Online Approximator Research Articles

Fault-tolerant control of underactuated unmanned surface vessels in presence of deception and injection attacks

This paper studies the trajectory tracking control problem of underactuated unmanned surface vessels (USVs) under the influence of internal and external uncertainties, actuator faults, and injection and deception attacks. In the control design, we separately designed virtual adaptive laws to compensate for the time-varying gains suffered by the kinematics channel and combined the event-triggered control (ETC) mechanism to establish an online approximator to compensate for the time-varying gains of the kinematics channels and the loss-of-effectiveness (LOE) and bias faults suffered by the system. Combining robust neural damping technology and finite-time disturbance observer (FTDO), the dynamic uncertainties and external disturbances are suppressed. Finally, a novel robust adaptive trajectory tracking control scheme is proposed. The scheme achieves active compensation for heterogeneous uncertainties including internal and external uncertainties, actuator faults, and attack signals. The Lyapunov stability theory analysis shows that all signals of the tracking system are bounded. The simulation results prove the effectiveness of this control scheme.

Practical Finite-Time Event-Triggered Control of Underactuated Surface Vessels in Presence of False Data Injection Attacks

Abstract The results of studies on a trajectory-tracking problem affected by false data injection attacks (FDIAs) and internal and external uncertainties are presented in this paper. In view of the FDIAs experienced by the system, we compensate for the serious navigation deviation caused by malicious attacks by designing an online approximator. Next, we study the internal and external uncertainties introduced by environmental factors, system parameter fluctuations, or sensor errors, and we design adaptive laws for these uncertainties to approximate their upper bounds. To further enhance the response velocity and stability of the system, we introduce finite-time technology to ensure that the unmanned underactuated surface vessels (USVs) reach the predetermined trajectory-tracking target within finite time. To further reduce the update frequency of the controller, we introduced event-triggered control (ETC) technology. This saves the system’s communication resources and optimizes the system. Through Lyapunov stability theory, a strict and complete stability analysis is provided for the control scheme. Finally, the effectiveness of the control scheme is verified using two sets of simulations.

Adaptive tracking control-based Nussbaum gain for a class of multi-input and multi-output nonlinear systems with time-varying state constraints

This article studies an adaptive backstepping barrier Lyapunov function-based control scheme for a class of multi-input and multi-output nonlinear systems in the presence of time-varying asymmetric full-state constraints and external disturbances. Simultaneously, a prominent feature of these systems is the unknown time-varying control direction. To stabilize such systems, Nussbaum gain technique is constructively framed to overcome the unknown control direction problem. To prevent that the constraints are overstepped, the time-varying asymmetric barrier Lyapunov functions are employed in each step of the backstepping design. The design involves an adaptive-based online approximator to cope with unknown dynamics of the system. A simulation example on aircraft skin inspection robot with three-dimensional trajectory is given to show the effectiveness of the proposed control scheme.

Fixed-Time Recurrent NN Learning Control of Uncertain Robotic Manipulators with Time-Varying Constraints: Experimental Verification

This paper proposes a learning control framework for the robotic manipulator’s dynamic tracking task demanding fixed-time convergence and constrained output. In contrast with model-dependent methods, the proposed solution deals with unknown manipulator dynamics and external disturbances by virtue of a recurrent neural network (RNN)-based online approximator. First, a time-varying tangent-type barrier Lyapunov function (BLF) is introduced to construct a fixed-time virtual controller. Then, the RNN approximator is embedded in the closed-loop system to compensate for the lumped unknown term in the feedforward loop. Finally, we devise a novel fixed-time, output-constrained neural learning controller by integrating the BLF and RNN approximator into the main framework of the dynamic surface control (DSC). The proposed scheme not only guarantees the tracking errors converge to the small neighborhoods about the origin in a fixed time, but also preserves the actual trajectories always within the prescribed ranges and thus improves the tracking accuracy. Experiment results illustrate the excellent tracking performance and verify the effectiveness of the online RNN estimate for unknown dynamics and external disturbances.

Memory Augmented Neural Network-Based Intelligent Adaptive Fault Tolerant Control for a Class of Launch Vehicles Using Second-Order Disturbance Observer

This paper focuses on the MANN-based intelligent adaptive fault tolerant control for a class of launch vehicles. Firstly, the attitude dynamic model of the launch vehicles suffering from the actuator faults and disturbances has been formulated. Secondly, the second-order disturbance observer has been designed for the launch vehicle to achieve the exact estimation and compensation of the time-varying disturbances. Meanwhile, the MANN has been introduced as online approximator, suppressing the adverse influence of the unknown nonlinearities. Moreover, several adaptive laws have been proposed to achieve the quick response to the actuator faults and the update of the MANN weights. As a result, the MANN-based intelligent adaptive fault tolerant control structure has been constructed for the launch vehicles. It has been proven that all the signals in the closed-loop system are bounded. Simulation results demonstrate the desired performance and the advantages of the proposed control algorithm.

