Guaranteed Tracking Performance Research Articles

Adaptive neural fault-tolerant prescribed performance control of a rehabilitation exoskeleton for lower limb passive training

This article studies the passive tracking problem of a wearable exoskeleton for lower limb rehabilitation therapy in the face of unmodeled dynamics, interactive friction, disturbance, prescribed performance constraints, and actuator faults. Adaptive neural networks and a smooth performance function are incorporated to establish a novel fault-tolerant tracking scheme, which can not only compensate for the nonlinear uncertainties and disturbance, but also handle the actuator fault with guaranteed tracking performance. A state feedback controller is presented by using the full state information and an output feedback controller is developed when the angular velocity is unavailable. The differential explosion issue of the backstepping technique is resolved by constructing a first-order filter and the unmeasurable velocity is estimated by a nonlinear observer. Semiglobal uniform boundedness stabilities of the exoskeleton system are proved via the Lyapunov direct method. The tracking performances of the designed control approaches are tested by comparative simulations.

Least squares adaptive control for uncertain system based on modified predictive model

AbstractThis research addresses the tracking problem of least squares adaptive control for a class of nonlinear system with mismatched uncertainties. Different from most of existing solutions, modified predictive model is integrated into the proposed least squares adaptive control architecture. The significant role of modified predictive model in the adaptive control architecture is to achieve smooth transient by filtering out the high‐frequency oscillations, which cannot be canceled out by use of the hypothetical parameterized uncertainty models. Meanwhile, in order to guarantee tracking performance, a generalized restricted potential function (GRPF) is designed to constrain the weighted Euclidean norm of the predictive error of the modified predictive model to be less than a predefined scalar worst‐case bound. Finally, comparative simulations via the generic transport model (GTM) are conducted to examine the effectiveness of the proposed method. The results show that the transient performance and tracking performance of the controlled system can be improved simultaneously by the proposed method.

Asynchronous H∞ output tracking control for uncertain networked switched systems with mode-dependent average dwell time: an event-driven mechanism

This paper considers the problem of event-triggered H ∞ output tracking control for uncertain networked switched systems with both communication constraints and asynchronous switching. A new sampled delay-dependent error tracking uncertain networked switched system is constructed on the basis of event-triggered communication mechanism (ETCM) and the given reference model. By introducing a parameter-dependent Lyapunov–Krasovskii functional and employing the mode-dependent average dwell time (MDADT) method, results on exponential stability and robust H ∞ performance are proposed. Furthermore, the gains of the output tracking controller with matched system mode are obtained by solving a set of linear matrix inequalities (LIMs), at the same time, the parallel results with the mismatched case are also obtained. Simulation results show that the proposed design scheme not only guarantees tracking performance but also saves communication resources effectively.

A Novel Dual-Phase Based Approach for Distributed Event-Triggered Control of Multiagent Systems With Guaranteed Performance.

This article presents a novel dual-phase based approach for distributed event-triggered control of uncertain Euler-Lagrange (EL) multiagent systems (MASs) with guaranteed performance under a directed topology. First, a fully distributed robust filter is designed to estimate the reference signal for each agent with guaranteed observation performance under continuous state feedback, which transforms the distributed event-triggered control problem into a centralized one for multiple single systems. Second, an event-triggered controller is constructed via intermittent state feedback, making the output of each agent follow the corresponding estimated signal with guaranteed tracking performance. The proposed co-design scheme is of relatively low complexity in structure and cheap in computation since a priori knowledge of system nonlinearities or estimation of their bounds is not required in building the control scheme, and yet neither approximating structures nor adaptive online updating algorithms are needed. It is shown that the output tracking error of each agent is ensured to shrink into a prescribed precision set at an arbitrarily assignable convergence rate, although the plant states and the actuation signal are triggered simultaneously. All the internal signals are uniformly bounded and the occurrence of Zeno behavior is precluded. The efficiency of the proposed method is verified via numerical simulation.

Cooperative Online Learning for Multiagent System Control via Gaussian Processes With Event-Triggered Mechanism.

