Learning Control For Nonlinear Systems Research Articles

Data-Driven Internal Model Learning Control for Nonlinear Systems.

A novel data-driven internal model learning control (DIMLC) strategy is developed for a nonlinear nonaffine system subject to unknown nonrepetitive uncertainties. At first, an iterative dynamic linearization (IDL) approach is employed for reformulating the nonlinear plant to an iterative linear data model (iLDM). Then, the nominal form of the IDL-based iLDM is used as an internal model of the nonlinear plant whose parameters are estimated by an iterative adaptive updating mechanism using only input-output (I/O) data. The equivalent feedback-principle-based internal model inversion is further applied to the subsequent controller design and analysis. The proposed DIMLC contains two parts. One is a nominal controller designed by the inversion of the internal model which achieves a perfect tracking of the target output; the other is a compensatory controller which offsets the uncertainties. The novel DIMLC is data-driven and does not require an explicit model. It can deal with model-plant mismatch and disturbances, enhancing the robustness against uncertainties. The theoretical results are verified by simulation study.

Feedback higher-order iterative learning control for nonlinear systems with non-uniform iteration lengths and random initial state shifts

For nonlinear discrete-time systems with non-uniform iteration lengths and random initial state shifts, this paper developed a feedback higher-order iterative learning control (ILC) approach. To compensate the absent information of last iteration caused by non-uniform iteration lengths, the tracking information in both iteration domain and time domain is included in ILC design with the help of higher-order control and feedback control, respectively, while the general ILC schemes just adopt the information in iteration domain. A sufficient condition based on the higher-order ILC gains is derived. It is guaranteed that as the iteration number goes to infinity, the asymptotic bound of tracking error is proportional to random initial state shifts in mathematical expectation sense. Specifically, as the expectation of initial state shifts is zero, the ILC tracking error can be controlled to zero along the iteration direction. Two examples with different initial conditions are provided to validate the proposed ILC approach.

Fault-tolerant design of non-linear iterative learning control using neural networks

The design of neural-network-based iterative learning control for non-linear systems is addressed in the setting of a fault tolerant control regime. Taking advantage of the repetitive character of the control task, the inherent uncertainty related to a potential faulty system state can be properly accommodated in terms of a data-driven iterative learning scheme with neural networks used for forward/inverse modeling as well as for controller synthesis. The resulting control technique is supposed to be flexible enough to accurately compensate the faults occurring on both the sensors and actuators and, additionally, take into account the disturbances and noise acting on the system. A complete characterization of the novel fault-tolerant iterative learning scheme is provided including system identification, fault detection and accommodation. Also, the painstaking convergence analysis is presented and the resulting sufficient conditions can be constructively used to determine the update of control law in the consecutive process trial. The excellent performance of the developed control scheme is illustrated by a nontrivial example of tracking control for a magnetic brake system on various scenarios involving actuator and/or sensor faults.

Adaptive learning control for nonlinear systems: A single learning estimation scheme is enough

In this brief, continuous-time nonlinear systems with extended matching uncertainties are considered. The problem of designing a state-feedback adaptive learning control of reduced complexity — just including a single adaptive learning estimation scheme in the upper subsystem and a high-gain proportional action in the input channel — is addressed. By properly setting the control parameters, exponential output tracking of (sufficiently smooth) periodic reference signals with a known period is achieved. Fourier series expansions are used and estimates of the resulting Fourier coefficients are continuously adapted based on the persistency of excitation conditions that naturally hold due to the orthogonal nature of the sinusoidal basis functions.

Learning controllers for nonlinear systems from data

This article provides an overview of a new approach to designing controllers for nonlinear systems using data-driven control. Data-driven control is an important area of research in control theory, and this novel method offers several benefits. It can recreate from a data-centred perspective many of the results available in the model-based case, including local stabilization based on Taylor or polynomial expansion, absolute stabilization, as well as approximate and exact feedback linearization. Moreover, the method is analytically and computationally simple, and permits to infer regions of attraction and invariant sets, also when the data are corrupted by noise.

