Unknown Ideal Controller Research Articles

Finite-time output-feedback fault tolerant adaptive fuzzy control framework for a class of MIMO saturated nonlinear systems

This paper presents a finite-time fault-tolerant fuzzy adaptive controller for uncertain interconnected nonlinear systems in strict-feedback form. The controller addresses input saturation, state-dependent actuator faults, external disturbances, and unavailable states for measurement. To avoid any unexpected alteration due to failures, the proposed control scheme design addresses all types of actuator faults that are bias, drift, and loss of accuracy as additive faults, as well as a multiplicative fault that results in loss of effectiveness with nonaffine state-dependency. Restrictions on control gains and unmatched interconnections are eliminated, and the explosion complexity caused by recursive back-stepping designs is avoided. Fuzzy Systems approximate the unknown ideal control laws along side the acutator faults and disturbances. The stability analysis guarantees that tracking errors converge to a small compact set around the origin in finite time. Simulation results on a quad-rotor UAV and a mathematical system confirm the effectiveness of the proposed approach.

Finite-time event-triggered output-feedback adaptive decentralized echo-state network fault-tolerant control for interconnected pure-feedback nonlinear systems with input saturation and external disturbances: A fuzzy control-error approach

In this paper, we introduce a decentralized Event-Triggered fault-tolerant echo-state network (ESN) direct adaptive controller for uncertain interconnected nonlinear systems in pure-feedback form. The proposed controller addresses input saturation, actuator faults, external disturbances, and unavailable states for measurement. Unlike the existing works in the literature that adapts the ESN weights using the tracking error, our method employs the control error that is estimated using a fuzzy inference system, to derive the adaptation laws. The complexity explosion typically seen with recursive back-stepping and Dynamic Surface Control (DSC) designs is completely avoided. Our control scheme addresses four types of state-dependent actuator faults: bias, drift, loss of accuracy, as well as loss of effectiveness. The ESNs approximate unknown ideal control laws, while robust terms are added to enhance the stability of the closed-loop system. Stability analysis ensures that tracking errors converge, in finite time, to a small compact set near the origin due to the strictly positive real (SPR) property. Simulation results of a quadrotor UAV and a mathematical system are presented. A comparative analysis is performed with another approach to emphasize the effectiveness of the proposed method.

Neural network‐based output‐feedback adaptive control for a class of uncertain strict feedback fractional‐order nonlinear systems subject to input saturation

SummaryThis paper presents neural networks (NNs) adaptive controller for an uncertain fractional‐order nonlinear system in strict‐feedback form, subject to input saturation, unavailable states for measurement, and external disturbances. The fractional‐order adaptive laws are derived based only on the output tracking error thanks to the implementation of the strictly positive real (SPR) property, differently from the existing results in the literature of fractional‐order strict‐feedback systems where all system states are used in the adaptive laws. The proposed design approach addresses the nonaffine nature of the control input due to saturation nonlinearity by using the mean value theorem and follows a nonrecursive design by using a state transformation where the advantage is twofold. First, it eliminates the explosion complexity found in back‐stepping control‐based approaches design, and second, it reduces the approximators units and parameters in controller implementation. Furthermore, an observer is introduced to estimate the unavailable newly defined states, and then an output adaptive feedback control design is ensured. An NN is used to approximate the unknown ideal control law, and an auxiliary control term is appended to deal with saturation effect, unknown disturbance, and approximation errors. The tracking error is proved to converge asymptotically to a bounded set using the Lyapunov theory. Simulation results on three examples show the effectiveness of the proposed approach.

