Indirect Adaptive Control Scheme Research Articles

Nonlinear dynamical system approximation and adaptive control based on hybrid‐feed‐forward recurrent neural network: Simulation and stability analysis

AbstractWe proposed an online identification and adaptive control framework for the nonlinear dynamical systems using a novel hybrid‐feed‐forward recurrent neural network (HFRNN) model. The HFRNN is a combination of a feed‐forward neural network (FFNN) and a local recurrent neural network (LRNN). We aim to leverage the simplicity of FFNN and the effectiveness of RNN to capture changing dynamics accurately and design an indirect adaptive control scheme. To derive the weights update equations, we have applied the gradient‐descent‐based Back‐Propagation (BP) technique, and the stability of the proposed learning strategy is proven using the Lyapunov stability principles. We also compared the proposed method's results with those of the Jordan network‐based controller (JNC) and the local recurrent network‐based controller (LRNC) in the simulation examples. The results demonstrate that our approach performs satisfactorily, even in the presence of disturbance signals.

Double Dynamic Linearization-Based Higher Order Indirect Adaptive Iterative Learning Control.

In this article, a higher order indirect adaptive iterative learning control (HO-iAILC) scheme is developed for nonlinear nonaffine systems. The inner loop adopts a P -type controller whose set-point is updated iteratively by learning from the iterations. To this end, an ideal nonlinear learning control law is designed in the outer loop. It is then transferred to a linear parametric-learning controller with a corresponding parameter estimation law by introducing an iterative dynamic linearization (IDL) method. This IDL method is also used to gain an iterative linear data model of the nonlinear system. A parameter iterative updating algorithm is utilized for estimating the unknown parameters of the obtained linear data model. Finally, the HO-iAILC is presented that utilizes additional error information to improve the control performance and employs two iterative adaptive mechanisms to deal with uncertainties. The convergence of the proposed HO-iAILC scheme is proved by using two basic mathematical tools, namely: 1) contraction mapping and 2) mathematical induction. Simulation studies are conducted for the verification of the theoretical results.

Enhanced P-Type Control: Indirect Adaptive Learning From Set-Point Updates

In this article, an indirect adaptive iterative learning control (iAILC) scheme is proposed for both linear and nonlinear systems to enhance the P-type controller by learning from set points. An adaptive mechanism is included in the iAILC method to regulate the learning gain using input–output measurements in real time. An iAILC method is first designed for linear systems to improve control performance by fully utilizing model information if such a linear model is known exactly. Then, an iterative dynamic linearization (IDL)-based iAILC is proposed for a nonlinear nonaffine system, whose model is completely unknown. The IDL technique is employed to deal with the strong nonlinearity and nonaffine structure of the systems such that a linear data model can be attained consequently for the algorithm design and performance analysis. The convergence of the developed iAILC schemes is proved rigorously, where contraction mapping, two-dimensional (2-D) Roesser’s system theory, and mathematical induction are employed as the basic analysis tools. Simulation studies are provided to verify the developed theoretical results.

Indirect adaptive control of multi-input-multi-output nonlinear singularly perturbed systems with model uncertainties

In this paper, two indirect adaptive control schemes for a class of multi-input-multi-output nonlinear singularly perturbed systems with partially unknown models and parameters are presented. Firstly, the original system dynamic equation is reformulated into a new form with identity control gain matrices, and a new multi-time-scale singularity-free neural network is employed to represent the new dynamic equation. Subsequently, an online identification scheme is proposed to update neural network weights where a set of auxiliary weight error vectors are used such that better convergence property can be achieved. Based on identification results, a singularity-free singular perturbation controller is developed to control the unknown nonlinear system. By using the singularity-free neural network and singular perturbation technique, the complexity in controller design for a singularly perturbed system is reduced, and the potential singularity problem is avoided. Moreover, a singularity-free dynamic surface control scheme is also proposed, and the “explosion of complexity” issue is relieved. Compared to conventional direct adaptive dynamic surface control schemes which use gradient-like updating laws and tracking errors to train the neural networks, the singularity-free dynamic surface controller is designed indirectly and the neural networks are updated using the identification errors. Therefore, better identification and control performance is achieved, and the potential singularity problem is also circumvented. The stability of the closed-loop system is rigorously proved via the Lyapunov approach, and the effectiveness of proposed identification and control schemes is demonstrated by simulations.