Data-Driven Iterative Learning Control of Nonlinear Systems by Adaptive Model Matching

Iterative learning control (ILC) has proven successful in the industry for enhancing tracking performance of repetitive tasks. The high accuracy and fast convergence of ILC algorithms hinge on: 1) the knowledge of the system model and 2) an effective learning algorithm. For general industrial systems with nonlinear dynamics, this raises technical challenges because acquiring a nonlinear dynamical model or several linearized models at different operating points may be difficult and costly. It is also nontrivial to determine the learning algorithm for the complex model obtained. To address these challenges, this article proposes a novel data-driven ILC algorithm for single-input-single-output nonlinear systems. Without explicit nonlinear models, our algorithm treats the nonlinear system as an unknown linear time-varying system linearized on a specified input–output (I/O) trajectory in each ILC iteration. A linearly parameterized time-varying adaptive filter is constructed in each ILC iteration so that, when cascading with the nonlinear plant, the I/O dynamics around the specified trajectory follow a linear time-invariant reference model. The ILC error trajectory is then filtered by the adaptive time-varying filter, which represents the inverse dynamics with a bandwidth specified by the reference model, to render fast convergence. The benefits of the proposed data-driven algorithm is demonstrated by comparing to a gradient and Hessian-based data-driven ILC algorithm on a prototypical two-degree-of-freedom nonlinear pendulum.

Resilient Model-Free Adaptive Iterative Learning Control for Nonlinear Systems Under Periodic DoS Attacks via a Fading Channel

This article studies the resilient control problem for a class of unknown nonlinear systems with fading measurements under malicious denial-of-service (DoS) attacks. The system output is assumed to be transmitted through a fading channel, where the fading phenomenon is described by a Rice fading model. The strategy of the attacker is to periodically interfere with the networked channels to reduce the success rate of data transmissions. First, a dynamic linearization method along the iteration domain is introduced to convert the nonlinear system into an equivalent data-related model. Then, a model-free adaptive iterative learning control (MFAILC) scheme is presented, which is independent of model information. The convergence of the MFAILC scheme is deduced theoretically and the influence of DoS attacks and stochastic fading phenomenon on system stability are also analyzed. Finally, the effectiveness of the design is verified by a numerical simulation and a trajectory tracking example of wheeled mobile robots (WMRs).

An indirect iterative learning controller for nonlinear systems with mismatched uncertainties and matched disturbances

ABSTRACT The article proposes an intelligent controller for output regulation of nonlinear non-autonomous continuous-time systems with mismatched uncertainties and matched disturbances. This controller is established by firstly converting the original system into an input-to-state stable one via learning-based compensation of lumped system disturbances and then applying the standard P-type iterative learning control. The learning-based disturbance compensator is basically created with the numerical backward differentiation in iterative mode. The control performance of the obtained sampled data system using the proposed controller has been verified throughout both in theory and comparison with the existing method via numerical simulations.

IBLF‐based event‐triggered adaptive learning control of nonlinear systems with full state constraints

SummaryThis article focuses on the adaptive asymptotic learning tracking control problem of nonlinear systems with full state constraints. First, an adaptive neural network tracking algorithm is proposed which combines a time‐varying feedback element and robust compensation feedback element in the form of smooth function to guarantee that output signal tracks the reference signal asymptotically. Apart from this, a time‐varying integral barrier Lyapunov function is utilized to ensure that the system states are always kept in the constraint region. Furthermore, the event‐triggered mechanism is designed to efficiently reduce unnecessary transmissions. Compared with the other literatures, the original state constraint problem is directly solved by the proposed adaptive control algorithm. Finally, simulation is included to validate the built theoretical results.

Hybrid deep learning controller for nonlinear systems based on adaptive learning rates

In this paper, a hybrid deep learning neural network controller (HDLNNC) for nonlinear systems is proposed. The proposed controller structure consists of a multi-layer feed-forward neural network, which can be trained based on the hybrid deep learning. The Lyapunov stability criterion is used to develop an adaptive learning rate due to the learning rate of the updating parameters plays a worthy role in achieving the stability of a system. To show the robustness of the proposed controller and its performance, several tests such as disturbance signals and parameter variations are carried on a numerical example. In this concern, the practical implementation of the proposed HDLNNC is executed on a real system. The results indicate that the proposed controller is able to improve the system performance compared with other existing controllers.

