Persistent External Disturbances Research Articles

Neural Networks Trained via Reinforcement Learning Stabilize Walking of a Three-Dimensional Biped Model With Exoskeleton Applications.

Our group is developing a cyber-physical walking system (CPWS) for people paralyzed by spinal cord injuries (SCI). The current CPWS consists of a functional neuromuscular stimulation (FNS) system and a powered lower-limb exoskeleton for walking with leg movements in the sagittal plane. We are developing neural control systems that learn to assist the user of this CPWS to walk with stability. In a previous publication (Liu et al., Biomimetics, 2019, 4, 28), we showed a neural controller that stabilized a simulated biped in the sagittal plane. We are considering adding degrees of freedom to the CPWS to allow more natural walking movements and improved stability. Thus, in this paper, we present a new neural network enhanced control system that stabilizes a three-dimensional simulated biped model of a human wearing an exoskeleton. Results show that it stabilizes human/exoskeleton models and is robust to impact disturbances. The simulated biped walks at a steady pace in a range of typical human ambulatory speeds from 0.7 to 1.3 m/s, follows waypoints at a precision of 0.3 m, remains stable, and continues walking forward despite impact disturbances and adapts its speed to compensate for persistent external disturbances. Furthermore, the neural network controller stabilizes human models of different statures from 1.4 to 2.2 m tall without any changes to the control parameters. Please see videos at the following link: 3D biped walking control.

Motion Planning and Adaptive Neural Tracking Control of an Uncertain Two-Link Rigid–Flexible Manipulator With Vibration Amplitude Constraint

This article deals with an uncertain two-link rigid-flexible manipulator with vibration amplitude constraint, intending to achieve its position control via motion planning and adaptive tracking approach. In motion planning, the motion trajectories for the two links of the manipulator are planned based on virtual damping and online trajectories correction techniques. The planned trajectories can not only guarantee that the two links can reach their desired angles, but also have the ability to suppress vibration, which can be adjusted to meet the vibration amplitude constraint by limiting the parameters of the planned trajectories. Then, the adaptive tracking controller is designed using the radial basis function neural network and the sliding mode control technique. The developed controller makes the two links of the manipulator track the planned trajectories under the uncertainties including unmodeled dynamics, parameter perturbations, and persistent external disturbances acting on the joint motors. The simulation results verify the effectiveness of the proposed control strategy and also demonstrate the superior performance of the motion planning and the tracking controller.

Dry Clutch Control of Two-Speed Electric Vehicles by Using an Optimal Control Scheme With Persistent Time-Varying Disturbance Rejection

A novel two-speed inverse automatic mechanical transmission (I-AMT) is proposed to eliminate the torque interruption in conventional AMT and improve the working performance of electric vehicles (EVs). However, due to the intrinsic structural characteristics of I-AMT, the requirements for clutch slip control are different from current AMT. Besides, clutch slip control is sensitive to internal uncertainties and external persistent time-varying disturbances during gear shifting. This study proposes a unified framework to build a clutch slip model for gear upshift and downshift. A high-order disturbance observer-based optimal controller is developed to reject persistent time-varying disturbances in a dry clutch system. During controller deduction, a novel multiplier function λ is introduced, and the optimal control law is presented as a feedback form of system states, the disturbance, and the derivatives of the disturbance. The controller is then applied to the clutch slip processes during gear shifting of an EV equipped with I-AMT. Simulation and experimental results under gear upshift and downshift demonstrate that the controller guarantees consistent performance under various working scenarios with different kinds of disturbances. The rapidity and smoothness of the clutch slip process are ensured without large speed or torque fluctuation, thus improving the overall gear shift quality.

External Disturbances Rejection for Vector Field Sensors in Attitude and Heading Reference Systems.

