explicitly incorporates prescribed performance control (PPC) to enforce state constraints while handling input saturation, ensuring operational safety and reliability. Rigorous theoretical analysis establishes the FxT stability of the learning process and the closed-loop system under these constraints. The effectiveness of the FxT-IOC framework is validated through comprehensive numerical simulations and physical hardware experiments, demonstrating superior trajectory tracking precision, accelerated learning convergence, and robust constraint satisfaction compared to human demonstrations. This work offers a principled and practical solution for developing high-performance, reliable human-UAV collaborative systems.

This paper establishes a short-term decision model, based on robust optimization, for an electricity retailer to determine the electricity procurement and electricity retail prices. The electricity procurement process includes purchasing electricity from generation companies and from the spot market. The selling prices of electricity for the customers are based on time-of-use (TOU) pricing which is widely employed in modern electricity market as a demand response program. The objective of the model is to maximize the expected profit of the retailer through optimizing the electricity procurement strategy and electricity pricing scheme. A price elasticity matrix (PEM) is adopted to model the demand response. Also, uncertainty in spot prices is modeled using a robust optimization approach, in which price bounds are considered instead of predicted values. Using a robust optimization approach, the retailer can adjust the level of robustness of its decisions through a robust control parameter. A case study is presented to illustrate the performance of the model. The simulation results demonstrate that the developed model is effective in increasing the expected profit of the retailer and flattening the load profiles of customers.