Barrier Robust Iterative Learning Control for Nonlinear Systems With Both Nonparametric Uncertainties and Time-Iteration-Varying Parametric Uncertainties Under Alignment Condition

Barrier Robust Iterative Learning Control for Nonlinear Systems With Both Nonparametric Uncertainties and Time-Iteration-Varying Parametric Uncertainties Under Alignment Condition

Quantisation compensated data-driven iterative learning control for nonlinear systems

This work presents a quantisation compensation-based data-driven iterative learning control (QC-DDILC) scheme by incorporating a uniform quantiser and an encoding–decoding mechanism (E-DM) to deal with the problem of limited communication resources in a networked control system. Since it is directly aimed at a nonlinear nonaffine system, an iterative dynamic linearisation method is employed to transfer it to a linear data model. Then, the QC-DDILC method is developed by the use of optimisation technique for the learning control law and the parameter updating law, respectively, where the quantised output from the E-DM is used. Since the direct output measurement of the system is unavailable, the linear data model is also acted as an iterative predictive model to estimate the system outputs utilised as the compensator in the consequent QC-DDILC. The proposed QC-DDILC is a data-driven method without relying on any explicit mechanism model information. The convergence analysis is conducted by using the mathematical tools of contraction mapping and induction. Simulations verify the theoretical results.

Robust Optimization-Based Iterative Learning Control for Nonlinear Systems With Nonrepetitive Uncertainties

This paper aims to solve the robust iterative learning control (ILC) problems for nonlinear time-varying systems in the presence of nonrepetitive uncertainties. A new optimization-based method is proposed to design and analyze adaptive ILC, for which robust convergence analysis via a contraction mapping approach is realized by leveraging properties of substochastic matrices. It is shown that robust tracking tasks can be realized for optimization-based adaptive ILC, where the boundedness of system trajectories and estimated parameters can be ensured, regardless of unknown time-varying nonlinearities and nonrepetitive uncertainties. Two simulation tests, especially implemented for an injection molding process, demonstrate the effectiveness of our robust optimization-based ILC results.

Data-driven gradient-based point-to-point iterative learning control for nonlinear systems

Iterative learning control (ILC) is a well-established methodology which has proved successful in achieving accurate tracking control for repeated tasks. However, the majority of ILC algorithms require a nominal plant model and are sensitive to modelling mismatch. This paper focuses on the class of gradient-based ILC algorithms and proposes a data-driven ILC implementation applicable to a general class of nonlinear systems, in which an explicit model of the plant dynamics is not required. The update of the control signal is generated by an additional experiment executed between ILC trials. The framework is further extended by allowing only specific reference points to be tracked, thereby enabling faster convergence. Necessary convergence conditions and corresponding convergence rates for both approaches are derived theoretically. The proposed data-driven approaches are demonstrated through application to a stroke rehabilitation problem requiring accurate control of nonlinear artificially stimulated muscle dynamics.

Neural-network-based iterative learning control of nonlinear systems

This work reports on a novel approach to effective design of iterative learning control of repetitive nonlinear processes based on artificial neural networks. The essential idea discussed here is to enhance the iterative learning scheme with neural networks applied for controller synthesis as well as for system output prediction. Consequently, an iterative control update rule is developed through efficient data-driven scheme of neural network training. The contribution of this work consists of proper characterization of the control design procedure and careful analysis of both convergence and zero error at convergence properties of the proposed nonlinear learning controller. Then, the resulting sufficient conditions can be incorporated into control update for the next process trial. The proposed approach is illustrated by two examples involving control design for pneumatic servomechanism and magnetic levitation system.