Decentralized event‐triggered output feedback adaptive neural network control for a class of MIMO uncertain strict‐feedback nonlinear systems with input saturation

SummaryFor a class of multiple‐input multiple‐output large‐scale nonlinear systems in strict‐feedback form with input saturation, external disturbances and immeasurable states, an adaptive decentralized neural network (NN) control strategy on the basis of event triggered mechanism is investigated in this article. In contrast to the literature, the proposed method is centered on the control‐error as a replacement to the tracking‐error that leads to a simplified derivation approach of adaptive laws. Furthermore, the control gains for this class of systems are considered unknown nonlinear functions and not assumed as simple unity or known gains as always done in the literature. Moreover, the challenge of losing controllability that typically arises in state transformation‐based methods, as reported in the literature, is entirely resolved in our approach. Last and not least, all restrictions imposed on unmatched interconnections are eliminated along with avoiding the complexity explosion caused by recursive back‐stepping designs. For this end, the unknown ideal control laws are approximated using NNs, while additional control terms are added to handle saturation effects, unknown interactions, and approximation errors. Additionally, fuzzy inference systems are employed to estimate unknown control errors. Due to the strictly positive real property, the tracking errors are proved to belong to a small compact set using Lyapunov theory. Simulation results demonstrate the effectiveness of the proposed approach.

Data-driven adaptive compensation control for a class of nonlinear discrete-time system with bounded disturbances

This paper considers the compensation control problem for a class of nonlinear discrete-time systems subject to bounded disturbances. With the help of the dynamic linearization technique (DLT), an equivalent data model to the unknown disturbed controlled plant is first established. Based on the data model, two data-driven controllers are designed through novel disturbance-related compact-form and partial-form DLT, which are equivalent to the unknown ideal compensation controller in theory. Adaptive gains designed for the proposed controllers are time-varying and are adaptively updated by directly utilizing the I/O data without involving any model information of the controlled plant, making both controllers purely data-driven adaptive disturbance compensation controllers. Further, in practice, unmeasurable disturbances are commonly encountered due to expensive measuring instruments, unreliable performance or large lags. Therefore, both proposed control laws provide solutions for measurable disturbance (MD) and unmeasurable disturbance (UD) in a unified framework, where the time-varying adaptive gains fuse more system dynamics when disturbance is completely unknown except for some boundedness. The stability of the proposed controllers are strictly guaranteed, and their effectiveness and applicability are verified by a numerical simulation and a distillation column.

A Data-Driven ILC Framework for a Class of Nonlinear Discrete-Time Systems.

In this article, we propose a data-driven iterative learning control (ILC) framework for unknown nonlinear nonaffine repetitive discrete-time single-input-single-output systems by applying the dynamic linearization (DL) technique. The ILC law is constructed based on the equivalent DL expression of an unknown ideal learning controller in the iteration and time domains. The learning control gain vector is adaptively updated by using a Newton-type optimization method. The monotonic convergence on the tracking errors of the controlled plant is theoretically guaranteed with respect to the 2-norm under some conditions. In the proposed ILC framework, existing proportional, integral, and derivative type ILC, and high-order ILC can be considered as special cases. The proposed ILC framework is a pure data-driven ILC, that is, the ILC law is independent of the physical dynamics of the controlled plant, and the learning control gain updating algorithm is formulated using only the measured input-output data of the nonlinear system. The proposed ILC framework is effectively verified by two illustrative examples on a complicated unknown nonlinear system and on a linear time-varying system.

Data-Driven Iterative Learning Control for Nonlinear Discrete-Time MIMO Systems.

This article considers the tracking control of unknown nonlinear nonaffine repetitive discrete-time multi-input multi-output systems. Two data-driven iterative learning control (ILC) schemes are designed based on two equivalent dynamic linearization data models of an unknown ideal learning controller, which exists theoretically in the iteration domain. The two control schemes provide ways of selecting learning controllers based on the complexity of the controlled nonlinear systems. The learning control gain matrixes of the two learning controllers are optimized through the steepest descent method using only the measured input-output data of the nonlinear systems. The proposed ILC approaches are pure data-driven since no model information of the controlled systems is involved. The stability and convergence of the proposed ILC approaches are rigorously analyzed under reasonable conditions. Numerical simulation and an experiment based on a Gantry-type linear motor drive system are conducted to verify the effectiveness of the proposed data-driven ILC approaches.

