Closed-loop Error Research Articles

Hierarchical Robust Adaptive Control for Wind Turbines With Actuator Fault

Abstract This article solves the problem of regulating the rotor speed tracking error for wind turbines in the full-load region by an effective robust adaptive control strategy. The developed controller compensates for the uncertainty in the control input effectiveness caused by a pitch actuator fault, unmeasurable wind disturbance, and nonlinearity in the model. Wind turbines have multilayer structures such that the high-level structure is nonlinearly coupled through an aggregation of the low-level control authorities. Hence, the control design is divided into two stages. First, an L2 controller is designed to attenuate the influence of wind disturbance fluctuations on the rotor speed. Then, in the low-level layer, a controller is designed using a proposed adaptation mechanism to compensate for actuator faults. The theoretical results show that the closed-loop equilibrium point of the regulated rotor speed tracking error dynamics in the high level is finite-gain L2 stable, and the closed-loop error dynamics in the low level is globally asymptotically stable. Simulation results show that the developed controller significantly reduces the root mean square of the rotor speed error compared to some well-known works, despite the largely fluctuating wind disturbance, and the time-varying uncertainty in the control input effectiveness.

Closed-Loop Torque and Kinematic Control of a Hybrid Lower-Limb Exoskeleton for Treadmill Walking.

Restoring and improving the ability to walk is a top priority for individuals with movement impairments due to neurological injuries. Powered exoskeletons coupled with functional electrical stimulation (FES), called hybrid exoskeletons, exploit the benefits of activating muscles and robotic assistance for locomotion. In this paper, a cable-driven lower-limb exoskeleton is integrated with FES for treadmill walking at a constant speed. A nonlinear robust controller is used to activate the quadriceps and hamstrings muscle groups via FES to achieve kinematic tracking about the knee joint. Moreover, electric motors adjust the knee joint stiffness throughout the gait cycle using an integral torque feedback controller. For the hip joint, a robust sliding-mode controller is developed to achieve kinematic tracking using electric motors. The human-exoskeleton dynamic model is derived using Lagrangian dynamics and incorporates phase-dependent switching to capture the effects of transitioning from the stance to the swing phase, and vice versa. Moreover, low-level control input switching is used to activate individual muscles and motors to achieve flexion and extension about the hip and knee joints. A Lyapunov-based stability analysis is developed to ensure exponential tracking of the kinematic and torque closed-loop error systems, while guaranteeing that the control input signals remain bounded. The developed controllers were tested in real-time walking experiments on a treadmill in three able-bodied individuals at two gait speeds. The experimental results demonstrate the feasibility of coupling a cable-driven exoskeleton with FES for treadmill walking using a switching-based control strategy and exploiting both kinematic and force feedback.

A Digital Glucose Control Strategy via Subcutaneous Insulin Infusion

In this paper, the plasma glucose regulation problem for Type 2 diabetic patients by subcutaneous insulin infusion is studied. A nonlinear time-delay model of the glucose-insulin regulatory system, which takes into account the subcutaneous infusion of insulin, is exploited for the design of a quantized sampled-data static state feedback glucose controller. Quantization in both input/output channels is considered. Spline interpolation methodologies are used in order to obtain an approximation of suitable needed past values of the system state that cannot be always available from the buffer. The stabilization in the sample-and-hold sense is used in order to prove that the proposed digital glucose regulator ensures the semi-global practical stability of the related closed-loop tracking error system, with arbitrarily small final target ball. The proposed digital glucose regulator is validated through simulations.

A Robust Sliding-Mode Based Data-Driven Model-Free Adaptive Controller

In this letter, a novel data-driven control algorithm is presented coupling Model-Free Adaptive Control and Sliding Mode Control, which addresses general discrete-time Single-Input Single-Output nonlinear nonaffine systems and is aimed at strengthening standard techniques in the presence of a class of output-dependent perturbations. Use is made of an equivalent dynamic linearization model obtained adopting a dynamic linearization technique based on pseudo-partial derivatives. A stability proof of convergence of the closed loop system is provided, showing that the closed-loop tracking error is an asymptotically vanishing sequence and ensuring boundedness of the I/O sequences. Validation of the technique has been performed using a discrete-time test plant taken from the literature in the presence of perturbations. Simulation results show a remarkable improvement in terms of control authority and of tracking accuracy with respect to recently published analogous approaches.