Self-Organizing Adaptive Fuzzy Brain Emotional Learning Control for Nonlinear Systems

This paper aims to develop a more efficient adaptive control system for uncertain nonlinear systems. A novel self-organizing fuzzy brain emotional learning controller (FBELC) is proposed. The FBELC neural network is the mathematical replica of human brain emotions incorporated with fuzzy inference rules, which mimics the judgments and emotions of the brain. The FBELC contains two sub-neural networks, namely a sensory neural network and an emotional neural network. These duet networks influence each other, thus improving the learning ability of the system. The proposed control system also merges sliding mode control to simplify the input space dimension of FBELC. In this study, the self-organization algorithm for the structure of FBELC is developed; thus, the growing and pruning of input layers of FBELC can be automatically proceeded to give the most efficient network structure. Moreover, the parameter adaptive law is derived using gradient descent method to achieve effective learning ability of the network. The proposed control system comprises the self-organizing adaptive FBELC (SOAFC) used as the main controller and a fuzzy compensator designed to obtain robust stability of the system for handling uncertain nonlinear systems. The developed SOAFC is then applied to a double inverted pendulum system and a biped robot to illustrate its effectiveness.

Model-free Gradient Iterative Learning Control for Non-linear Systems

Iterative learning control (ILC) is a well-established approach to precision tracking for systems that perform a repeated task. Gradient-based update laws are amongst the most widely applied in practice due to their attractive robustness properties. However, they are limited by requiring a model of the system dynamics to be identified. This paper shows how gradient ILC can be extended for use with a general class of nonlinear systems, and additionally how the update can be generated using an extra experiment conducted between trials. This ‘model-free’ algorithm extends previous work for linear systems, and is illustrated by a nonlinear rehabilitation application requiring accurate control of human upper-limb movement.

Low-Dimensional Learning Control using Generic Signal Parametrizations

Iterative learning control (ILC) can yield superior performance for repetitive tasks while only requiring approximate models, making this control strategy very appealing for industry. However, applying it to non-linear systems involves solving of optimization problems, which limits the industrial uptake, especially for learning online to compensate for variations throughout the system’s lifetime. Industry tackles this by designing simple rule-based learning controllers. However, these are often designed in an ad-hoc manner, which potentially limits performance. In this paper, we will couple a low-dimensional parametrized learning control algorithm with a generic signal parametrization method on the basis of machine learning, and specifically using autoencoders. This will allow high control performance, while limiting implementational complexity and maintaining interpretability, paving the way for a higher industrial uptake of learning control for non-linear systems. We will illustrate the parametrized approach in simulation on a non-linear slider-crank system, and provide an example of using the learning approach to perform a tracking task for this system.

Robust learning control for nonlinear systems with nonparametric uncertainties and nonuniform trial lengths

SummaryThis paper proposes robust iterative learning control schemes for continuous‐time nonlinear systems with various nonparametric uncertainties under nonuniform trial length circumstances. The nonuniform trial length is described by a random variable, which causes a random data missing problem while designing and analyzing algorithms for the precise tracking problem. Three common types of nonparametric uncertainties are taken into account: norm‐bounded uncertainty, variation‐norm‐bounded uncertainty, and norm‐bounded uncertainty with unknown coefficients. A novel composite energy function is introduced with the help of a newly defined virtual tracking error for the asymptotical convergence of the proposed schemes. Extensions to multiple‐input–multiple‐output cases are also elaborated. Illustrative simulations are provided to verify the theoretical results.

Adaptive Learning Control for Nonlinear Systems With Randomly Varying Iteration Lengths.

This paper proposes adaptive iterative learning control (ILC) schemes for continuous-time parametric nonlinear systems with iteration lengths that randomly vary. As opposed to the existing ILC works that feature nonuniform trial lengths, this paper is applicable to nonlinear systems that do not satisfy the globally Lipschitz continuous condition. In addition, this paper introduces a novel composite energy function based on newly defined virtual tracking error information for proving the asymptotical convergence. Both an original update algorithm and a projection-based update algorithm for estimating the unknown parameters are proposed. Extensions to cases with unknown input gains, iteration-varying tracking references, nonparametric uncertainty, high-order nonlinear systems, and multi-input-multi-output systems are all elaborated upon. Illustrative simulations are provided to verify the theoretical results.