The attitude and heading reference system (AHRS), which consists of tri-axial magnetometer, accelerometer, and gyroscope, has been widely adopted for three-dimensional attitude determination in recent years. It provides an economical means of passive navigation that only relies on gravity and geomagnetic fields. However, despite the advantages of small size, low cost, and low power, the magnetometer and accelerometer are susceptible to external disturbances, such as the magnetic interference from nearby ferromagnetic objects and current-carrying conductors, as well as the motional acceleration of the carrier. To eliminate such disturbances, a vector-based parallel structure is introduced for the attitude filter design, which can avoid the mutual interference between gravity and geomagnetic vectors. Meanwhile, an approach to estimate and compensate the external disturbances in real time for magnetometer and accelerometer is also presented. Compared with existing designs, the proposed filter architecture and external disturbance rejection algorithm can feasibly and effectively cooperate with mainstream data fusion techniques, including complementary filter and Kalman filter. According to experiment results, in the case that large and persistent external disturbances exist, the proposed method can improve the accuracy and robustness of attitude estimation, and it outperforms the existing methods such as switching filter and adaptive filter. Furthermore, through the experiments, the critical role of fading factor in handling the external disturbance is revealed.

Robust Position Control of a Two-Sided 1-DoF Impacting Mechanical Oscillator Subject to an External Persistent Disturbance by Means of a State-Feedback Controller

This paper proposes a state-feedback controller using the linear matrix inequality (LMI) approach for the robust position control of a 1-DoF, periodically forced, impact mechanical oscillator subject to asymmetric two-sided rigid end-stops. The periodic forcing input is considered as a persistent external disturbance. The motion of the impacting oscillator is modeled by an impulsive hybrid dynamics. Thus, the control problem of the impact oscillator is recast as a problem of the robust control of such disturbed impulsive hybrid system. To synthesize stability conditions, we introduce the S-procedure and the Finsler lemmas by only considering the region within which the state evolves. We show that the stability conditions are first expressed in terms of bilinear matrix inequalities (BMIs). Using some technical lemmas, we convert these BMIs into LMIs. Finally, some numerical results and simulations are given. We show the effectiveness of the designed state-feedback controller in the robust stabilization of the position of the impact mechanical oscillator under the disturbance.

Combined Backstepping/Second-Order Sliding-Mode Boundary Stabilization of an Unstable Reaction–Diffusion Process

In this letter we deal with a class of open-loop unstable reaction-diffusion PDEs with boundary control and Robin-type boundary conditions. A second-order sliding mode algorithm is employed along with the backstepping method to asymptotically stabilize the controlled plant while providing at the same time the rejection of an external persistent boundary disturbance. A constructive Lyapunov analysis supports the presented synthesis, and simulation results are presented to validate the developed approach.

Agreement coordination of fractional-order multi-agent systems with reaction–diffusion and persistent disturbances

Agreement coordination problem of fractional-order multi-agent systems (FOMASs) with reaction–diffusion term and unknown persistent external disturbances is mainly investigated in this paper. Firstly, based on the output information, some estimators are designed to obtain the information of all agents and unknown persistent external disturbances, and a novel distributed control protocol is designed. And then, the convergence analysis of the closed-loop system is finished by using the theories of algebraic graph and Mittag-Leffler stability, and some sufficient consensus matrix inequalities conditions are deduced. Finally, the effectiveness of the obtained results are verified by several simulations.

Adaptive tracking control of uncertain Euler–Lagrange systems subject to external disturbances

This paper addresses the adaptive trajectory tracking problem of uncertain Euler–Lagrange systems subject to external disturbances. In comparison with existing literature, our work has its distinctive characteristics. First, a large class of persistent external disturbances with unbounded energy can be accommodated, which can be a combination of finite number of step signals with unknown magnitudes and sinusoidal signals with unknown frequencies, amplitudes and phase angles. Second, asymptotic trajectory tracking can be achieved, in other words, disturbance rejection, instead of disturbance attenuation, can be attained. Third, the proposed control law is sufficiently smooth and its design does not require a prior bound for either external disturbances or unknown system parameters. Last but not least, the obtained result is global in the sense that it does not depend on initial conditions of the system.