UKF-Based Neural Training for Nonlinear Systems Identification and Control Improvement

Numerous academic works have addressed the identification and control problem for complex dynamic systems. In recent decades, the use of control algorithms based on neural networks (NNs) has been highlighted, which have shown satisfactory results in the trajectory tracking control for a class of discrete-time nonlinear systems. The present work proposes an efficient learning law for discrete-time recurrent high order neural networks (RHONNs), using a training algorithm based on an unscented Kalman filter (UKF). This learning law is applied through a decentralized neural block control using UKF (DNBC-UKF), for trajectory tracking control of a class of discrete-time nonlinear systems. The proposed controller is experimentally evaluated by means of real-time tests in a two degrees of freedom (DOF) vertical direct-drive robotic manipulator against a decentralized neural block control using EKF (DNBC-EKF). The Lyapunov stability theory is used to show that the identification errors of RHONNs are semi-globally uniformly ultimately bounded (SGUUB), the RHONN weights remains bounded, and the closed-loop tracking errors go to zero.

CLARQ: A Dynamic ARQ Solution for Ultra-High Closed-Loop Reliability

Emerging wireless control applications demand for extremely high closed-loop reliability under strict latency constraints, which the conventional Automatic Repeat reQuest (ARQ) solutions with static schedules fail to provide. To overcome this issue and enable data-link layer error control for ultra reliable low-latency communication (URLLC) services, we propose a novel protocol: the Closed-Loop ARQ (CLARQ), which forces to accomplish an information exchange round within a fixed loop-back latency, and dynamically re-allocates the remaining resource between uplink and downlink slots upon the result of last uplink transmission. The proposed method guarantees to meet the latency requirement, while delivering high communication reliability and power efficiency. It can be efficiently offline optimized by means of dynamic programming techniques, and is capable of real-time deployment with a low-cost implementation based on look-up tables. Numerical evaluations have verified that CLARQ outperforms baselines with significantly improved closed-loop reliability and reduced energy consumption. Especially, over a Rayleigh channel with 0dB mean SNR, it is able to provide a closed-loop error rate below 1e-7 within 10ms loop-back latency, which makes our proposal competitive for practical URLLC applications in future 5G-and-beyond networks.

Synchronization of Multi-Agent Systems under Time-Varying Network via Time-Delay Approach to Averaging

This paper studies the leader-tracking problem of Multi-Agents Systems under a periodic time-varying communication topology, without requiring the connectivity of the network for all t ≥ 0. The case of both state and communication delays is considered. A fully distributed control protocol, along with the constructive time-delay approach to periodic averaging, are combined in order to solve the problem, thus ensuring that a time-dependent switching control rule preserves the input-to-state stability (ISS) of the entire network, despite the presence of disconnected topologies, state and communication delays. The original closed-loop error systems is transformed into a neutral-type system with discrete and distributed delays. ISS analysis of the neutral system employs appropriate Lyapunov-Krasovskii functionals leading to simple ISS conditions in terms of Linear Matrix Inequalities (LMIs), whose solution allows finding upper bounds on small parameter, state and communication delays that preserve ISS. Numerical simulations illustrate the effectiveness of the theoretical results.