Stability analysis of adaptive control using fuzzy adapting rate neural emulator: Experimental validation on a thermal process

In this study, an adaptive control based on fuzzy adapting rate for neural emulator of nonlinear systems having unknown dynamics is proposed. The indirect adaptive control scheme is composed by the neural emulator and the neural controller which are connected by an autonomous algorithm inspired from the real-time recurrent learning. In order to ensure stability and faster convergence, a neural controller adapting rate is established in the sense of the continuous Lyapunov stability method. Numerical simulations are included to illustrate the effectiveness of the proposed method. The performance of the proposed control strategy is also demonstrated through an experimental simulation.

Direct Adaptive Fuzzy Control Scheme With Guaranteed Tracking Performances for Uncertain Canonical Nonlinear Systems

In our recent work, we propose an indirect adaptive fuzzy control scheme for uncertain unparametrizable nonlinear systems, which ensures that the number of adaptive laws does not increase with the number of fuzzy rules, and the time derivative of the chosen Lyapunov function is negative semidefinite. However, the scheme involves a class of high-order smooth functions and their time derivatives, which can make the controller structure become sophisticated especially when the relative degree of system is quite large. To overcome this problem, in the article, we propose a new direct adaptive fuzzy control scheme based on a class of reduced-order smooth functions. With the scheme, no partial-derivative term is involved in controller and virtual controllers, only one adaptive law is used regardless of the increase of fuzzy rules, and also the time derivative of Lyapunov function can be ensured negative semidefinite. It is proved that all closed-loop signals are bounded, and the output tracking error converges to a prescribed interval asymptotically. The transient tracking performance and robustness of the proposed control scheme are also considered. The effectiveness of the obtained results is illustrated by two practical control systems.

Robust indirect adaptive sliding model control for Wiener nonlinear systems

ABSTRACTWiener model structures have attracted considerable attentions due to their powerful modelling abilities to solve industrial problems. This paper considers a new class of Wiener model structure, which consists of a linear transfer function and a radial basis function (RBF) network. Based on this structure, the unstable zero-dynamics, the added disturbances and the approximation errors problems can be dealt with. Since the model parameters are assumed unknown, we develop a new indirect adaptive control scheme. It is a consensus that the certainty equivalence principle is the key that connects the adaptation algorithm with the control law. This paper explains that, for indirect adaptive control of Wiener model, this principle may not be applied directly. The main contribution of this paper is to address this issue by presenting a rigorous theoretical analysis. Representative examples including a simulated pH process control problem are studied to test the control performance. Comparison results indicate that the proposed controller has much wider applicability than some alternative methods, especially for its improved performance and smoother adaptation.

Safety‐constrained robust adaptive control for a class of MIMO non‐linear systems

This study proposes two new safety-constrained robust indirect adaptive control schemes for a class of multi-input multi-output non-linear systems subject to unstructured additive model uncertainties and external disturbances. The controllers are designed using a novel error transformation and a new asymptotically stable closed-loop non-linear error dynamics. The model uncertainties of the actual system are approximated by constructing a neural network-based auxiliary observer dynamics. The weights of the neural network are updated using a robust Lyapunov stable weight update rule. Using the estimation information of model uncertainties, two different asymptotically and finite-time exponentially stable tracking controllers are designed to minimise the error between auxiliary observer states and reference signals. It is proven that the closed-loop states of the actual system will remain bounded by the imposed state constraints and the steady-state tracking error of the system will converge asymptotically (or exponentially in finite time) to a user-defined domain. The beauty of the proposed control designs lies in the fact that they are easy to design and implement, and provide design freedom to impose constraints on an individual component of the system states. The effectiveness of the proposed techniques is shown by controlling a two-link robot manipulator in a constrained environment.