Optimal Tracking Control for PMSM With Partially Unknown Dynamics, Saturation Voltages, Torque, and Voltage Disturbances

This article proposes a novel optimal tracking control scheme for permanent magnet synchronous motors (PMSMs) with partially unknown dynamics, saturation voltages, and disturbances in both speed and current dynamics. The strict-feedback nonlinear system is employed to present the PMSM model. Augmented feedforward control inputs are proposed to transform a speed and current tracking control problem of conventional cascade structures to an optimal control problem of a new structure. Consequently, the saturated adaptive optimal control law is designed for the problem. The optimal solution of Hamilton–Jacobi–Issac equation, which provides the value to the control law, is approximated by a simple online approximator. An integral reinforcement learning technique is used to tune the approximator without observing unknown dynamics. It is proven that the optimal value function, the control law, and the worst disturbance law converge to the near-optimal values. The simulation and experiment on a PMSM prototype model of a load drive application with a digital signal processing board TMS320F28379D of Texas Instrument are conducted to justify the effectiveness of the proposed scheme.

Adaptive Neural-Network Control of MIMO Nonaffine Nonlinear Systems With Asymmetric Time-Varying State Constraints.

In this paper, a novel robust adaptive barrier Lyapunov function (BLF)-based backstepping controller has been proposed for a class of interconnected, multi-input-multi-output (MIMO) unknown nonaffine nonlinear systems with asymmetric time-varying (ATV) state constraints. The design involves a neural-network-based online approximator to cope with uncertain dynamics of the system. To tune its weights, a novel adaptive law is proposed based on the Hadamard product. A theorem has also been proposed to have the bounds on virtual control signals beforehand. This theorem eliminates the need for tedious offline computation for the feasibility condition on the virtual controller in BLF-based controller design. To overcome the problem of unknown control gain in the nonaffine system, Nussbaum gain has been used during the design. A simulation study on the robot manipulator in task space has been performed to illustrate the effectiveness of the proposed methodology.

Authors’ Reply to “Comments on “A Novel Fault Diagnosis and Prediction Scheme Using a Nonlinear Observer With Artificial Immune System as an Online Approximator””

We realized that the statement of [1, Th. 2] must be revised since the mathematical derivations shown in [1, eq. (A.8)] only guarantees the first difference of the Lyapunov equation to be uniformly ultimately bounded (UUB) [2] without an additional stringent assumption which was inadvertently omitted. Therefore, in this note, we have revised the statement of Theorem 2 , and only included the part of the proof that renders boundedness. In addition, we have provided clarifications regarding the use of Lemma 1. No other change is needed in other parts of the paper.

Comments on “A Novel Fault Diagnostics and Prediction Scheme Using a Nonlinear Observer With Artificial Immune System as an Online Approximator”

In this letter, we point out that the asymptotic convergence, claimed in Theorem 2 , of the output residual and parameter estimation error after fault occurrence are guaranteed by the performance of the fault diagnosis observer is not quite right. The proof of the asymptotic convergence is contributed by Lemma 1 and negative semidefiniteness of the first difference of Lyapunov candidate function. Here, it is shown that utilizing Lemma 1 yields in some disputed points in the proof of Theorem 2 . On the other hand, the proof of Theorem 2 is not mathematically correct. Therefore, the guarantee of the asymptotic convergence mentioned for FD observer in Theorem 2 is not realizable.

Output Feedback-Based Boundary Control of Uncertain Coupled Semilinear Parabolic PDE Using Neurodynamic Programming.

In this paper, neurodynamic programming-based output feedback boundary control of distributed parameter systems governed by uncertain coupled semilinear parabolic partial differential equations (PDEs) under Neumann or Dirichlet boundary control conditions is introduced. First, Hamilton-Jacobi-Bellman (HJB) equation is formulated in the original PDE domain and the optimal control policy is derived using the value functional as the solution of the HJB equation. Subsequently, a novel observer is developed to estimate the system states given the uncertain nonlinearity in PDE dynamics and measured outputs. Consequently, the suboptimal boundary control policy is obtained by forward-in-time estimation of the value functional using a neural network (NN)-based online approximator and estimated state vector obtained from the NN observer. Novel adaptive tuning laws in continuous time are proposed for learning the value functional online to satisfy the HJB equation along system trajectories while ensuring the closed-loop stability. Local uniformly ultimate boundedness of the closed-loop system is verified by using Lyapunov theory. The performance of the proposed controller is verified via simulation on an unstable coupled diffusion reaction process.