Robust Stabilization of Inverter-Based Resources Using Virtual Resistance-Based Control

This paper proposes a virtual resistance-based nonlinear control to stabilize and robustify the current layer of inverter-based resources, subject to the grid voltage disturbances, and the grid parameter uncertainties. A class of virtual resistances is proposed and analyzed using concepts from dissipative systems theory. Moreover, specific nonlinear virtual resistance-based controllers are derived, with their corresponding performance analytically bounded. The theoretical and simulation results show that the proposed nonlinear virtual resistance-based controllers significantly reduce the L2 gain of the closed-loop error system to grid voltage variation and parametric uncertainties. Significant improvements of the transient and steady-state current responses are also demonstrated over linear virtual resistance counterparts.

Filtering linear systems with large time-varying measurement delays

In this paper we consider the estimation problem for linear stochastic systems affected by multiple known and time-varying delays on all the output signals. Based on a modification of a previous proposal we prove for the first time the result that a filter based on simple eigenvalue assignment of the closed-loop error system may achieve uniform performance, with respect to the delay bound and estimation variance, in presence of both constant and time-varying delays that are differentiable. A new and simple demonstration technique provides non conservative delay bounds for time-varying delays. A cascaded version of the filter can cope with arbitrarily large delays.

Pinning synchronization and adaptive synchronization of complex-valued inertial neural networks with time-varying delays in fixed-time interval

This article concentrates on pinning synchronization and adaptive synchronization problems of complex-valued inertial neural networks with time-varying delays in fixed-time interval. First, regarding complex-valued inertial neural networks model as an entirety instead of reducing this system to first-order differential equation, separating the real and imaginary parts of this system into an equivalent real-valued one, and establishing a novel Lyapunov function, the fixed-time stability for the closed-loop error system is guaranteed via partial nodes controlled directly by a new pinning controller which involves the state derivatives and other proper terms. Then, from the point of saving cost and avoiding resources waste, a new pinning adaptive controller is further developed and sufficient condition ensuring the adaptive fixed-time stability for the closed-loop error system is also derived. In the end, the effectiveness of these results is verified by a numerical example.

Error Uncertainty Analysis in Planar Closed-Loop Structure with Joint Clearances

For planar closed-loop structures with clearances, the angular and positional error uncertainties are studied. By using the vector translation method and geometric method, the boundaries of the errors are analyzed. The joint clearance is considered as being distributed uniformly in a circle area. A virtual link projection method is proposed to deal with the clearance affected length error probability density function (PDF) for open-loop links. The error relationship between open loop and closed loop is established. The open-loop length PDF and the closed-loop angular error PDF both approach being Gaussian distribution if there are many clearances. The angular propagation error of multi-loop structures is also investigated by using convolution. The positional errors of single and multiple loops are both discussed as joint distribution functions. Monte Carlo simulations are conducted to verify the proposed methods.

Reinforcement learning-based finite-time tracking control of an unknown unmanned surface vehicle with input constraints

In this paper, subject to completely unknown system dynamics and input constraints, a reinforcement learning-based finite-time trajectory tracking control (RLFTC) scheme is innovatively created for an unmanned surface vehicle (USV) by combining actor-critic reinforcement learning (RL) mechanism with finite-time control technique. Unlike previous RL-based tracking which requires infinite-time convergence thereby rather sensitive to complex unknowns, an actor-critic finite-time control structure is created by employing adaptive neural network identifiers to recursively update actor and critic, such that learning-based robustness can be sufficiently enhanced. Moreover, deduced from the Bellman error formulation, the proposed RLFTC is directly optimized in a finite-time manner. Theoretical analysis eventually shows that the proposed RLFTC scheme can ensure semi-global practical finite-time stability (SGPFS) for a closed-loop USV system and tracking errors converge to an arbitrarily small neighborhood of the origin in a finite time, subject to optimal cost. Both mathematical simulation and virtual-reality experiments demonstrate remarkable effectiveness and superiority of the proposed RLFTC scheme.

