Sliding mode control (SMC) is an attractive for nonlinear systems due to its invariance for both parametric and nonparametric uncertainties. However, the invariance of SMC is not guaranteed in a reaching phase. Integral SMC (ISMC) eliminates the reaching phase such that the invariance is achieved in an entire system response. To reduce chattering in ISMC, it was suggested that the switching element is smoothed by using a low-pass filter and an integral sliding variable is modified. This study discusses several crucial problems regarding the performance, modification, and improvement of ISMC. Firstly, the modification of the integral sliding variable is revealed to be unnecessary as it degrades the performance of a sliding phase; secondly, ISMC is shown to be a kind of global SMC; thirdly, it is manifested that \tcolor{a high-order ISMC design with super twisting} involves in a stability condition that may be infeasible in theory; finally, an efficient solution is suggested to attenuate chattering in ISMC without the degradation of tracking accuracy and the solution is extended to the case with uncertain control gain functions. Comprehensive simulation results have verified the arguments of this study.

Backstepping control for fractional-order nonlinear systems (FONSs) requires the analytic calculation of fractional derivatives of certain complicated stabilizing functions, which becomes prohibitive as the order of the system increases. This article aims to facilitate the adaptive neural network (NN) backstepping control design for FONSs with actuator faults whose parameters and patterns are fully unknown. A fractional filtering approach, which obviates the requirement of analytic fractional differentiation, is used to generate command signals together with their fractional derivatives. Compensated tracking errors that can eliminate approximation errors of command signals are generated by fractional filters. The proposed adaptive NN command filtered backstepping control (ANNCFBC) approach, together with fractional adaptive laws, guarantees not only the boundedness of all involved variables but also the convergence of both the tracking error and the compensated tracking error to a sufficiently small region. Finally, simulation studies are given to indicate the effectiveness of the proposed control method.

Compliant actuators are significant for safe physical human-robot interaction. Series elastic actuator (SEA) is the most popular type of compliant actuators, which possesses several attractive features, such as low output impedance, back drivability, shock tolerance, smooth force transmission, and energy efficiency. This brief focuses on the adaptive command-filtered backstepping control (CFBC) design for robot arms driven by SEAs. The CFBC alleviates the complexity problem in integrator backstepping control and has attracted great attention. However, experimental results of adaptive CFBC have not been reported. In this brief, a simplified adaptive CFBC framework is developed for robot arms driven by SEAs, where discontinuous friction is compensated for by an adaptive mechanism. Closed-loop stability is rigorously established by the Lyapunov synthesis and time-scales separation. Experimental results based on a single-link SEA-driven robot arm have been provided to verify the effectiveness of the proposed control strategy.

This article presents a novel efficient experience-replay-based adaptive dynamic programming (ADP) for the optimal control problem of a class of nonlinear dynamical systems within the Hamiltonian-driven framework. The quasi-Hamiltonian is presented for the policy evaluation problem with an admissible policy. With the quasi-Hamiltonian, a novel composite critic learning mechanism is developed to combine the instantaneous data with the historical data. In addition, the pseudo-Hamiltonian is defined to deal with the performance optimization problem. Based on the pseudo-Hamiltonian, the conventional Hamilton–Jacobi–Bellman (HJB) equation can be represented in a filtered form, which can be implemented online. Theoretical analysis is investigated in terms of the convergence of the adaptive critic design and the stability of the closed-loop systems, where parameter convergence can be achieved under a weakened excitation condition. Simulation studies are investigated to verify the efficacy of the presented design scheme.

This brief aims to show that a linear proportional-integral-derivative (PID) controller is theoretically valid for tracking control of robotic manipulators driven by compliant actuators. The control problem is formulated into a three-time-scale singular perturbation formula, including a slow time scale at the rigid robot dynamics, one actual fast time scale at the actuator dynamics, and another virtual fast time scale at the controller dynamics. A PID-type controller is derived to guarantee semiglobal practical exponential stability of the rigid robot dynamics, and a derivative-type controller is applied to establish global exponential stability of the actuator dynamics. Based on a state transformation to the closed-loop rigid robot dynamics and the extended Tikhonov's theorem, it is proven that the entire system has semiglobal practical exponential stability under a proper choice of control parameters. The proposed controller is not only structurally simple and model-free resulting in low implementation cost, but also robust against external disturbances and parameter variations. The current design is only valid while the spring stiffness is relatively large compared with other parameters of the robot dynamics. Experimental results based on a single-link compliant robotic manipulator have verified effectiveness of the proposed approach.

This paper presents a control scheme for robot manipulators with the consideration of output error constraints, unknown dynamics and bounded disturbances. A modified virtual input variable in the second stage design of the dynamic surface control scheme is proposed, which can enhance the robustness of the controller. Bounded disturbances due to the situations that the base is not well fixed if the robot manipulator is mounted at a mobile platform are considered and suppressed. Besides, the detailed implementation process of the composite learning laws adopted for enhancing the radical basis function neural network is presented. Lyapunov stability analysis verifies that the proposed control scheme ensures the trajectory tracking errors stay within predefined boundaries and parameter estimate errors converge without a stringent condition termed persistent excitation. Experimental results show the superiority of the proposed controller regarding parameter estimation and tracking capabilities.