Time-varying Tracking Research Articles

Four-stage cascaded adaptive sliding mode control for automatic carrier landing with airwake disturbances and uncertainties

ObjectiveThis paper addresses the carrier landing affected by airwake, parametric uncertainties, and carrier deck motion, its main target being the design of a novel sliding mode based automatic carrier landing system to obtain accurate tracking of the reference trajectory, robustness in terms of disturbances and uncertainties, as well as excellent touchdown accuracy. ApproachFor an aircraft nonlinear dynamics, written under a four-stage cascaded strict feedback form, the design of the novel landing control architecture involves the design of a guidance subsystem, robust sliding mode controllers (for the control of the heading angle, attitude angles, and angular rates), an approach power compensation system, adaptive control laws suppressing the uncertainties and disturbances, a Kalman filter for deck motion prediction, a block computing the reference trajectory, a tracking differentiator block for deck motion compensation, and first-order command filters. Main resultsThe software validation process proves the effectiveness of the sliding mode based control scheme and the suppression of the uncertainties and disturbances. Also, the comparison between the performances of the sliding mode control based carrier landing system and the ones associated to other automatic carrier landing systems shows the superiority of the sliding mode based control scheme, as well as its better touchdown accuracy and landing success rate. SignificanceThis study innovatively transforms the general carrier landing problem into a time-varying tracking control problem for cascaded strict feedback dynamics with disturbances and uncertainties. The new designed automatic carrier landing system is the first control architecture in the literature employing the sliding mode control augmented by adaptive control laws for carrier landing, subjected to airwake, deck motion, and uncertainties.

Resilient exponential tracking for disturbed systems with communication links faults

Resilience is to appraise the ability of disturbed systems to recover cooperative performance after suffering from failures or disturbances. In this paper, the improvement on the exponential tracking resilience for disturbed Euler–Lagrange systems is explored by settling the unknown time-variant faults imposed on the communication interaction between agents. First, we transform the resilient exponential tracking problem into designing the trajectory and velocity observers for leaders, and showcase that the proposed observers are resilient to communication interaction malfunctions. Second, a disturbance observer is manifested to estimate disturbances precisely, which is needless to know the upper bound of disturbance. The reliable observers and estimator are incorporated into the resilient tracking control frame. Further, the global exponential stabilization of the tracking systems is performed by utilizing the Lyapunov theory. Moreover, benefiting from feasible and reliable observation and estimation results, the proposed control framework enables to realize a satisfactory resilient exponential tracking performance even in the case of communication links faults (CLFs) and disturbances. Comprehensive studies are executed on a group of satellite systems, and the simulations results verify the effectiveness of the proposed resilient approaches in a time-variant tracking case.

Evolutionary Optimization of Fuzzy Reinforcement Learning and Its Application to Time-Varying Tracking Control of Industrial Parallel Robotic Manipulators

This paper contributes to the development of evolutionary optimization of fuzzy reinforcement learning and its application to time-varying tracking control for industrial parallel robotic manipulators. An improved evolutionary social spider optimization (SSO) paradigm with Cauchy mutation is presented to address the optimal fuzzy reinforcement learning problem. The SSO swarm intelligence incorporated with the fuzzy Q-learning strategy, called SSOFQ, is applied to the time-varying tracking control of parallel robotic Stewart manipulators with six degrees of freedom (DOFs). Having the derived kinematics and dynamics of six-DOF Stewart platforms, the SSOFQ is employed to synthesize an intelligent real-time tracking control scheme. More importantly, a custom experimental Stewart platform is constructed using hardware/software codesign and the system-on-a- programmable chip (SoPC) technique. Finally, the simulations, experimental results and comparative works are provided to validate the efficacy and superiority of the presented SSOFQ control method.

A Novel Finite-Time-Gain-Adjustment Controller Design Method for UAVs Tracking Time-Varying Targets

As for time-varying tracking control problems, many neural-dynamics-based control methods have been proposed because of their high efficiency. The varying-parameter convergent neural dynamics design method with the characteristic of super-exponential convergence has been applied to design controllers for unmanned aerial vehicles. Although the varying-parameter convergent neural dynamics controller has a fast convergence speed, it still needs long enough time to achieve tracking theoretically. By combining the finite-time activation function with the varying-parameter convergent neural dynamics design method, a finite-time-gain-adjustment design method is proposed and proved theoretically in this paper. This controller can make state variables of the system converge to their time-varying targets in finite time. Compared with some traditional methods, contrastive experiments and application to a multi-rotor unmanned aerial vehicle system illustrate that the proposed controller has finite convergence time, better anti-noise performance, and faster convergence speed, which enable the multi-rotor unmanned aerial vehicles to track time-varying targets more quickly and accurately, so as to achieve more complex and efficient control tasks.