Fault-Tolerant Adaptive Fuzzy Tracking Control for Nonaffine Fractional-Order Full-State-Constrained MISO Systems With Actuator Failures.

The problem of fault-tolerant adaptive fuzzy tracking control against actuator faults is investigated in this article for a type of uncertain nonaffine fractional-order nonlinear full-state-constrained multi-input-single-output (MISO) system. By means of the existence theorem of the implicit function and the intermediate value theorem, the design difficulty arising from nonaffine nonlinear terms is surmounted. Then, the unknown ideal control inputs are approximated by using some suitable fuzzy-logic systems. An adaptive fuzzy fault-tolerant control (FTC) approach is developed by employing the barrier Lyapunov functions and estimating the compounded disturbances. Moreover, under the drive of the reference signals, a sufficient condition ensuring semiglobal uniform ultimate boundedness is obtained for all the signals in the closed-loop system, and it is proved that all the states of nonaffine nonlinear fractional-order systems are guaranteed to remain inside the predetermined compact set. Finally, two numerical examples are provided to exhibit the validity of the designed adaptive fuzzy FTC approach.

Adaptive Fuzzy Control for Multivariable Nonlinear Systems with Indefinite Control Gain Matrix and Unknown Control Direction

Abstract In this paper, we focus on the direct adaptive fuzzy control design for a class of uncertain MIMO nonlinear systems with indefinite control gain matrix and unknown control direction. The control design is based on the approximation of an unknown ideal control law that can meet the control objective by using fuzzy systems. The adjustable parameters of the used fuzzy systems are adjusted online using the error between the unknown ideal controller and the fuzzy controller. In this paper, unlike most existing works, the Nussbaum gain technique is not used to overcome the obstacle of the unknown control direction. In fact, with the help of a matrix decomposition technique, the unknown control direction is redefined as an unknown constant vector, which is estimated online by a suitable update law. The stability of the closed-loop system is studied using the Lyapunov direct approach. Numerical simulation results are provided to illustrate the effectiveness of the proposed control design approach.

Adaptive neural networks event-triggered fault-tolerant consensus control for a class of nonlinear multi-agent systems

This paper studies the event-triggered fault-tolerant control problem of nonlinear multi-agent systems. The goal is to ensure the stability of event-based sampling multi-agent systems when the actuator faults occurs. The neural networks approximate property is used to approximate unknown ideal control parameters, which can reduce the exact requirements of control parameters. Based on the states information of neighboring agents, a distributed fault-tolerant consensus controller is designed for the leaderless multi-agent systems. Moreover, an event-triggered mechanism with special definition of event-triggered error is applied to reduce the amount of communications. In addition, the Zeno behaviour is avoided. By using Lyapunov stability theory, it is proved that all signals are bounded in the closed-loop systems. Finally, a numerical simulation result is presented to prove the effectiveness of the proposed method.

Direct Adaptive Fuzzy Control of Nonlinear Descriptor Systems

This paper deals with direct adaptive fuzzy control for uncertain affine nonlinear descriptor systems. Two cases are considered: in the first one, it is assumed that the control gain is known, while in the second one, it is an unknown-but-bounded symmetric positive definite matrix. To account for uncertainties in the system dynamics, a fuzzy system is employed to directly approximate the unknown ideal controller. The adjustable parameters of the fuzzy system are updated by either a Lyapunov-based adaptative law in the first case, or a gradient descent algorithm minimizing a suitable quadratic cost function in the second case. Furthermore, an auxiliary compensating signal is designed to guarantee that the tracking error asymptotically vanishes in both cases. Simulation results show how the proposed methods exhibit satisfactory performance thus demonstrating their effectiveness.