The boundary control strategy for a fractional wave equation with external disturbances

Abstract This paper is concerned with the boundary control of the fractional wave equation when the boundary is subject to persistent external disturbances. By developing the sliding mode control approach to infinite-dimensional fractional order systems, the fractional order sliding mode boundary control law is designed for the infinite dimensional setting. Moreover, based on the fractional asymptotical stability theorem, the asymptotical stability for the fractional wave equation under the control strategies proposed is addressed. Finally, numerical examples are provided to illustrate the viability of the theoretical results.

Trajectory tracking for autonomous underwater vehicle: An adaptive approach

During missions at sea, underwater vehicles are exposed to changes in the parameters of the system and subject to persistent external disturbances. These issues make the design of a robust controller a quite challenging task. This paper focuses on the design of an adaptive high order sliding mode controller for trajectory tracking. The main feature of the proposed control law is that it preserves the advantages of robust control. Moreover, it does not need the knowledge of the upper bound of the disturbance and it is easy to tune in real applications. Using Lyapunov concept, asymptotic stability of the closed-loop tracking system is ensured. The robustness of the proposed controller for trajectory tracking in depth and yaw dynamics is demonstrated through real-time experiments.

A new approach for the nonlinear fractional optimal control problems with external persistent disturbances

The aim of this manuscript is to investigate an efficient iterative approach for the nonlinear fractional optimal control problems affected by the external persistent disturbances. For this purpose, first the internal model principle is employed to transform the fractional dynamic system with disturbance into an undisturbed system with both integer- and fractional-order derivatives. The necessary optimality conditions are then reduced into a sequence of linear algebraic equations by using a series expansion approach and the Grünwald–Letnikov approximation for the fractional derivatives. The convergence of the latter sequence to the optimal solution is also studied. In addition, an iterative algorithm designing the suboptimal control law is presented. Numerical simulations confirm that the new approach is efficient to reject the external disturbance and provides satisfactory results compared to the other existing methods.

Adaptive coordinated attitude control for spacecraft formation with saturating actuators and unknown inertia

In this paper, an adaptive attitude coordination control problem for spacecraft formation flying is investigated under a general directed communication topology containing a directed spanning tree with a leader as the root. In the presence of unknown time-varying inertia, persistent external disturbances and control input saturation, a novel robust adaptive coordinated attitude control algorithm with no prior knowledge of inertia for spacecraft is proposed to coordinately track the common time-varying reference states. Aiming at optimizing the control algorithm, a dynamic adjustment function is introduced to adjust the control gain according to the tracking errors. The effectiveness of the proposed control scheme is illustrated through numerical simulation results.

An efficient numerical method for the optimal control of fractional-order dynamic systems

This paper aims to investigate an efficient numerical scheme for the optimal control of fractional-order dynamic systems. By using the Grünwald–Letnikov approximation for the fractional derivatives and introducing a new transformation in the calculus of variations, the fractional optimal control problem under consideration is converted into a linear programming problem. Then, the internal model principle is employed in order to extend the new scheme for the fractional dynamic systems affected by the external persistent disturbances. Numerical examples and comparative results verify the validity and applicability of the new technique.

Modeling and energy-based fuzzy controlling for underactuated overhead cranes with load transferring, lowering, and persistent external disturbances

In practice, vertical load motion is always involved in overhead cranes. In this case, the cable length turns from a constant to a variable, which may induce large amplitude load swing and make it ...

Sliding mode control for underactuated overhead cranes suffering from both matched and unmatched disturbances

Overhead cranes, which are known as typical underactuated systems, are extensively studied in recent years. However, many existing methods for overhead cranes are developed based on a relatively ideal model, with little consideration for persistent external disturbances, unmodeled dynamics, uncertain system parameters and so on. Thus, their performance may badly degrade when it comes to practical applications, and this problem is made even worse when the system suffers from unmatched disturbances. To tackle this issue, a sliding mode control (SMC) method is proposed in this paper, which ensures satisfactory control performance even when the crane works under unfavorable conditions. The asymptotic stability of the desired equilibrium point is backed up with rigorous Lyapunov-based analysis. Furthermore, to alleviate the chattering problem inherent to SMC, a disturbance observer is further designed for overhead cranes to estimate and then eliminate the influence of the disturbances. Both simulation and hardware experimental results are provided to validate the efficiency and robustness of the proposed control strategy. To the best of our knowledge, this paper proposes the first method that can solve the control problem of overhead cranes suffering from both matched and unmatched disturbances, without tuning to linearizations or approximations.