Fault-Tolerant Cooperative Control for Multiple Vehicle Systems Based on Topology Reconfiguration.

In this article, the fault-tolerant synchronization and time-varying tracking control problem is investigated for nonlinear multivehicle systems (MVSs) in the presence of partial loss-of-control-effectiveness (LoCE) faults. Based on the graph theory, a two-level fault-tolerant cooperative control framework is proposed, namely, the low-level distributed nominal control scheme and the high-level topology reconfiguration protocols. The low-level scheme is developed to guarantee system performances in the fault-free scenario. With the low-level scheme, the high-level topology reconfiguration protocols, each of which corresponds to one partial LoCE fault scenario, are then proposed to mitigate the fault impact by adjusting the underlying topology. Accordingly, without modifying the structure or the design parameter of the low-level control scheme, the proposed framework can guarantee the synchronization and tracking errors of the MVS asymptotically convergent to zero in both fault-free and fault scenarios. Finally, the effectiveness of the proposed control method is verified via a simulation study of three degree-of-freedom helicopters.

Robust asynchronous switching predictive control for multi-phase batch processes with time-varying tracking trajectory and delay

To solve the delay condition of the controller during adjacent phases and the change of the set value in multi-phase batch processes, a robust asynchronous switching predictive control scheme is proposed based on the mode-dependent average dwell time method. Firstly, the model of multi-phase batch processes including stable and unstable subsystems is established. Secondly, the LMI conditions to ensure that the system is asymptotically stable at each phase and exponentially stable at each batch are given. By solving these LMI conditions, not only the control law can be calculated, but also the shortest running time in the stable subsystems and the longest running time in the unstable subsystems can be obtained. Finally, according to these times, the controller is switched ahead of time to avoid the appearance of unstable subsystems. The comparison results of the injection moulding processes with the existing switching methods verifies the feasibility of the proposed method.

Manoeuvrable multi-agent formation control via time-varying flocking and iterative learning tracking

Manoeuvrable (or time-varying) formation control of second-order integral multi-agent networks with single virtual leaders is contrived by incorporating time-varying weighting matrices into flocking algorithms. Existence and properties are examined, including control bounded-ness, average trajectory and formation manoeuvrability with respect to the weighting matrices and virtual leader reference input. More specifically, it is shown that under the time-varying flocking algorithms, the multi-agents ultimately run into lattice formations and their kinematical features in terms of orientation, scaling, subspace specification and homogeneous/heterogeneous consensus can be manoeuvred. Moreover, by gain-scheduling assignment for the leader-average dynamics via the variation-of-constant formula and iterative learning optimisation, trajectory-tracking manoeuvrable formation control can be achieved. Technical advantages include: flexible formations rather than rigid ones can be dealt with; formation and trajectory tracking can be designed separately and implemented simultaneously; diverse formations are achievable by selecting the weighting matrices; trajectory-tracking control is independent of trajectory modelling. Numerical examples are illustrated to show the main results.

Multivariate recursive Bayesian linear regression and its applications to output-only identification of time-varying mechanical systems

This article focuses on the output-only recursive identification of time-varying systems by using parametric time-domain methods. A novel multivariate recursive Bayesian linear regression method is proposed based on the vector time-dependent autoregressive moving average model. The standard setup of univariate batch Bayesian linear regression is first extended to the multivariate case for multiple response signal modeling and further extended to the recursive case to meet the output-only recursive identification requirement of practical systems. A sliding window mechanism is finally applied to deemphasize data from the remote past and fix the computational complexity for each consecutive update, allowing the proposed method to be capable of tracking the time-varying dynamics online. The proposed multivariate recursive Bayesian linear regression method is first validated by a simple numerical system and subsequently applied to identify two mechanical systems with typical time-varying dynamics. Comparative identification results via Monte Carlo tests numerically and experimentally demonstrate the superior achievable accuracy and time-varying tracking capability of the proposed method.

