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Robot manipulators exhibit highly nonlinear dynamics influenced by uncertainties such as external disturbances and varying loads. Ensuring robust control and accurate simulation of their dynamical response is crucial for industrial applications. This article presents a novel two-stage robust optimal control approach for robotic manipulators operating under load mass uncertainties and external disturbances. In the first stage, a Linear Quadratic Regulator is applied with optimized weights to handle varying payloads of the nonlinear system in the absence of disturbances. In the second stage, a hybrid approach combining robust optimal control and Integral Sliding Mode Control is utilized to handle both payload uncertainties and external disturbances, ensuring robust stability across a wide range of operating conditions. The effectiveness of this approach is demonstrated using a two-joint SCARA robot, analyzing key variables like angular displacement, velocities, and joint torques across different payloads and bounded disturbances. The simulation results confirm the system’s stable convergence, with phase portraits of sliding surfaces providing geometric insights into the stability of the nonlinear system.

A novel dynamic event-triggered control strategy is proposed by utilizing the adaptive critic learning (ACL) technique for nonlinear continuous-time systems subject to disturbances in this paper. To address the transformation of the robust-optimal control problem, a modified cost function containing the disturbance term is introduced. The dynamic event-triggered controller is obtained by incorporating an internal variable into the static triggering strategy. An ACL method is employed to design static and dynamic triggering controllers. Critic neural networks are used to approximate the cost function and the corresponding Hamilton–Jacobi–Bellman equation, leading to the establishment of adaptive critic event-triggered controllers. Stability analysis of the closed-loop system is also provided, and simulation results demonstrate the effectiveness of the developed dynamic triggering strategy with two examples.

The field of adaptive dynamic programming with diverse applications in control engineering has undergone rapid progress over the past few years. A new theory called “Robust Adaptive Dynamic Programming” (for short, RADP) is developed for the design of robust optimal controllers for linear and nonlinear systems subject to both parametric and dynamic uncertainties. A central objective of this paper is to give a brief overview of our recent contributions to the development of the theory of RADP and to outline its potential applications in engineering and biology.

Expanding upon the well-established Takagi–Sugeno (T–S) fuzzy model, the T–S fuzzy descriptor model emerges as a robust and flexible framework. This article introduces the development of optimal and robust-optimal controllers grounded in the principles of stability control and fuzzy descriptor systems. By transforming complicated inequalities into linear matrix inequalities (LMI), we establish the essential conditions for controller construction, as delineated in theorems. To substantiate the utility of these controllers, we employ the rotary inverted pendulum as a testbed. Through diverse simulation scenarios, these controllers, rooted in fuzzy descriptor systems, demonstrate their practicality and effectiveness in ensuring the stable control of inverted pendulum systems, even in the presence of uncertainties within the model. This study highlights the adaptability and robustness of fuzzy descriptor-based controllers, paving the way for advanced control strategies in complex and uncertain environments.

External disturbances and asymmetric input constraints may cause a major problem to the optimal control of the system. Aiming at such problem, this article presents a safe and optimal robust control method based on adaptive dynamic programming (ADP) to ensure the system operated in a safe region and with the optimal performance. Initially, a novel nonquadratic form cost function is imported for the system to address the asymmetric input constraints. Then, to ensure the safety of the system, a control barrier function (CBF) is appended to the cost function to penalize the unsafe behavior. And a damping factor is also introduced to the CBF to balance safety and optimality. Finally, one single critic network is utilized to simplify the complex computational steps, which is different from the traditional actor-critic networks to address the Hamilton-Jacobi-Bellman Equation (HJBE) for obtaining the optimal neural controller. Additionally, based on Lyapunov method, all signals in the closed-loop system are proven to be uniformly ultimately bounded (UUB). At last, the experimental results confirm the effectiveness of the designed approach.

A new optimal robust control strategy is designed based on the modified backstepping method in this paper. Using this strategy, stable, accurate and real-time trajectory tracking for the wheeled mobile robot in the presence of unavoidable disturbances is achieved. The control strategy consists of a kinematic controller, a dynamical controller and an online optimization algorithm. The kinematic controller, which considers non-holonomic constraint and the resulting under-actuated nature, has fewer gains and reduces the computational burden. The dynamical controller introduces a saturation function for error compensation and effectively suppresses disturbances. The optimization algorithm is used to achieve online tuning of controllers, thus achieving fast and accurate convergence of the trajectory tracking error. The stability of the control strategy is proved theoretically. Various numerical simulation scenarios with different types of disturbances and the experiment test verify the superiority of the trajectory tracking effect.

The present paper is devoted to the study of robust control problems of parabolic stochastic partial differential equations under model uncertainty. To be more precise, the robust control problem under investigation is expressed as a stochastic differential game in a real separable infinite dimensional Hilbert space. By resorting to the theory of mild solutions, we prove that the elliptic partial differential equation associated with the problem at hand, also known as the Hamilton-Jacobi-Bellman-Isaacs equation, admits a unique solution, which is the value function of the game. Furthermore, we investigate the problem of existence of an optimal control pair that satisfies a saddle point property. Finally, as a demonstration of the proposed approach, we apply our results to the study of a certain robust control problem arising in the spatiotemporal management of natural resources.

This paper presents an adaptive learning structure based on neural networks (NNs) to solve the optimal robust control problem for nonlinear continuous-time systems with unknown dynamics and disturbances. First, a system identifier is introduced to approximate the unknown system matrices and disturbances with the help of NNs and parameter estimation techniques. To obtain the optimal solution of the optimal robust control problem, a critic learning control structure is proposed to compute the approximate controller. Unlike existing identifier-critic NNs learning control methods, novel adaptive tuning laws based on Kreisselmeier’s regressor extension and mixing technique are designed to estimate the unknown parameters of the two NNs under relaxed persistence of excitation conditions. Furthermore, theoretical analysis is also given to prove the significant relaxation of the proposed convergence conditions. Finally, effectiveness of the proposed learning approach is demonstrated via a simulation study.

This paper concludes a robust optimal tracking control law for a class of nonlinear systems. A characteristic of this paper is that the designed controller can guarantee both robustness and optimality under nonlinearity and mismatched disturbances. Optimal controllers for nonlinear systems are difficult to obtain, hence a reinforcement learning method is adopted with two neural networks (NNs) approximating the cost function and optimal controller, respectively. We designed weight update laws for critic NN and actor NN based on gradient descent and stability, respectively. In addition, matched and mismatched disturbances are estimated by fixed-time disturbance observers and an artful transformation based on backstepping method is employed to convert the system into a filtered error nonlinear system. Through a rigorous analysis using the Lyapunov method, we demonstrate states and estimation errors remain uniformly ultimately bounded. Finally, the effectiveness of the proposed method is verified through two illustrative examples.

Trajectory optimization is an essential tool for the high-fidelity planning of missions in aerospace engineering in order to increase their safety. Robust optimal control methods are utilized in the present study to address environmental or system uncertainties. To improve robustness, holistic approaches for robust trajectory optimization using sensitivity minimization with system feedback and predicted feedback are presented. Thereby, controller gains to handle uncertainty influences are optimized. The proposed method is demonstrated in an application for UAV trajectories. The resulting trajectories are less prone to unknown factors, which increases mission safety.