This paper proposes a continuous nonsingular terminal sliding mode control with integral-type sliding surface (CNTSMC-ISS) framework for disturbed systems, in which we consider two types of finite-time controller: the state feedback CNTSMC-ISS and the disturbance observer-based CNTSMCISS. Compared with the existing sliding mode controllers, the noteworthy contributions of two finite-time controllers in the proposed CNTSMC-ISS framework are the alleviation of the chattering phenomenon, the fast finite-time stability, the singularity-free, and the ease-of-implementation characteristics. In the proposed CNTSMC-ISS framework, we first introduce a nonsingular integral terminal sliding mode surface (NITSMS) such that the finite-time convergence of the system state to zero in the sliding phase is ensured and the singularity problem is avoided. Besides, a finite-time observer is developed to recover the external disturbance. Then, based on the constructed NITSMS with the super-twisting-like algorithm, the state feedback CNTSMC-ISS and the disturbance observer-based CNTSMC-ISS are proposed, which generate the continuous control signals and guarantee the fast finite-time convergence of the system state to the designed sliding surface. Rigorous finite-time stability of the closed-loop system under two proposed controllers is provided. Lastly, we apply two finite-time controllers in the proposed CNTSMC-ISS framework to the attitude control for quadrotor UAVs under external disturbances. Extensive simulation and experimental results are illustrated to prove the effectiveness of the proposed attitude controllers.

This paper considers the stabilization problem for under-actuated rotary inverted pendulum systems (RotIPS) via a fuzzy-based continuous sliding mode control approach. Various sliding mode control (SMC) methods have been proposed for stabilizing the under-actuated RotIPS. However, there are two main drawbacks of these SMC approaches. First, the existing SMCs have a discontinuous structure; therefore, their control systems suffer from the chattering problem. Second, a complete proof of closed-loop system stability has not been provided. To address these two limitations, we propose a fuzzy-based (continuous) super-twisting stabilization algorithm (FBSTSA) for the under-actuated RotIPS. We first introduce a new sliding surface, which is designed to resolve the under-actuation problem, by combining the fully-actuated (rotary arm) and the under-actuated (pendulum) variables to define one sliding surface. Then, together with the proposed sliding surface, we develop the FBSTSA, where the corresponding control gains are adjusted based on a fuzzy logic scheme. Note that the proposed FBSTSA is continuous owing to the modified super-twisting approach, which can reduce the chattering and enhance the control performance. With the proposed FBSTSA, we show that the sliding variable can reach zero in finite time and then the closed-loop system state converges to zero asymptotically. Various simulation and experimental results are provided to demonstrate the effectiveness of the proposed FBSTSA. In particular, (i) compared with the existing SMC approaches, chattering is alleviated and better stabilization is achieved; and (ii) the robustness of the closed-loop system (with the proposed FBSTSA) is guaranteed under system uncertainties and external disturbances.

In this letter, we propose a multivariable disturbance observer-based finite-time sliding mode attitude control (MDOB-FT-SM-AC) for fixed-wing UAVs in the presence of both matched and mismatched disturbances. Compared with existing sliding mode attitude controllers, the significant improvements of the proposed MDOB-FT-SM-AC are the multivariable control structure, strong robustness, and high precision performance with continuous control input signal. In the proposed MDOB-FT-SM-AC, we first develop multivariable finite-time disturbance observers such that the precise estimation of both matched and mismatched disturbances is ensured. Next, a nonsingular terminal sliding manifold is designed such that the fixed-wing UAV is driven to track its desired attitude command in finite time. We finally present a multivariable super-twisting reaching law such that the finite-time convergence of the sliding variable and its derivative to zero is guaranteed. Attentive finite-time convergence analysis is derived based on the Lyapunov and homogeneity theories. Simulation results are given to illustrate the superiority of the proposed MDOB-FT-SM-AC.

This article proposes finite-time continuous nonsingular terminal modified adaptive-gain super-twisting control (FT-CNT-MAG-STC) for the second-order disturbed systems. Compared with existing sliding-mode controllers, the noteworthy improvements of the proposed framework are the fast finite-time convergence, continuous control signal, ease-of-implementation feature, and relaxation of the assumption related to the information on the bounds of the disturbance and its derivative. In the proposed framework, a fast nonsingular terminal sliding surface is first developed such that the singularity problem is avoided and the convergence rate is improved. Then, we design a continuous modified super-twisting algorithm with an adaptive gain, under which the need for the bounds information of the disturbance and its derivative is relaxed and the performance of the closed-loop system is enhanced. Rigorous analysis is provided to prove the finite-time convergence of the system states to small regions containing the origin. We apply the proposed framework to the position control for a 2-DOF planar robot manipulator system. Various experimental results are illustrated to evaluate the effectiveness of the designed position controller.

This paper proposes a distributed safety-critical optimal flocking control algorithm for the multi-agent system. In general, safety (i.e., collision avoidance) could be guaranteed by the use of a control barrier function (CBF) as constraints in the optimal control problem. However, the existence of conflicting safety constraints from multiple agents could lead to a feasibility problem (i.e., the absence of a feasible control command) in distributed optimal flocking control algorithms. To deal with this issue, we propose two effective feasibility enhancement approaches. First, we develop a high-order CBF associated with the collision risk to alleviate the burden of distributed safety constraints on agents with a high risk of collision. Second, to enhance feasibility, a relaxation method is used to enlarge the allowable control space of agents. In particular, to decrease the number of optimization variables in the relaxation method, a selective strategy is adopted. This involves applying the relaxation method only to specific CBF based on the decision variable related to the overlap of admissible control spaces among agents. Numerical simulations demonstrate the superiority and validity of the proposed optimal flocking algorithm compared with existing approaches.