Decentralized fault tolerant control of a class of nonlinear interconnected systems

In this paper, a novel decentralized fault tolerant controller (DFTC) is proposed for interconnected nonlinear continuous-time systems by using local subsystem state vector alone in contrast with traditional distributed fault tolerant controllers or fault accommodation schemes where the measured or the estimated state vector of the overall system is needed. The proposed decentralized controller uses local state and input vectors and minimizes the fault effects on all the subsystems. The DFTC in each subsystem includes a traditional controller term and a neural network based online approximator term which is used to deal with the unknown parts of the system dynamics, such as fault and interconnection terms. The stability of the overall system with the proposed DFTC is investigated by using Lyapunov approach and the boundedness of all signals is guaranteed in the presence of a fault. Therefore, the proposed controller enables the system to continue its normal operation after the occurrence of a fault, as long as it does not cause failure or break down of a component. Although the decentralized fault tolerant controller is designed mainly for large-scale systems where continuous transmissions between subsystems is not possible, it can also be applied to small-scale systems where sensor measurements are available for use in all subsystems. Finally the proposed methods are verified and compared in simulation environment.

Fault detection and identification for a class of nonlinear systems with model uncertainty

In this paper, we present a novel fault detection and identification (FDI) scheme for a class of nonlinear systems with model uncertainty. At the heart of this approach is an on-line approximator, referred to as fault tracking approximator (FTA). Differently from the other approximators, the FTA uses iterative algorithms to detect and identify nonlinear system faults, even in the presence of model uncertainty, which is motivated by predictive control theory and iterative learning control theory. The FTA can simultaneously detect and identify the shape and magnitude of the faults. The rigorous stability analysis and fault tracking properties of the FTA are also proved. Finally, two examples are given to illustrate the feasibility and effectiveness of the proposed approach.

Adaptive Neural Control of Nonaffine Systems With Unknown Control Coefficient and Nonsmooth Actuator Nonlinearities.

This brief considers the asymptotic tracking problem for a class of high-order nonaffine nonlinear dynamical systems with nonsmooth actuator nonlinearities. A novel transformation approach is proposed, which is able to systematically transfer the original nonaffine nonlinear system into an equivalent affine one. Then, to deal with the unknown dynamics and unknown control coefficient contained in the affine system, online approximator and Nussbaum gain techniques are utilized in the controller design. It is proven rigorously that asymptotic convergence of the tracking error and ultimate uniform boundedness of all the other signals can be guaranteed by the proposed control method. The control feasibility is further verified by numerical simulations.

Adaptive control of variable-speed wind energy conversion systems with inaccurate wind speed measurement

This paper deals with the power acquisition control of variable-speed wind energy conversion systems under inaccurate wind speed measurements. The control goal is to optimize the power capture from wind by tracking the maximum power curve. Firstly, the controller is designed for the case with known aerodynamic torque, which is a common assumption in many literatures. In this controller, the need for the exact knowledge of the system model is waived by using adaptive technologies. The chattering phenomenon in the generator torque, which can result in high mechanical stress, is avoided by adopting a modified robust term. Then, by utilizing an online approximator to learn an auxiliary term induced by the uncertain aerodynamics, the need for the exact knowledge of the aerodynamic torque is waived. Both of the proposed controllers are capable of providing good performance under inaccurate wind speed measurements. The control objective is obtained in the sense that the tracking error is guaranteed to converge to an arbitrarily small set. It is theoretically proved that all the signals in the closed-loop system are bounded via Lyapunov synthesis. Finally, the performance of our proposed controller is shown by simulating on a 1.5 MW three-blade wind turbine using the FAST (Fatigue, Aerodynamics, Structures, and Turbulence) code developed by the National Renewable Energy Laboratory.

Zero-Sum Two-Player Game Theoretic Formulation of Affine Nonlinear Discrete-Time Systems Using Neural Networks

In this paper, the nearly optimal solution for discrete-time (DT) affine nonlinear control systems in the presence of partially unknown internal system dynamics and disturbances is considered. The approach is based on successive approximate solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which appears in optimal control. Successive approximation approach for updating control and disturbance inputs for DT nonlinear affine systems are proposed. Moreover, sufficient conditions for the convergence of the approximate HJI solution to the saddle point are derived, and an iterative approach to approximate the HJI equation using a neural network (NN) is presented. Then, the requirement of full knowledge of the internal dynamics of the nonlinear DT system is relaxed by using a second NN online approximator. The result is a closed-loop optimal NN controller via offline learning. A numerical example is provided illustrating the effectiveness of the approach.