Robust Time-Varying Tracking Control of Sandwich Nonlinear Systems with Sandwiched Saturation Nonlinearity

This paper addresses the output-tracking control problem for a class of nonlinear sandwich systems with external disturbances and model uncertainties. Sandwich systems are a special class of nonlinear systems in the cascade structure, which are made up of several distinct subsystems while the non-smooth nonlinear functions are sandwiched among their separate subsystems. This paper concentrates on the sandwich systems consisting of two arbitrary-order nonlinear cascaded subsystems, while the saturation nonlinearity is sandwiched between them. The robust control law is designed such that the output of the sandwich system tracks the desired time-varying reference signal despite the saturation occurrence. Due to the characteristics of the saturation function and also the existence of the external disturbances and model uncertainties, the considered problem is facing some serious challenges. To deal with these difficulties, the design procedure is divided into two phases. In the first phase, the second subsystem and the sandwiched saturation nonlinearity are considered. In this phase, by utilizing the backstepping approach, the desired input signal of the saturation function is designed. In the second phase, the control input of the first subsystem is designed based on the sliding mode technique in a way that the output of the first subsystem tracks the desired signal which is obtained in the first phase. Finally, to verify the effectiveness of the proposed method, it is applied to a practical sandwich system.

Nonlinear Model Predictive Trajectory Tracking Control of Underactuated Marine Vehicles: Theory and Experiment

The article studies the trajectory tracking control problem of underactuated marine vehicles via the nonlinear model predictive control (NMPC) strategy, where practical control and state constraints present. It is a well-known challenging issue that the conventional NMPC is not applicable for underactuated marine vehicles, due to the fact that there does not exist a local static continuous state-feedback controller to stabilize the underactuated dynamics. To resolve this issue, this article proposes to construct an auxiliary time-varying tracking controller to aid terminal constraint design in the NMPC framework, where the time-varying tracking controller borrows the ideas from Lyapunov's direct method and backstepping approach. Based on this, a novel NMPC algorithm is designed to ensure trajectory tracking control of underactuated marine vehicles. Furthermore, a systematic parameter design approach is developed. Under the designed parameters, we show that the tracking error system is input-to-state stable (ISS). Finally, the effectiveness of the designed algorithm is verified by thorough simulation and hardware experiments.

Simultaneous identification, tracking control and disturbance rejection of uncertain nonlinear dynamics systems: A unified neural approach

Previous works of traditional zeroing neural networks (or termed Zhang neural networks, ZNN) show great success for solving specific time-variant problems of known systems in an ideal environment. However, it is still a challenging issue for the ZNN to effectively solve time-variant problems for uncertain systems without the prior knowledge. Simultaneously, the involvement of external disturbances in the neural network model makes it even hard for time-variant problem solving due to the intensively computational burden and low accuracy. In this paper, a unified neural approach of simultaneous identification, tracking control and disturbance rejection in the framework of the ZNN is proposed to address the time-variant tracking control of uncertain nonlinear dynamics systems (UNDS). The neural network model derived by the proposed approach captures hidden relations between inputs and outputs of the UNDS. The proposed model shows outstanding tracking performance even under the influences of uncertainties and disturbances. Then, the continuous-time model is discretized via Euler forward formula (EFF). The corresponding discrete algorithm and block diagram are also presented for the convenience of implementation. Theoretical analyses on the convergence property and discretization accuracy are presented to verify the performance of the neural network model. Finally, numerical studies, robot applications, performance comparisons and tests demonstrate the effectiveness and advantages of the proposed neural network model for the time-variant tracking control of UNDS.

Novel adaptive methods for output-only recursive identification of time-varying systems subject to gross errors

Gross errors are generally used to model intermittent sensor failures and occasional data packet losses or corruption, which arise in many engineering communities. In this work, we propose to deal with the problem of output-only recursive identification of time-varying systems subject to gross errors by using an adaptive weighting and forgetting combined strategy. Under the assumption that gross errors are unknown and can be of arbitrarily large magnitude, time-dependent autoregressive model-based adaptive recursive identification methods are proposed by minimizing the sum of norm errors and achieving a sparse prediction error sequence. The adaptive weighting strategy is used to deemphasize data observations contaminated by gross errors, and the forgetting mechanism is used to deemphasize data from the remote past, allowing the proposed methods to track time-varying dynamics of the system subject to gross errors. The proposed methods are numerically and experimentally tested, and the comparative results demonstrate the superior time-varying tracking capability of the proposed methods in extremely challenging gross error circumstances.