In the realm of the cooperative control of multiagent systems (MASs) with unknown dynamics, Gaussian process (GP) regression is widely used to infer the uncertainties due to its modeling flexibility of nonlinear functions and the existence of a theoretical prediction error bound. Online learning, which involves incorporating newly acquired training data into GP models, promises to improve control performance by enhancing predictions during the operation. Therefore, this article investigates the online cooperative learning algorithm for MAS control. Moreover, an event-triggered data selection mechanism, inspired by the analysis of a centralized event-trigger (CET), is introduced to reduce the model update frequency and enhance the data efficiency. With the proposed learning-based control, the practical convergence of the MAS is validated with guaranteed tracking performance via the Lyapunov theory. Furthermore, the exclusion of the Zeno behavior for individual agents is shown. Finally, the effectiveness of the proposed event-triggered online learning method is demonstrated in simulations.

Safe Planning and Control Under Uncertainty: A Model-Free Design With One-Step Backward Data

Autonomous systems are desired to safely accomplish predetermined tasks with guaranteed performance despite uncertainties. This paper proposes a safe planning and performance-guaranteed control (SP-PGC) scheme to accomplish safe execution of autonomous systems suffering from uncertainties and disturbances. This is realized by investigating mutual influences between planning and control levels, either explicitly considering control-level attainable performance bounds into safe planning algorithms, or directly relating planned safe boundaries to control-level performance bounds. In particular, we first utilize one-step backward data to construct incremental systems, which are equivalent representations of the investigated autonomous systems but without using explicit model information (kinematics and/or dynamics). The formulated incremental systems transform the influence of uncertainties and disturbances into the effect of provably bounded estimation errors, caused by the difference between current and one-step backward states. Then, we introduce the concept of input-to-state stable with provable safety barrier Lyapunov function (ISS-PS-BLF) to facilitate the performance-guaranteed tracking controller design based on the incremental systems, wherein the estimation errors are rigorously analyzed through an input-to-state stable approach. Finally, either the guaranteed tracking performance bound of the ISS-PS-BLF based controller is considered in the safe planning algorithm to guide the reference trajectory generation, or the safe planned boundary is used to determine the explicit value of the control-level performance bound for safe execution under uncertainty. The efficiency of our developed SP-PGC scheme is validated through both numerical and experimental validations.

Adaptive NN Tracking Control for Uncertain MIMO Nonlinear System With Time-Varying State Constraints and Disturbances.

In this article, an adaptive neural network (NN) tracking control scheme is proposed for uncertain multi-input-multi-output (MIMO) nonlinear system in strict-feedback form subject to system uncertainties, time-varying state constraints, and bounded disturbances. The radial basis function NNs (RBFNNs) are adopted to approximate the system uncertainties. By constructing the intermediate variables, the external disturbances that cannot be directly measured are approximated by the disturbance observers. The time-varying barrier Lyapunov function (TVBLF) is constructed to guarantee the boundedness of the errors lie in the sets. To overcome the potential singularity problem that the denominator of the barrier function term approaches zero in controller design, the adaptive NN tracking control scheme with time-varying state constraints is proposed. Based on the TVBLF, the controller will be designed to guarantee tracking performance without violating the appropriate error constraints. The analysis of TVBLF shows that all closed-loop signals remain semiglobally uniformly ultimately bounded (SGUUB). The simulation results are performed to validate the validity of the proposed scheme.

1 bit encoding–decoding-based event-triggered fixed-time adaptive control for unmanned surface vehicle with guaranteed tracking performance

This paper investigates the fixed-time prescribed performance trajectory tracking control for the unmanned surface vehicle with unknown dynamics and disturbances. At first, an improved prescribed performance function was introduced to transformation of coordinate for achieving a user-defined performance including the transient and steady-state performance of the USV. Then, an adaptive fixed-time trajectory tracking controller is designed by integrating the fixed-time stability and the event-triggered control (ETC) mechanism. Stability results prove that the proposed controller not only guaranteed that all the signals in the closed-loop system are the semi-global uniform ultimate bounded (SGUUB), but also ensured the tracking errors can converge to a preassigned area in a fixed-time. Moreover, by proposing a co-design of the ETC and 1-bit signal encoding–decoding mechanisms between controller and actuator, the trade-off between tracking performance and communication cost is achieved. Finally, the effectiveness of the developed control approach is verified through simulation results.