Adaptive fuzzy control method for a linear switched reluctance motor

A new direct adaptive fuzzy speed control method for a linear switched reluctance motor with unknown control gain sign is presented. The proposed control system consists of two parts: a fuzzy system and an adaptive law. Fuzzy system approximates an unknown ideal control law with unknown adjustable parameters. After determination of the control law, an appropriate adaptation law is designed to update the adjustable parameters to achieve control objectives. The adaptation law is designed using the error between the unknown ideal control law and fuzzy control law. Unlike previous works, in this study, the unknown control gain sign is taken as an unknown constant parameter and is determined online by an appropriate adaptation law. Proposed control method along with a fuzzy sliding mode speed control and a proportional integral speed control strategies are experimentally studied and the performance index is used to evaluate each strategy. The robustness of the proposed method to the parameters and external load force change has been verified via simulation and experiments. The results indicate that the proposed control method has an acceptable performance.

Adaptive Reinforcement Learning Control Based on Neural Approximation for Nonlinear Discrete-Time Systems With Unknown Nonaffine Dead-Zone Input.

In this paper, an optimal control algorithm is designed for uncertain nonlinear systems in discrete-time, which are in nonaffine form and with unknown dead-zone. The main contributions of this paper are that an optimal control algorithm is for the first time framed in this paper for nonlinear systems with nonaffine dead-zone, and the adaptive parameter law for dead-zone is calculated by using the gradient rules. The mean value theory is employed to deal with the nonaffine dead-zone input and the implicit function theory based on reinforcement learning is appropriately introduced to find an unknown ideal controller which is approximated by using the action network. Other neural networks are taken as the critic networks to approximate the strategic utility functions. Based on the Lyapunov stability analysis theory, we can prove the stability of systems, i.e., the optimal control laws can guarantee that all the signals in the closed-loop system are bounded and the tracking errors are converged to a small compact set. Finally, two simulation examples demonstrate the effectiveness of the design algorithm.

Adaptive Fuzzy PID Control for a Class of Uncertain MIMO Nonlinear Systems with Dead-zone Inputs’ Nonlinearities

This paper proposes an adaptive fuzzy PID control for a class of multi-input multi-output disturbed nonlinear systems with unknown dynamics and unknown dead-zone inputs’ nonlinearities. Within this scheme, a fuzzy system is used in order to approximate the PID gains instantaneously according to whole control system objective. Specifically, a gradient descent algorithm is used to update online the fuzzy system parameters such that the error between the fuzzy PID control and the unknown ideal control converges to an adjustable region. The control design and the stability analysis of the closed-loop system are given by the Lyapunov approach. The effectiveness of the proposed controller is highlighted by simulated examples .

Adaptive Fuzzy Control for a Class of Multivariable Nonlinear Systems with Unknown Control Direction

In this paper, a direct adaptive fuzzy control scheme is presented for a class of uncertain MIMO nonlinear systems with unknown sign of the control gain matrix. Within this scheme, fuzzy systems are employed to approximate an unknown ideal controller which can achieve the control objectives. The free parameters of the used fuzzy systems are adjusted online using the error between the unknown ideal controller and the fuzzy controller. Unlike previous works, the Nussbaum function technique is not used to deal with the unknown sign of the control gain matrix. In fact, in this paper, the unknown control direction is considered as an unknown constant parameter and it is estimated online by an appropriate adaptation law. The stability of the closed-loop system is analyzed using a Lyapunov approach. Simulation results are given to demonstrate the effectiveness of the proposed control design.

An Overview of Dynamic-Linearization-Based Data-Driven Control and Applications

A brief overview on the model-based control and data-driven control methods is presented. The data-driven equivalent dynamic linearization, as a foundational analysis tool of data-driven control methods for discrete-time nonlinear systems, is introduced in detail with motivations and distinct features. The prototype model-free adaptive control schemes by using the dynamic linearization to an unknown nonlinear plant model, as well as the alternative model-free adaptive control methods by using the dynamic linearization to an unknown ideal nonlinear controller, are discussed. Furthermore, the extensions of the dynamic linearization to unknown nonlinear repetitive systems and the corresponding model-free adaptive iterative learning control methods are also overviewed and summarized. This work highlights the characteristics and comments of the different model-free adaptive control schemes in detail to facilitate the understanding of the readers. Finally, some perspectives on data-driven control methods in information-rich age are given.

