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A translational oscillator with a rotational actuator (TORA) is an underactuated nonlinear mechanical system with two degrees of freedom (DOF). This paper concerns the robust stabilization control problem for the system with multiple external disturbances. First, a disturbance observer is constructed based on the internal nonlinear dynamic behavior of the system. Second, a robust stabilization controller is designed by the estimated disturbances and the fixed-time sliding mode control method. The controller realizes the global robust stabilization control objective of the TORA system, and the stability of both disturbance observer and robust closed-loop control system are analyzed using the Lyapunov theorem. Finally, the effectiveness of the theoretical results are verified by numerical experiments.

This paper presents fractional order fixed-time nonsingular terminal sliding mode control for stabilization and synchronization of fractional order chaotic systems with uncertainties and disturbances. First, a novel fractional order terminal sliding mode surface is proposed to guarantee the fixed-time convergence of system states along the sliding surface. Second, a nonsingular terminal sliding mode controller is designed to force the system states to reach the sliding surface within fixed-time and remain on it forever. Furthermore, the fractional Lyapunov stability theory is used to prove the fixed-time stability and the robustness of the proposed control scheme and estimate the upper bound of convergence time. Next, the proposed control scheme is applied to the synchronization of two nonidentical fractional order Liu chaotic systems and chaos suppression of fractional order power system. Simulation results verify the effectiveness of the proposed control scheme. Finally, some application issues about the proposed scheme are discussed.

Quantum superpositions of macroscopically distinct classical states—so-called Schrödinger cat states—are a resource for quantum metrology, quantum communication and quantum computation. In particular, the superpositions of two opposite-phase coherent states in an oscillator encode a qubit protected against phase-flip errors 1 , 2 . However, several challenges have to be overcome for this concept to become a practical way to encode and manipulate error-protected quantum information. The protection must be maintained by stabilizing these highly excited states and, at the same time, the system has to be compatible with fast gates on the encoded qubit and a quantum non-demolition readout of the encoded information. Here we experimentally demonstrate a method for the generation and stabilization of Schrödinger cat states based on the interplay between Kerr nonlinearity and single-mode squeezing 1 , 3 in a superconducting microwave resonator 4 . We show an increase in the transverse relaxation time of the stabilized, error-protected qubit of more than one order of magnitude compared with the single-photon Fock-state encoding. We perform all single-qubit gate operations on timescales more than sixty times faster than the shortest coherence time and demonstrate single-shot readout of the protected qubit under stabilization. Our results showcase the combination of fast quantum control and robustness against errors, which is intrinsic to stabilized macroscopic states, as well as the potential of these states as resources in quantum information processing 5 – 8 . A qubit generated and stabilized in a superconducting microwave resonator by encoding it into Schrödinger cat states produced by Kerr nonlinearity and single-mode squeezing shows intrinsic robustness to phase-flip errors.

This paper investigates the finite-time and fixed-time stabilization (FFTS) of switched systems with discontinuous dynamics, external disturbances and delays. Firstly, a new parameterized discontinuous stabilizer is designed to ensure the FFTS of switched discontinuous systems in the sense of Filippov solutions. Secondly, a detailed analysis is provided on how to regulate the power parameters to determine the settling time is finite or fixed. Thirdly, a new adaptive controller is further designed to stabilize the considered system in a finite time, and the corresponding settling time is estimated as well. Finally, two examples are given to demonstrate the efficiency of the proposed method.

This paper is devoted to the topic of robust stabilization for uncertain multi-machine power systems (MMPSs) using input delay-based sampled-data control. The study explores the sampled-data control for a nonlinear MMPS with parametric uncertainties exacerbated with sector saturating actuators. A saturated controller is considered for the system to recover the loss of stability in the continuous time domain. An approach, comprising linear matrix inequality technique and average dwell time method, is exploited, employing proper Lyapunov–Krasovskii functional, to show that the proposed saturated sampled-data control renders exponential stability. More precisely, the existence condition of sampled-data control law is developed in form of linear matrix inequalities. In order to simplify the derivation in main results, Schur complement and Wirtinger inequalities are used. Through the simulation tests on a two-machine infinite bus system model, the effectiveness and robustness of the proposed controller over the time delays and parameter uncertainties are verified.