MPC-based Torque Distribution for Planar Motion of Four-wheel Independently Driven Electric Vehicles: Considering Motor Models and Iron Losses

The most critical obstacle for four-wheel independently driven electric vehicles (4WID-EVs) is the driving range. Being the actuators of 4WID-EVs, motors account for its major power consumption. In this sense, by properly distributing torques to minimize the power consumption, the driving range of 4WID-EV can be effectively improved. This paper proposes a model predictive control (MPC)-based torque distribution scheme, which minimizes the power consumption of 4WID-EVs while guaranteeing its tracking performance of planar motions. By incorporating the motor model considering iron losses, the optimal torque distribution can be achieved without an additional torque controller. Also, for this reason, the proposed control scheme is computationally efficient, since the power consumption term to be optimized, which is expressed as the product of the motor voltages and currents, is much simpler than that derived from the efficiency map. With reasonable simplification and linearization, the MPC problem is converted to a quadratic programming problem, which can be solved efficiently. The simulation results in MATLAB and CarSim co-simulation environments demonstrate that the proposed scheme effectively reduces power consumption with guaranteed tracking performance.

Extended State Observer-Based Adaptive Neural Networks Backstepping Control for Pneumatic Active Suspension with Prescribed Performance Constraint

Pneumatic actuator is one of the key technologies in the field of active suspension due to its low cost, cleanliness, and high power-to-weight ratio characteristics. However, the dynamic models and control strategies of the pneumatic suspension have not been well demonstrated because they are nonlinear systems. Besides, the vertical displacement stability of sprung mass is very important for ensuring ride comfort, but accurate control is still a challenging problem in the presence of parametric uncertainties. In this study, an adaptive neural networks backstepping scheme is designed for the stability control of the pneumatic suspension. Firstly, a mathematical model of the pneumatic system is studied to investigate the dynamic system behavior and to obtain the control algorithm. Secondly, an extended state observer is applied to estimate uncertain parameters, unmodeled dynamics, and external disturbances. Thirdly, unknown masses of various load passengers are approximated by using radial basis function neural networks (RBFNNs). To enhance the system stability, a proposed control with a prescribed performance function (PPF) is designed to guarantee the vertical displacement of the chassis. Adaptive backstepping control with PPF is developed to stabilize the perturbed system and guarantee tracking performance. Finally, the simulation examples for the pneumatic suspension are employed to investigate the effectiveness of the proposed method.

Motion control of connected and automated vehicles in a lane‐changing scenario with guaranteed tracking performance

AbstractThe coupled, nonlinear vehicle dynamics and multi‐vehicle cooperative strategies make the lane‐changing maneuver control of vehicle platoons a challenging task. This paper presents the dynamic modeling and motion control of connected and automated vehicles (CAVs) for lane‐changing maneuver, utilizing the ideology of constraint‐following servo control. To guarantee a transient and steady tracking performance, a series of equality constraints and bilateral inequality constraints bounded by decaying functions or scalar constants are imposed on the dynamic state to formulate a constrained dynamical system. Since the original Udwadia‐Kalaba (UK) approach cannot handle inequality constraints and underactuated systems, a creative diffeomorphism method is applied to transform the bounded state into an unbounded one. Then, based on the UK approach and Lyapunov stability theory, a novel constraint‐following controller is designed to render the transformed states asymptotically stable in a full actuated system, and to achieve uniform stability performance in an underactuated system. Finally, numerical simulations are used to validate the effectiveness of the proposed control methodology.

IBLF-based adaptive finite-time control and modeling for continuous stirred tank reactor with output constraint

This paper studies a finite-time adaptive fuzzy control approach for a continuous stirred tank reactor (CSTR) with percent conversion constraint and uncertainties. This system is seen as a class of non-affine systems, and the system is resolved by the mean value theorem. Integral barrier Lyapunov functions (iBLFs) are used to handle output constraint in the design process of the finite-time adaptive controller. In order to calculate the time derivative of the virtual controller, a finite-time convergent differentiator (FTCD) is proposed, which can avert the issue of “explosion of complexity” in the backstepping design. Based on the finite time stability theory, the proposed approach not only ensures the closed-loop stability, but also guarantees tracking performance in a finite time. Finally, the simulation results on CSTR are showed to reveal the availability of the developed control scheme.