Spacecraft trajectory tracking and parameter estimation around a splitting contact binary asteroid

Increasing interest in asteroid mining and in-situ resource utilization will lead to an increase in asteroid surface operations. The geophysical properties of asteroids are often unknown and play a significant role in the resulting gravitational fields. Surface operations such as mining may significantly alter the asteroid's structure or, in the case of contact binary asteroids, cause the asteroid to split depending on the rotational condition. The coupled problem of estimating unknown parameters of a splitting contact-binary system and controlling a spacecraft's trajectory in the system's vicinity is investigated. An indirect adaptive control scheme is utilized to simultaneously meet both objectives. The results are compared with the traditional 2-body controller and the improvement enabled by the proposed scheme is demonstrated.

Indirect Adaptive Fuzzy Control for Nonaffine Nonlinear Pure-Feedback Systems

In this article, an indirect adaptive fuzzy control scheme is proposed for single-input, single-output (SISO) nonaffine nonlinear systems in a pure-feedback form. In this scheme, the unknown nonlinear functions are approximated by Takagi–Sugeno (T–S) fuzzy logic systems with an state observer. The adaptive laws are developed to adjust the parameters of the fuzzy systems. The stability of the closed-loop system is proved with all state variables being uniformly bounded in the Lyapunov sense and the tracking error is confirmed to zero asymptotically. Finally, simulation results obtained for two practical examples show the feasibility and effectiveness of the proposed scheme.

Synchronization Adaptive Fuzzy Gain Scheduling PID Controller for a Class of MIMO Nonlinear Systems

This paper presents a new Synchronization Adaptive Fuzzy Gain Scheduling PID controller (SAFGS-PIDc) for a class of Multiple-input multiple-output (MIMO) nonlinear systems with uncertainties. To achieve better adaptation properties, weighting factor is adapted to sum together the adaptive fuzzy control scheme and Fuzzy Gain Scheduler PID control (FGS-PIDc) method, such that both controllers can be incorporated at the same time. The FGS adjusts online the parameters of the conventional PID controller, and an Indirect Adaptive Fuzzy control (IAFc) scheme that uses feedback error function as inputs is constructed. In addition, each subsystem of MIMO system is able to adaptively compensate for uncertainties and external disturbance. Also, a robust control term is designed that aims to provide added robustness in the presence of uncertainties. The proposed scheme can overcome the controller singularity problem. While the proposed controller scheme requires the uncertainties to be bounded, it does not require this bound to be known. Thus, this control law can be used for the systems that the system’s models are quite unknown. The proposed method guarantees the stability of the closed-loop system based on Lyapunov theory. Finally, simulation studies demonstrate the usefulness and effectiveness of the proposed technique for controlling nonlinear.

Adaptive Control of Precision Guided Airdrop Systems with Highly Uncertain Dynamics

The bulk of research in the field of precision guided airdrop systems has focused on improving landing accuracy in the presence of atmospheric winds that can exceed vehicle airspeed. One important challenge of parafoil systems is their highly uncertain flight dynamic behavior and control response, which can result from canopy degradation or an offnominal inflation event. This significantly impacts the ability to reach the target and can often lead to very large miss distances. This work addresses guided airdrop system model uncertainty with a novel combined direct and indirect adaptive control strategy to quickly characterize vehicle dynamics and lateral control sensitivity in flight. Extensive simulation and experimental flight testing indicate that the proposed adaptive algorithm is capable of high-accuracy landing in a large variety of degraded conditions, including unknown nonlinear changes in control sensitivity as well as control reversals. In comparison, current industry standard algorithms experience over an order of magnitude decrease in accuracy when tested under identical scenarios.