We demonstrate the first successful non-invasive stabilisation of nonlinear travelling waves in a straight cylindrical pipe using time-delayed feedback control working in various symmetric subspaces. By using an approximate linear stability analysis and by analysing the frequency-domain effect of the control using transfer functions, we find that solutions with well-separated unstable eigenfrequencies can have narrow windows of stabilising time delays. To mitigate this issue we employ a ‘multiple time-delayed feedback’ approach, where several control terms are included to attenuate a broad range of unstable eigenfrequencies. We implement a gradient descent method to dynamically adjust the gain functions in order to reduce the need for tuning a high-dimensional parameter space. This results in a novel control method where the properties of the target state are not needed in advance, and speculative guesses can result in robust stabilisation. This enables travelling waves to be stabilised from generic turbulent states and unknown travelling waves to be obtained in highly symmetric subspaces.

A robust fixed-time control framework is presented to stabilize flexible spacecraft’s attitude system with external disturbance, uncertain parameters of inertia, and actuator uncertainty. As a stepping stone, a nonlinear system having faster fixed-time convergence property is preliminarily proposed by introducing a time-varying gain into the conventional fixed-time stability method. This gain improves the convergence rate. Then, a fixed-time observer is proposed to estimate the uncertain torque induced by disturbance, uncertain parameters of inertia, and actuator uncertainty. Fixed-time stability is ensured for the estimation error. Using this estimated knowledge and the full-states’ measurements, a nonsingular terminal sliding controller is finally synthesized. This is achieved via a nonsingular and faster terminal sliding surface with faster convergence rate. The closed-loop attitude stabilization system is proved to be fixed-time stable with the convergence time independent of initial states. The attitude stabilization performance is robust to disturbance and uncertainties in inertia and actuators. Simulation results are also shown to validate the attitude stabilization performance of this control approach.

Rehabilitation exoskeleton robots play a crucial role in restoring functional lower limb movements for individuals with locomotor disorders. Numerous research studies have concentrated on adapting the control of these rehabilitation robotic systems. In this study, we investigate an affine state-feedback control law for robust position control of a knee exoskeleton robot, taking into account its nonlinear dynamic model that includes solid and viscous frictions. To ensure robust stabilization, we employ the Lyapunov approach and propose three methods to establish stability conditions using the Schur complement, the Young inequality, the matrix inversion lemma, and the S-procedure lemma. These conditions are formulated as Linear Matrix Inequalities (LMIs). Furthermore, we conduct a comprehensive comparison among these methods to determine the most efficient approach. At the end of this work, we present simulation results to validate the developed LMI conditions and demonstrate the effectiveness of the adopted control law in achieving robust position control of the knee exoskeleton robot.

Neuroscientific studies show that humans tend to stabilize their head orientation, while accomplishing a locomotor task. This is beneficial to image stabilization and in general to keep a reference frame for the body. In robotics, too, head stabilization during robot walking provides advantages in robot vision and gaze-guided locomotion. In order to obtain the head movement behaviors found in human walk, it is necessary and sufficient to be able to control the orientation (roll, pitch and yaw) of the head in space. Based on these principles, three controllers have been designed. We developed two classic robotic controllers, an inverse kinematics based controller, an inverse kinematics differential controller and a bio-inspired adaptive controller based on feedback error learning. The controllers use the inertial feedback from a IMU sensor and control neck joints in order to align the head orientation with the global orientation reference. We present the results for the head stabilization controllers, on two sets of experiments, validating the robustness of the proposed control methods. In particular, we focus our analysis on the effectiveness of the bio-inspired adaptive controller against the classic robotic controllers. The first set of experiments, tested on a simulated robot, focused on the controllers response to a set of disturbance frequencies and a step function. The other set of experiments were carried out on the SABIAN robot, where these controllers were implemented in conjunction with a model of the vestibulo-ocular reflex (VOR) and opto-kinetic reflex (OKR). Such a setup permits to compare the performances of the considered head stabilization controllers in conditions which mimic the human stabilization mechanisms composed of the joint effect of VOR, OKR and stabilization of the head. The results show that the bio-inspired adaptive controller is more beneficial for the stabilization of the head in tasks involving a sinusoidal torso disturbance, and it shows comparable performances to the inverse kinematics controller in case of the step response and the locomotion experiments conducted on the real robot.

A novel observer-based control policy based on an interval type-3 fuzzy logic system is developed to tackle the main limitations of fuzzy-based controllers in sense of approximation of uncertainties and analyzing nonlinear complex systems without detailed dynamics model information. For this purpose, a novel scheme is proposed that includes online optimized tuning rules, a simple type reduction method, and adaptive mechanisms. Also, an adaptive compensator is implemented to enhance the robust performance of the closed-loop system and reduce the effect of approximation errors. For the stability analysis, appropriate Lyapunov functions and Barbalat’s lemma are employed. By both simulations and experimentally implementation, it is shown that the suggested approach results in a more accurate approximation of unknown models and complicated nonlinearities, and good resistance against uncertainties and parameter variations.