Adaptive appointed-time formation tracking control for multiple spacecraft with collision avoidance under a dynamic event-triggered mechanism

This paper focuses on the appointed-time formation control problem for multiple spacecraft with limited communication and control resources. The control objective is to make each spacecraft move along its reference trajectory with guaranteed tracking performance while avoiding collision with each other. To this end, we attempt to propose an event-triggered formation tracking control protocol to achieve this objective. Firstly, a sliding mode manifold containing formation tracking and velocity errors is designed. Then, a group of prescribed performance constraints are imposed on the transient and steady-state behaviors of the newly defined sliding mode manifold, to derive a formation controller with performance guarantees and appointed-time convergence. By integrating the artificial potential function, a collision-free control term is devised, which is plus after the foregoing formation tracking controller to avoid the collision between the neighboring spacecraft. Furthermore, to reduce unnecessary data transmission and improve resource utilization, a dynamic event-triggered strategy is proposed to determine when the developed controller updates. In this case, the threshold parameter in triggering condition is dynamically changed over time rather than being fixed, in order to achieve a desired balance between communication frequency and system performance. Compared with the existing works, the major advantage of the proposed control protocol is that the formation tracking performance, the collision avoidance and the communication transmission preservation can be assured simultaneously. Finally, comparative simulations illustrate the effectiveness of the proposed protocol.

Output feedback disturbance rejection control for full-state constrained hydraulic systems with guaranteed tracking performance

In this paper, a practical output feedback disturbance rejection controller holding the desired dynamic behavior is proposed for precise movement control of hydraulic systems with disturbances, unknown states, and severe measurement noise. To relieve the noise and deal with unknown states, the estimated values obtained by the state observer are used to replace the actual states. Considering the matched and mismatched disturbances in hydraulic systems, the state observer and disturbance observer are combined to obtain their estimations. A prescribed performance function constraining tracking performance and the barrier Lyapunov function maintaining the desired dynamics are synthesized to guarantee the tracking error and all state errors within desired boundaries. Then, an integrated output feedback disturbance rejection controller is constructed through backstepping design to stabilize the closed-loop system. Finally, abundant comparative experimental results validate the tracking performance of the proposed controller.

Featured Cover

The cover image is based on the Research Article Fault-tolerant control of an aerial manipulator with guaranteed tracking performance by Yadong Ding et al., https://doi.org/10.1002/rnc.5863.

Fault‐tolerant control of an aerial manipulator with guaranteed tracking performance

AbstractIn this article, a fault‐tolerant control (FTC) scheme of an aerial manipulator is proposed, which can guarantee the transient and steady‐state tracking performance under actuator faults. A novel performance function (NPF) with simple form and explicit terminal time is designed to constrain the tracking errors. First, backstepping technique combined with the NPF is adopted as control framework to guarantee the asymptotic stability. Then, adaptive nonsingular terminal sliding mode with estimated actuator faults is used as the robust controller to deal with actuator fault. Finally, extended state observer is used to estimate and compensate complex coupling effects between the main‐body UAV and loading manipulator, and external disturbance. The stability of the aerial manipulator system with actuator faults and external disturbance is proved by Lyapunov analysis. Besides, the effect of the turbulent wind field on the body of the vehicle is analyzed. Several comparative simulations are carried out to show the effectiveness of the proposed FTC scheme.