Multi-agent consensus with heterogeneous time-varying input and communication delays in digraphs

This paper investigates the distributed consensus tracking control problem for general linear multi-agent systems with external disturbances and heterogeneous time-varying input and communication delays under a directed communication graph topology, containing a spanning tree. First, for all agents whose state matrix has no eigenvalues with positive real parts, a communication-delay-related observer, which is used to construct the controller, is designed for followers to estimate the leader’s state information. Second, by means of the output regulation theory, the results are relaxed to the case that only the leader’s state matrix needs to be asymptotically stable or marginally stable and, under these relaxed conditions, the controller is redesigned. Both cases lead to a closed-loop error system of which the stability is guaranteed via a Lyapunov–Krasovskii functional with sufficient conditions in terms of input-delay-dependent linear matrix inequalities (LMIs). An extended LMI is proposed which, in conjunction with the rest of LMIs, results in a solution with a larger upper bound on delays than what would be feasible without it. It is highlighted that the integration of communication-delay-related observer and input-delay-related LMI to construct a fully distributed controller (which requires no global information) is scalable to arbitrarily large networks. The efficacy of the proposed scheme is demonstrated via an illustrative numerical example.

Neural adaptive attitude tracking control for uncertain spacecraft with preassigned performance guarantees

In this article, two novel neural adaptive attitude control strategies are presented for the attitude tracking of rigid spacecraft affected by inertia uncertainty, external disturbance, and torque saturation with guaranteed prescribed performance. Under the backstepping framework, a neural adaptive state feedback controller is designed first by utilizing the neural network (NN) approximation and barrier Lyapunov function (BLF). Then, on the basis of the state feedback controller, a neural adaptive output feedback controller is exploited by integrating with a high-gain observer. Lyapunov stability analysis shows that all the closed-loop error signals are uniformly ultimately bounded under the both proposed neural adaptive attitude controllers. In comparisons with the most existing researches, the distinctive advantages of the proposed neural adaptive attitude controllers are threefold. (1) With the help of NN approximation, the proposed attitude controllers are model-independent and still applicable even when the spacecraft attitude dynamics are completely unknown. (2) Benefiting from the BLF, the proposed attitude controllers can guarantee the attitude tracking error always satisfies the preassigned performance. (3) Both the state feedback control and output feedback control are considered. The angular velocity information of the spacecraft is not required for the output feedback control design. At last, numerical simulations and comparisons are conducted to verify and highlight the proposed neural adaptive attitude control strategies.

Adaptive tracking control of switched cyber-physical systems with cyberattacks

This study investigates the problem of adaptive tracking control for switched cyber-physical systems against cyberattacks. A tracking signal is generated using an exogenous system. An adaptive tracking controller is designed to compensate for the attacks and then stabilize the studied systems. A switching signal is constructed using the mode-dependent average dwell time (MDADT) method. By using the multiple Lyapunov function approach, which is associated with the adaptive estimated signal, the closed-loop error systems with cyberattacks are asymptotically stable under the designed adaptive tracking controller and MDADT switching signal, and the system states can asymptotically track the reference signal. Finally, two examples are provided to validate the theoretical results.

Robust command filtered control for course tracking of ships under actuator dynamics with input magnitude and rate saturation

This article investigates the course tracking of ships subject to parametric uncertainties and environmental disturbances. Particularly, the actuator dynamics with input magnitude and rate saturation is also considered. When including the actuator dynamics, the ship course tracking system becomes a mismatching system, which brings a great difficulty to the control design. A novel robust command filtered control strategy is presented by incorporating a disturbance observer and an auxiliary anti-saturation system into the command filtered backstepping control architecture. The disturbance observer is designed to compensate for the mismatched lumped disturbance. The auxiliary anti-saturation system is introduced to tackle the effects of input magnitude and rate saturation. It is strictly proved that all the closed-loop error signals under the proposed controller are uniformly ultimately bounded and the course angle tracking error can converge to the adjustable small region around the origin. Moreover, the proposed controller is computationally simple and has the strong robustness against uncertainties and disturbances. The effectiveness and advantages of the proposed control strategy are verified through simulations and comparisons.

Adaptive Event-Triggered Synchronization of Uncertain Fractional Order Neural Networks with Double Deception Attacks and Time-Varying Delay.