A model-based fault prognostics scheme for uncertain non-linear discrete-time systems with multiple distinct faults

In this paper, an online prognostics framework is proposed for a class of uncertain non-linear discrete-time systems with multiple faults affecting the system state with all the states being considered measurable. Multiple faults imply that each system state is affected by several faults at the same time provided the faults are separable. In this framework, multiple faults (incipient or a combination of incipient faults) are detected by using the proposed fault detection (FD) estimator, which consists of an online approximator in discrete time and a robust adaptive term. Subsequently, the fault isolation (FI) module is initiated such that each state of the FI observer corresponds to a particular fault type in the case of single fault or fault combination in the case of multiple faults. The faults will be isolated successfully when the corresponding FI state residuals converge to zero in contrast with other FI schemes where they guarantee only boundedness. In addition, multiple isolation estimators are not required here since a decision scheme is utilized by using FD and FI estimators to determine the fault location, type and number of faults that occurred. Suitable mathematical conditions are derived to show the class of faults that could be isolated. Time to failure is determined by using the parameter update law of the FI estimator and the failure thresholds. Finally, a simulation example is used to demonstrate the proposed prognostics scheme.

Adaptive Power Capture Control of Variable-Speed Wind Energy Conversion Systems With Guaranteed Transient and Steady-State Performance

This paper deals with the power capture control of variable-speed wind energy conversion systems. The control objective is to optimize the capture of wind energy by tracking the desired power output. Arbitrary steady-state performance is achieved in the sense that the tracking error is guaranteed to converge to any predefined small set. In addition, to maximize the wind energy capture, transient performance is enhanced such that the convergence rate can be larger than an arbitrary value, which further limits the maximum overshoot. First, an adaptive controller is designed for the case where known aerodynamic torque is assumed. Then, by utilizing an online approximator to estimate the uncertain aerodynamics, the need for the exact knowledge of the aerodynamic torque is waived to imitate the practical experience. With the aid of a novel output error transformation technique, both of the proposed controllers are capable of shaping the system performance arbitrarily on transient and steady-state stages. Meanwhile, it is also proved that all the signals in the closed-loop system are bounded via Lyapunov synthesis. Finally, the feasibility of the proposed controllers is demonstrated on an 1.5-MW three-blade wind turbine using the FAST (Fatigue, Aerodynamics, Structures, and Turbulence) code developed by the National Renewable Energy Laboratory.

Fixed Final Time Optimal Adaptive Control of Linear Discrete-Time Systems in Input-Output form

Abstract In this paper, the fixed final time adaptive optimal regulation of discrete-time linear systems with unknown system dynamics is addressed. First, by transforming the linear systems into the input/output form, the adaptive optimal control design depends only on the measured outputs and past inputs instead of state measurements. Next, due to the time-varying nature of finite-horizon, a novel online adaptive estimator is proposed by utilizing an online approximator to relax the requirement on the system dynamics. An additional error term corresponding to the terminal constraint is defined and minimized overtime. No policy/value iteration is performed by the novel parameter update law which is updated once a sampling interval. The proposed control design yields an online and forward-in-time solution which enjoys great practical advantages. Stability of the system is demonstrated by Lyapunov analysis while simulation results verify the effectiveness of the propose approach

A Novel Fault Diagnostics and Prediction Scheme Using a Nonlinear Observer With Artificial Immune System as an Online Approximator

In this paper, an observer-based fault diagnostics and prediction (FDP) scheme for a class of nonlinear discrete-time systems via output measurements is introduced by using artificial immune system (AIS) and a robust adaptive term. Traditionally, AIS was considered as an offline tool for system identification and pattern recognition whereas here AIS is utilized as an online approximator in discrete-time (OLAD) in a fault detection (FD) observer. A fault is detected when the output residual exceeds a predefined threshold. Upon detection, the OLAD is initiated to learn the unknown fault dynamics online while the robust adaptive term ensure asymptotic convergence of the output residual for a state fault whereas a bounded result for an output fault. Additionally, a mathematical equation is introduced to estimate the time-to-failure (TTF) by using the output residual and the estimated fault parameters. Finally, the performance of the proposed FDP scheme is demonstrated on an axial piston pump hardware test-bed.

Universal neural network control of MIMO uncertain nonlinear systems.

In this brief, a continuous tracking control law is proposed for a class of high-order multi-input-multi-output uncertain nonlinear dynamic systems with external disturbance and unknown varying control direction matrix. The proposed controller consists of high-gain feedback, Nussbaum gain matrix selector, online approximator (OLA) model and a robust term. The OLA model is represented by a two-layer neural network. The continuousness of the control signal is guaranteed to relax the requirement for the actuator bandwidth and avoid the incurred chattering effect. Asymptotic tracking performance is achieved theoretically by standard Lyapunov analysis. The control feasibility is also verified in simulation environment.