Lyapunov-Based Real-Time and Iterative Adjustment of Deep Neural Networks

A real-time Deep Neural Network (DNN) adaptive control architecture is developed for general uncertain nonlinear dynamical systems to track a desired time-varying trajectory. A Lyapunov-based method is leveraged to develop adaptation laws for the output-layer weights of a DNN model in real-time while a data-driven supervised learning algorithm is used to update the inner-layer weights of the DNN. Specifically, the output-layer weights of the DNN are estimated using an unsupervised learning algorithm to provide responsiveness and guaranteed tracking performance with real-time feedback. The inner-layer weights of the DNN are trained with collected data sets to increase performance, and the adaptation laws are updated once a sufficient amount of data is collected. Building on the results in (Joshi and Chowdhary, 2019) and (Joshi et al., 2020), which focus on deep model reference adaptive control for linear systems with known drift dynamics and control effectiveness matrices, this letter considers general control-affine uncertain nonlinear systems. The real-time controller and adaptation laws enable the system to track a desired time-varying trajectory while compensating for the unknown drift dynamics and parameter uncertainties in the control effectiveness. A nonsmooth Lyapunov-based analysis is used to prove semi-global asymptotic tracking of the desired trajectory. Numerical simulation examples are included to validate the results, and the Levenberg-Marquardt algorithm is used to train the weights of the DNN.

Modified fuzzy neural network control using sliding mode technique for power quality improvement system with experimental verification

This study mainly focuses on the development of a second-order sliding mode-based meta-cognitive fuzzy neural network (MCFNN) control for power quality improvement, whereby an MCFNN is employed to learn modelling uncertainties. First, a second-order sliding mode control (SOSMC) is designed to track reference current for active power filter. Then, an MCFNN system with accurate approximation capability is further investigated to learn the unknown parts in SOSMC. Different from the existing predefined structure approaches, only necessary data can be extracted to adjust the structure and parameters of the networks in MCFNN. Subsequently, the Lyapunov stability analysis is presented to guarantee tracking performance and stability of the closed-loop system. Moreover, the excellent performance of the proposed MCFNN scheme is verified by simulation and experimental studies, and its remarkable characteristics are exhibited in comparison with other intelligent control schemes.

Backstepping-based adaptive control of a quadrotor UAV with guaranteed tracking performance

In this paper, a backstepping based indirect adaptive control design and an alternative direct adaptive control scheme, both with guaranteed transient and steady-state tracking performances, are proposed for trajectory tracking of a quadrotor unmanned aerial vehicle (UAV). Backstepping techniques, combined with a prescribed performance function based error transformation, are employed in both designs to achieve the bounded transient and steady-state tracking errors of the strict-feedback position system which comprises both lateral position and altitude dynamics. The effects of parametric inertia and drag uncertainties on attitude regulation are compensated using a least squares based parameter identification algorithm in the indirect adaptive control design, and using a constructive Lyapunov analysis approach in the direct adaptive control scheme. The stability of the closed-loop system for both designs is proven via Lyapunov analysis. Simulation and experimental test results are provided to verify the effectiveness of the proposed control designs.

Event-Triggered Output Feedback Control for MEMS Gyroscope With Prescribed Performance

This paper investigates an event-triggered output feedback control problem with guaranteed tracking performance for microelectromechanical system (MEMS) gyroscope subject to the lumped disturbances, including parameter uncertainties, coupling between driving mode and sensing mode, and unknown external disturbances. Firstly, to make the system output tracking errors evolve within the predetermined performance envelopes, a prescribed performance control (PPC) is employed in our controller design, such that a prescribed trajectory tracking with preselected settling time and steady-state tracking accuracy can be ensured. Besides, to simultaneously realize disturbance rejection and estimation of the immeasurable velocity state, linear extended state observers (LESOs) are designed to reconstruct the lumped disturbances and immeasurable velocity states for both MEMS gyroscope driving and sensing modes. In general, excessively energy and resource consumption are fundamentally neglected in most of the existing output feedback controllers for MEMS gyroscope, which will dramatically reduce the operational time of the close-loop system. To address this problem, we embed a fixed threshold event-triggered mechanism into the controller design procedure, such that the communication data size can be drastically reduced without sacrificing the tracking accuracy. Finally, to obtain the close-loop stability for MEMS gyroscope, robust control laws are designed to compensate for the measurement error and estimation error, meanwhile Zeno phenomena can be effectively eliminated. The simulation results and comparisons validate the effectiveness of the proposed scheme.