This paper investigates the problem of adaptive event-triggered synchronization for uncertain FNNs subject to double deception attacks and time-varying delay. During network transmission, a practical deception attack phenomenon in FNNs should be considered; that is, we investigated the situation in which the attack occurs via both communication channels, from S-C and from C-A simultaneously, rather than considering only one, as in many papers; and the double attacks are described by high-level Markov processes rather than simple random variables. To further reduce network load, an advanced AETS with an adaptive threshold coefficient was first used in FNNs to deal with deception attacks. Moreover, given the engineering background, uncertain parameters and time-varying delay were also considered, and a feedback control scheme was adopted. Based on the above, a unique closed-loop synchronization error system was constructed. Sufficient conditions that guarantee the stability of the closed-loop system are ensured by the Lyapunov-Krasovskii functional method. Finally, a numerical example is presented to verify the effectiveness of the proposed method.

Guaranteed Cost Leaderless Consensus Protocol Design for Fractional-Order Uncertain Multi-Agent Systems with State and Input Delays

This paper addresses the guaranteed cost leaderless consensus of delayed fractional-order (FO) multi-agent systems (FOMASs) with nonlinearities and uncertainties. A guaranteed cost function for FOMAS is proposed to simultaneously consider consensus performance and energy consumption. By employing the linear matrix inequality approach and the FO Razumikhin theorem, a delay-dependent and order-dependent consensus protocol is formulated for FOMASs with input delay. The proposed protocol not only guarantees the robust stability of the closed-loop system error but also ensures that the performance degradation caused by the system uncertainty is lesser than that obtained with other approaches. Two numerical examples are provided in order to verify the effectiveness and accuracy of the proposed protocol.

Inversion-Based Hysteresis Compensation Using Adaptive Conditional Servocompensator for Nanopositioning Systems

Abstract Nanopositioning stages are widely used in high-precision positioning applications. However, they suffer from an intrinsic hysteretic behavior, which deteriorates their tracking performance. This study proposes an adaptive conditional servocompensator (ACS) to compensate the effect of the hysteresis when tracking periodic references. The nanopositioning system is modeled as a linear system cascaded with hysteresis at the input side. The hysteresis is modeled with a modified Prandtl–Ishlinskii (MPI) operator. With an approximate inverse MPI operator placed before the system hysteresis operator, the resulting system takes a semi-affine form. The design of the ACS consists of two stages: first, we design a continuously implemented sliding mode control (SMC) law. The hysteresis inversion error is treated as a matched disturbance, and an analytical bound on the inversion error is used to minimize the conservativeness of the SMC design. The second part of the controller is the ACS. Under mild assumptions, we establish the well-posedness and periodic stability of the closed-loop system. In particular, the solution of the closed-loop error system will converge exponentially to a unique periodic solution in the neighborhood of zero. The efficacy of the proposed controller is verified experimentally on a commercial nanopositioning device under different types of periodic reference inputs, via comparison with multiple inversion-based and inversion-free approaches.

Multi-dimensional Taylor network adaptive predictive control for single-input single-output nonlinear systems with input time-delay

In this study, an adaptive predictive control approach based on the multi-dimensional Taylor network (MTN) is proposed for the real-time tracking control of single-input single-output nonlinear systems with input time-delay. Two MTNs are used to implement the accurate tracking control. First, to compensate for the influence of time-delay, MTN is taken as a predictor and the damped recursive least squares algorithm is used as its online learning algorithm. Second, a feed-forward MTN controller is developed on the basis of the proportional–integral–derivative controller, and the closed-loop errors between the reference input and the system output are directly chosen to be the MTN controller’s inputs. The back propagation algorithm is introduced for its learning which can update its weights online at stable learning rate by the errors caused by the system’s uncertain factors. Convergence and stability analysis are given to guarantee the performance of our proposed approach. Finally, two examples are given to verify the effectiveness of the proposed approach.