Time-Coordinated Control for Unmanned Aerial Vehicle Swarm Cooperative Attack on Ground-Moving Target

In this paper, cooperative attack control law analysis and design problems for unmanned aerial vehicle (UAV) swarm attack on ground-moving target with time-coordinated strategies are investigated. First, the time-coordinated control problem for a single UAV is formulated, which is the foundation of solving the problem of a single UAV arriving at the desired attack position relative to ground-moving target at a specific terminal time. Then, relative motion between each UAV and ground-moving target is considered as a finite-time time-varying tracking system problem, and the difference between expected output and system output is defined as tracking error vector. The control law is obtained by linear quadratic optimal control theory to minimize the energy cost in the whole process and the tracking error at the terminal time. Besides, time-coordinated function, which is critical to coordinate terminal time among all UAVs in the UAV swarm, is proposed to model time-coordinated strategies. Finally, numerical simulations show that the proposed control law can steer UAV swarm to arrive at the desired attack positions and achieve the time-coordinated strategies effectively.

Prescribed performance adaptive fault-tolerant tracking control for nonlinear time-delay systems with input quantization and unknown control directions

Abstract This paper addresses the adaptive prescribed performance tracking control problem for a class of nonlinear time-delay systems with actuator fault, input quantization, unknown control directions and disturbances. Neural networks (NNs) are employed to approximate the unknown nonlinear functions and the Nussbaum function is used to deal with the unknown control directions. Then, a novel adaptive prescribed performance controller is designed to reduce the effects of actuator fault, input quantization, NNs approximation errors and disturbances. Compared with the existing results, a new error transformation method is presented, and the knowledge of the quantization parameters and the control directions are unknown in the control design. Furthermore, the proposed control scheme can guarantee the semi-global boundedness of all the closed-loop signals and the prescribed time-varying tracking performance. Finally, simulation results are given to demonstrate the effectiveness of the proposed control method.

Observer-based adaptive prescribed performance tracking control for nonlinear systems with unknown control direction and input saturation

Abstract In this paper, the problem of observer-based adaptive tracking control is investigated for a class of nonlinear systems with unknown control direction, input saturation and tracking error constraint. The Nussbaum function is employed to address the unknown control direction and a state observer is constructed by neural networks (NNs) to estimate the unmeasurable states. A new error constraint transformation is proposed to guarantee that the tracking error satisfies the prescribed performance. Then, a novel adaptive prescribed performance neural network (NN) output feedback tracking control method is designed. It is proved that the designed controller can guarantee the boundedness of all the signals in the closed-loop system and the prescribed time-varying tracking performance. Finally, simulations on two examples are performed to illustrate the efficiency of the proposed control method.

Robust path-following control for a fully actuated marine surface vessel with composite nonlinear feedback

This paper presents a fast and accurate robust path-following control approach for a fully actuated marine surface vessel in the presence of external disturbances. The path following is realized by simultaneously converging the yaw rate and sway velocity to their respective desired values, which are generated according to the path-following demand. An improved combined control strategy using an integral terminal sliding mode (ITSM) based composite nonlinear feedback (CNF) technique considering the external disturbances, time-varying tracking reference, input saturations and transient performance improvement is proposed in this study. The proposed ITSM-CNF combines the advantages of the CNF control in improving the transient performance and of the ITSM control in guaranteeing good robustness and finite-time convergence. A continuous and smooth sliding mode controller, based on an integral nonsingular terminal sliding surface, is added to the CNF controller to eliminate chattering. The overall stability of the closed-loop system is strictly proved based on the Lyapunov method. Simulations verify the effectiveness of the ITSM-CNF controller in improving the transient path-following performance, inhibiting overshoots, eliminating steady-state errors, rejecting external disturbances and removing chattering effects, considering input saturations, varying path curvature and finite-time convergence.