A new approach for the optimal control of time-varying delay systems with external persistent matched disturbances

The aim of this study is to develop an efficient iterative approach for solving a class of time-delay optimal control problems with time-varying delay and external persistent disturbances. By using the internal model principle, the original time-delay model with disturbance is first converted into an augmented system without any disturbance. Then, we select a quadratic performance index for the augmented system to form an undisturbed time-delay optimal control problem. The necessary optimality conditions are then derived in terms of a two-point boundary value problem involving advance and delay arguments. Finally, a fast iterative algorithm is designed for the latter advance-delay boundary value problem. The convergence of the new iterative technique is also investigated. Numerical simulations verify that the proposed approach is efficient and provides satisfactory results.

Suboptimal control of fractional-order dynamic systems with delay argument

In this paper, an efficient linear programming formulation is proposed for a class of fractional-order optimal control problems with delay argument. By means of the Lagrange multiplier in the calculus of variations and using the formula for fractional integration by parts, the Euler–Lagrange equations are derived in terms of a two-point fractional boundary value problem including an advance term as well as the delay argument. The derived equations are then reduced into a linear programming problem by using a Grünwald–Letnikov approximation for the fractional derivatives and introducing a new transformation in the calculus of variations. The new scheme is also effective for the delay fractional optimal control problems influenced by the external persistent disturbances. Numerical simulations and comparative results verify that the proposed approach is efficient and easy to implement.

Distributed Parameter Control Strategies for the Wave Equation with Fractional Order Derivative

In this paper, the control strategies are studied for the fractional order uncertain wave equation subject to persistent external disturbances in Hilbert spaces. The twisting and super-twisting fractional order sliding mode controllers (SMCs) are designed for the infinite dimensional setting and they are applied for addressing the asymptotic state tracking of the fractional order perturbed wave equation. Furthermore, by introducing the adaptive control law to the twisting controller, the bound of the external disturbances which is unknown is dealt with, and for the design of the super-twisting SMC, a fractional order sliding mode manifold is utilized which results in a continuous input control and a chattering free signal. Both of the controllers are associated with the fractional order parameter, which influences the convergence rate of the proposed control algorithms. In addition, the relative theorem involved in the paper for the proof of the stability is proved. Then, the control algorithms are extended to globally asymptotically stabilize the fractional order uncertain wave equation by choosing the appropriate Lyapunov functional. Finally, numerical simulations are presented to verify the viability and efficiency of the proposed fractional order controllers.

An Efficient Finite Difference Method for The Time‐Delay Optimal Control Problems With Time‐Varying Delay

AbstractIn this paper, an efficient finite difference method is presented for the solution of time‐delay optimal control problems with time‐varying delay in the state. By using the Pontryagin's maximum principle, the original time‐delay optimal control problem is first transformed into a system of coupled two‐point boundary value problems involving both delay and advance terms. Then the derived system is converted into a system of linear algebraic equations by using a second‐order finite difference formula and a Hermite interpolation polynomial for the first‐order derivatives and delay terms, respectively. The convergence analysis of the proposed approach is provided. The new scheme is also successful for the optimal control of time‐delay systems affected by external persistent disturbances. Numerical examples are included to demonstrate the validity and applicability of the new technique. Some comparative results are included to illustrate the effectiveness of the proposed method.

An Optimal Consensus Control for Multiple Agents System with Time-Delay and Disturbances

The optimal disturbance rejection control problem is considered for a kind of consensus with control time-delay affected by external persistent disturbances and noise. An transformation method is used to convert the consensus with control time-delay to the consensus system without time-delay. The optimal estimated values of the converted consensus system states are obtained by recursive filtering with Kalman filter. Then the feedforward-feedback optimal control law is deduced by solving the Riccati equations and matrix equations. Lastly, simulations show the result is effectiveness to the consensus system with time-delay with respect to external persistent disturbances and noise.