Design of an indirect adaptive controller for the trajectory tracking of UVMS

For solving the trajectory tracking problem of the underwater vehicle and manipulator system (UVMS) in the presence of dynamic uncertainties and time-varying external disturbances, this paper presents an indirect adaptive control scheme which consists of three parts: an extended Kalman filter (EKF) estimation compensative system, a model-based computed torque controller (CTC), a H∞ robust compensative tracking controller. The contribution of our method is that it can overcome the disadvantages of existing control schemes, which are based on the accurate dynamic model of UVMS, known statistics unmodeled dynamics/external disturbances (e.g., constant or Gaussian), or the accurate, efficient system feedback measurement states by the sensors. According to the Lyapunov stability theorem, it is shown that the proposed indirect adaptive control scheme can guarantee its embedded H∞ robust controller tracking performance for our UVMS. Simulations show that the proposed control scheme can satisfy the design requirements of UVMS in rapid convergence, tracking accuracy, system stability and disturbance attenuation. Therefore, the method presented in this paper can provide a feasible way of controlling the nonlinear UVMS.

Indirect adaptive soft computing based wavelet-embedded control paradigms for WT/PV/SOFC in a grid/charging station connected hybrid power system.

This paper focuses on the indirect adaptive tracking control of renewable energy sources in a grid-connected hybrid power system. The renewable energy systems have low efficiency and intermittent nature due to unpredictable meteorological conditions. The domestic load and the conventional charging stations behave in an uncertain manner. To operate the renewable energy sources efficiently for harvesting maximum power, instantaneous nonlinear dynamics should be captured online. A Chebyshev-wavelet embedded NeuroFuzzy indirect adaptive MPPT (maximum power point tracking) control paradigm is proposed for variable speed wind turbine-permanent synchronous generator (VSWT-PMSG). A Hermite-wavelet incorporated NeuroFuzzy indirect adaptive MPPT control strategy for photovoltaic (PV) system to extract maximum power and indirect adaptive tracking control scheme for Solid Oxide Fuel Cell (SOFC) is developed. A comprehensive simulation test-bed for a grid-connected hybrid power system is developed in Matlab/Simulink. The robustness of the suggested indirect adaptive control paradigms are evaluated through simulation results in a grid-connected hybrid power system test-bed by comparison with conventional and intelligent control techniques. The simulation results validate the effectiveness of the proposed control paradigms.

Identification and Trajectory Tracking Control of Nonlinear Singularly Perturbed Systems

In this paper, a new identification and control scheme using multitime scale recurrent high-order neural networks is proposed to control the singularly perturbed nonlinear systems with uncertainties. First, a novel identification scheme using modified optimal bounded ellipsoid based weight's updating laws is developed to identify the unknown nonlinear systems. By adding two additional terms to the original optimal bounded ellipsoid based weight's updating laws, the new modified identification scheme can achieve high convergence speed due to the adaptively adjusted learning gain at the beginning of the identification process and remain effective during the whole identification process. Based on the identified model, a new indirect adaptive control scheme for trajectory tracking problem using singular perturbation theory is developed, which is different from the control scheme proposed previously that can only be applied to a regulation problem. The closed-loop stability is analyzed and the convergence of system states is guaranteed. Experimental results are presented to demonstrate the effectiveness of the identification and control scheme.

Identification and Adaptive Position Control of Uncertain Two-Mass Systems with Backlash Hard Nonlinearity

This paper presents a novel method for identification and direct and indirect adaptive position control of uncertain two-mass mechanical systems with unknown backlash. The identification process consists of two cascade blocks. The first block is a linear-in-parameter model, and the second block is an iterative algorithm for estimating physical parameters of the shaft. By merging the identification method with an indirect adaptive control strategy, simultaneous identification of the physical parameters and adaptive position control of the load will be applicable. Additionally, a direct adaptive controller based on model reference adaptive control theory is designed to control the position of the load with all unknown physical parameters. The simulation results on a sample two-mass system depict the effectiveness of the identification, direct and indirect adaptive control algorithms.