A Real-Time SOSM Super-Twisting Technique for a Compound DC Motor Velocity Controller

In this paper, a real-time robust closed-loop control scheme for controlling the velocity of a Direct Current (DC) motor in a compound connection is proposed. This scheme is based on the state-feedback linearization technique combined with a second-order sliding mode algorithm, named super-twisting, for stabilizing the system and achieving control goals. The control law is designed to track a periodic square reference signal, being one of the most severe tests applied to closed-loop systems. The DC motor drives a squirrel-cage induction generator which represents the load; this generator must work above the synchronous velocity to deliver the generated power towards the grid. A classical proportional-integral (PI) controller is designed for comparison purposes of the time-domain responses with the proposed second-order sliding mode (SOSM) super-twisting controller. This robust controller uses only a velocity sensor, as is the case of the PI controller, as the time derivative of the velocity tracking variable is estimated via a robust differentiator. Therefore, the measurements of field current and stator current, the signal from a load torque observer, and machine parameters are not necessary for the controller design. The validation and robustness test of the proposed controller is carried out experimentally in a laboratory, where the closed-loop system is subject to an external disturbance and a time-varying tracking signal. This test is performed in real time using a workbench consisting of a DC motor—Alternating Current (AC) generator group, a DC/AC electronic drive, and a dSPACE 1103 controller board.

Time-Varying Channel Tracking for Amplify-and-Forward Relay Network in High Doppler Spread

Next generation wireless communication technologies such as wireless metropolitan area network, long-term evolution (LTE), and LTE advanced are designed to deploy cooperative relaying incorporated with orthogonal frequency division multiplexing system. In addition to the higher data rate, these technologies allow users to have a faster mobility than the previous standards. However, due to the fast movement, Doppler frequency causes the carrier frequency offset resulting in intercarrier interference. Modeling and estimating this type of channel play a vital role to fulfill the data rate requirement of the network. In this paper, we develop a high mobility channel estimation method for amplify-and-forward relay-based network. Specifically, we use basis expansion modeling (BEM) to capture the time variation of the channel. Using pilot symbols, the BEM coefficients are estimated by least square and linear minimum mean square error estimators to reconstruct the channel in both time and frequency domains. In addition to the estimators, Cramer–Rao lower bound has been derived as a benchmark of the estimation performance of the channel estimators. It has been shown that the time-domain channel estimation method is simpler and can approximate the channel more efficiently than frequency-domain estimation in very high Doppler spread scenario.

Output-Tracking Quantized Explicit Nonlinear Model Predictive Control Using Multiclass Support Vector Machines

In applications involving digital control, the set of admissible control actions is finite/quantized. Coupled with state constraints and fast dynamics, explicit model predictive control (EMPC) provides an attractive control formalism. However, the design of data-driven EMPCs with finite admissible control sets is a challenging and relatively unexplored problem. In this paper, a systematic data-driven method is proposed for the design of quantized EMPCs (Q-EMPCs) for time-varying output tracking in nonlinear systems. The design involves: 1) sampling the admissible state space using low-discrepancy sequences to provide scalability to higher dimensional nonlinear systems; 2) at each sampled data point, solving for optimal quantized model predictive control actions and determining feasibility of the intrinsic mixed-integer nonlinear programming problem; and 3) constructing the Q-EMPC control surface using multiclass support vector machines (MC-SVMs). In particular, four widely used MC-SVM algorithms are employed to construct the proposed data-driven Q-EMPC. Extensive testing and comparison among the different MC-SVM algorithms is performed on 2-D and 5-D benchmark examples to demonstrate the effectiveness and scalability of the proposed methodology.

A self-optimization mechanism for generalized adaptive notch smoother

Tracking of nonstationary narrowband signals is often accomplished using algorithms called adaptive notch filters (ANFs). Generalized adaptive notch smoothers (GANSs) extend the concepts of adaptive notch filtering in two directions. Firstly, they are designed to estimate coefficients of nonstationary quasi-periodic systems, rather than signals. Secondly, they employ noncausal processing, which greatly improves their accuracy and can be applied whenever additional delay can be tolerated. The paper develops a novel performance assessment mechanism for GANS. It allows one to evaluate tracking accuracy of the smoother without prior knowledge of the true values of the system's frequency or coefficients. The extension can be employed to build a parallel bank of filters, which automatically chooses the one which is best matched to unknown and possibly time-varying tracking conditions.