An ℒ1 fuzzy adaptive controller for a class of SISO nonaffine nonlinear systems: application to the control of an electropneumatic actuator

This paper proposes an ℒ1 fuzzy adaptive controller for a class of uncertain continuous-time single-input single-output nonaffine nonlinear systems. The structure of this controller is derived based on ℒ1 adaptive control design methodology and integrates a fuzzy system. The latter is used to approximate as best as possible a function of an unknown ideal implicit controller, which provides good results and improves the performance significantly. The ℒ1 fuzzy adaptive controller consists of a predictor, a control law and its adaptive laws. The major advantage of the proposed control scheme is its ability to guarantee uniformly bounded transient and tracking performance for the controlled system. These performance bounds can be rendered arbitrarily small by the systematic choice of design parameters. The effectiveness and feasibility of the proposed ℒ1 fuzzy adaptive controller are examined experimentally in the position control of a pneumatic actuator system.

Design and experimentation of an observer‐based linear adaptive control applied to an electropneumatic actuator

This study proposes an observer-based linear adaptive control scheme for the position control of a pneumatic actuator system. The proposed controller does not rely on a physical model of the pneumatic actuator system to be controlled; it only needs the position measurement for its implementation, which is really a novelty in the field of such applications. First, based on the implicit function theory, the existence of an ideal position controller is demonstrated. Then, the objective is to construct this unknown ideal position controller using a linear control with a stable adaptation law and an extended observer. This latter is used to estimate both the tracking error vector and an unknown function of the error between the implicit ideal control and the actual control which is used in the adaptation mechanism. The stability of the overall closed-loop system is studied by using singular perturbation theory and Tikhonov's theorem. Finally, real-time experimental results are provided to show the performances of the proposed control scheme.

Observer-based adaptive robust control of nonlinear nonaffine systems with unknown gain sign

In this paper, a direct adaptive robust controller for a class of SISO nonaffine nonlinear systems is presented. The existence of an ideal controller is proved based on the Implicit Function Theorem. Since the Implicit Function Theorem only guarantees the existence of the controller and does not provide a way to construct it, a neural network is employed to approximate the unknown ideal controller. In addition, an observer is designed to estimate the system states because all the states may not be available for measurements. In this method, a priori knowledge about the sign of control gain is not required and, in order to cope with unknown control direction, the Nussbaum-type technique is used. Moreover, only one adaptive parameter is needed to be updated and also a robust term is used in the control signal to reduce the effect of external disturbances and approximation errors. Furthermore, the stability analysis for the closed-loop system is presented based on the Lyapunov stability method. Theoretical results are illustrated through a simulation example. These simulations show the effectiveness of the proposed method.

Design and experimentation of a self-tuning PID control applied to the 3DOF helicopter

Abstract The paper presents design and experimental validation of a stable self-tuning PID controller for three degrees of freedom (3-DOF) helicopter. At first, it is proposed a self-tuned proportional-integral-derivative (PID) controller for a class of uncertain second order multiinput multi-output nonlinear dynamic systems to which the 3-DOF helicopter dynamic model belongs. Within this scheme, the PID controller is employed to approximate unknown ideal controller that can achieve control objectives. PID controller gains are the adjustable parameters and they are updated online with a stable adaptation mechanism designed to minimize the error between the unknown ideal controller and the used by PID controller. The stability analysis of the closed-loop system is performed using Lyapunov approach. It is proven that all signals in the closed-loop system are uniformly ultimately bounded. The proposed approach can be regarded as a simple and effective model-free control since the mathematical model of the system is assumed unknown. Experimental results are presented to verify the effectiveness of the proposed controller.