Flatness-based adaptive neurofuzzy control of induction generators using output feedback

The functioning of doubly-fed induction generators (DFIGs) under harsh and varying conditions makes their control a non-trivial task. The article proposes an adaptive control approach that is capable of compensating for model uncertainty and parametric changes of the DFIG, as well as for lack of measurements for the DFIG's state vector elements. First it is proven that the DFIG's model is a differentially flat one. This means that all its state variables and its control inputs can be written as differential functions of key state variables which are the so-called flat outputs. Moreover, this implies that the flat output and its derivatives are linearly independent. By exploiting differential flatness properties it is shown that the 6-th order DFIG model can be transformed into the linear canonical form. For the latter description, the new control inputs comprise unknown nonlinear functions which can be identified with the use of neurofuzzy approximators. The estimated dynamics of the generator is used by a feedback controller thus establishing an indirect adaptive control scheme. Moreover, to robustify the control loop a supplementary control term is computed using H-infinity control theory. Another problem that has to be dealt with comes from the inability to measure the complete state vector of the generator. Thus, a state-observer is implemented in the control loop. The stability of the considered observer-based adaptive control approach is proven using Lyapunov analysis. Moreover, the performance of the control scheme is evaluated through simulation experiments.

Adaptive Fuzzy Control of a Class of MIMO Nonlinear System With Actuator Saturation for Greenhouse Climate Control Problem

This paper presents an indirect adaptive fuzzy control scheme for a class of MIMO non-affine nonlinear systems with unknown dynamics and actuator saturation for greenhouse climate control problems. The objective is to implement output tracking control on nonlinear systems. Using feedback linearization, control inputs with known control gains are first synthesized by well-modeled dynamics of the system, and Taylor series expansion is used to transform unknown non-affine dynamics into the corresponding affine forms. Fuzzy logic systems (FLS) are introduced to estimate the unknown nonlinearity of the transformed affine system and the saturation nonlinearity due to the actuator constraint. The control inputs corresponding to nonlinearity are constructed based on the estimations. By introducing a robust control term, estimation errors and external disturbances are well handled, so as to guarantee the stability when tracking the control process. The control gain estimation obtained by FLS is modified to avoid singularity. Lyapunov stability analysis is performed to derive the adaptive law. To validate the effectiveness of the proposed control scheme, we apply it to a greenhouse climate control problem. The ventilation rate in the greenhouse model is unknown; therefore, it is estimated by FLS. The simulation exhibits satisfactory results, in which the temperature and humidity inside the greenhouse are well tracked.

An Indirect Adaptive Fuzzy Control Scheme for a Class of Nonlinear Systems

AbstractThis paper presents an indirect adaptive control scheme, for a class of nonlinear systems in controller canonical form. Owing to the universal approximation property of a Takagi–Sugeno (T–S) fuzzy model, controller design is simplified by utilizing the T–S fuzzy model representation of a nonlinear system. An adaptation mechanism ensures that the estimator model asymptotically follow the actual T–S fuzzy model and thus removes the need of any a priori identification of the T–S fuzzy model of the system. The overall controller gain is a convex combination of the local linear gains which vary adaptively to ensure the convergence of the tracking error. Preliminary simulation results indicate the potential of the proposed method.

Observer-based indirect adaptive fuzzy control for SISO nonlinear systems with unknown gain sign

This paper develops an observer-based indirect adaptive fuzzy control scheme for a class of single-input single-output (SISO) nonlinear systems. The considered systems have unknown nonlinear functions, unknown control gain sign, and unmeasurable state variables. In this study, fuzzy systems are utilized to approximate unknown nonlinear functions, and a fuzzy adaptive state observer is designed to estimate the unmeasured state. A robust controller is used to compensate for the lumped errors, and the Nussbaum gain function is incorporated in the robust controller to estimate the unknown gain sign. Based on the strictly positive real Lyapunov design approach, the parameter adaptive laws are designed by the fuzzy basis functions rather than by its filtering. It is proved that all the signals in the closed-loop systems are bounded and that the tracking error converges asymptotically to zero. A simulation example is used to demonstrate the effectiveness of the proposed scheme.