Learning Control Law Research Articles

An Adaptive Spatial-Terminal Iterative Learning Strategy in Roll-to-Roll Control Problems

Abstract Roll-to-Roll (R2R) systems, featuring motorized or idle rollers, are crucial for high-volume, continuous production of flexible substrates. A significant challenge in R2R printing processes is maintaining tight alignment tolerances for multi-layer printed electronics. This alignment, known as registration, is complicated by the deformability of flexible substrates and complex roller dynamics, leading to registration errors (RE) caused by variations in substrate tensions and speeds. Despite using real-time feedback controllers like PID or MPC for tension control, these systems struggle with transient and angle-periodic disturbances common in R2R systems. We introduce a Spatial-Terminal Iterative Learning Control (STILC) method with an adaptive basis function to eliminate RE in R2R gravure printing. This function, along with the registration error, updates the STILC compensation profile via a P-type Iterative Learning Control law. Our numerical experiments demonstrate that STILC with the adaptive basis function effectively eliminates RE caused by roller-motor axis mismatches and provides better convergence than STILC with an invariant basis function. This novel approach shows promise for various industrial applications involving spatially periodic disturbances, particularly those with unknown dynamics and without given state trajectories to track rigorously, which is common in engineering practice.

Iterative learning consensus control for switched discrete-time multi-agent systems based on the 2-D linear discrete model

In this article, a class of switched nonlinear discrete-time heterogeneous (NDTH) multi-agent systems (MASs) with switching signals in both agent dynamics and communication topologies are considered, and a distributed iterative learning control (ILC) law is proposed for the output consensus of the switched NDTH MAS so that the outputs of all follower agents can well track the leader agent. With the proposed ILC controller, the iterative learning dynamic process of the switched NDTH MAS is firstly formulated as a two-dimensional (2-D) linear discrete Roesser model with specified boundary states at each switching sub-interval. Afterwards, according to the exploited properties on solution of the 2-D linear discrete Roesser model, a sufficient convergence theorem for the presented ILC controller is derived. At last, the validity of the ILC-based consensus controller is illustrated through a simulation experiment.

Iterative learning robust security predictive tracking control for small delay batch processes: Deception attacks on unreliable network channel

During the batch process, the need for security control is becoming increasingly urgent with the gradual penetration of network control technology. For small time delay batch processes subject to deception attacks, an iterative learning robust security predictive tracking control approach is developed. Reviewing previous studies for iterative learning control, the issue that the repetitive character of the batch process would mask the characteristics of deception attacks was not considered. Moreover, the gains of iterative learning control law are utilized offline, which makes large deviations for the system state as the operating time increases. This will lead to “excessive-input” conditions for control inputs, which means more consumption of energy and production resources. To address these challenges, we introduce robust security invariant sets to improve the robustness of the system by constraining the system state to be in a safe range. Also, the design of the iterative learning controller incorporates deception attack data for historical batches, which is continuously improved and optimized to withstand deception attacks. Meanwhile, by calculating stability conditions online, the real-time control law gain is obtained, which could make the control inputs adjusted online based on the real-time system’s dynamic characteristics, avoiding excessive inputs and improving the efficiency of energy and resource utilization. Additionally, the stability analysis proves that the system is input to state stability. Ultimately, simulation verifies the effectiveness and feasibility of the developed method.

A robust iterative learning control for linear system with variable initial state and trail length

AbstractTo address the variable initial state and trail length this paper first presents a robust PD‐type open‐closed‐loop iterative learning control (ILC) law for a multiple‐input‐multiple‐output (MIMO) linear discrete‐time system. It is demonstrated that the convergence condition is dependent on the PD‐type feed‐forward learning gains, while an appropriate feedback learning gain can improve the ILC convergence performance. As a special case of PD‐type open‐closed‐loop ILC law, P‐type and D‐type open‐closed‐loop ILC laws are deduced. The three developed ILC laws ensure that as the number of iterations approaches infinity, the expectation of ILC tracking error will be constrained within a limited range, where the boundary is proportional to the initial state variation. Through a numerical simulation, the effectiveness of the proposed ILC laws is illustrated.

Robust iterative learning control for discrete-time systems with random initial state shifts

This paper presents the sufficient conditions of the stability for discrete-time systems with random initial state shifts when applying iterative learning control. Different sufficient conditions have been developed for systems with different characteristics to ensure boundedness of tracking errors and convergence of the learning process under random initial condition. First, the relationship between the initial shifts of two adjacent iterations is addressed with the help of the transition matrix. And the different analysis models are established for each type of systems: one-dimensional matrix analysis model and 2-D Roesser model. Second, the new and sufficient conditions are established for the proposed learning control law to ensure systems convergence by matrix theory and two-dimensional system theory. Third, solving the linear matrix inequality (LMI) yields the control gains. Finally, digital simulations illustrate the effectiveness and sufficiency of the presented conditions.

Model-free compensation learning control of asymmetric hysteretic systems with initial state learning

In this article, a model-free compensation learning control scheme is presented for asymmetric hysteretic systems to achieve high-precision output tracking, where the effects of asymmetric input hysteresis nonlinearities are denoted by the asymmetric Prandtl–Ishlinskii model (APIM). In the presented control scheme, the feedforward iterative learning technique is generalized to the control design of asymmetric hysteretic systems. To improve the robustness and dynamic performance of the existing feedforward learning control for hysteretic systems, both the feedback action and the differential term are utilized to design a discrete-time PD-P open-closed-loop learning control law for simultaneously compensating the asymmetric input hysteresis nonlinearities and the linear dynamics effects without constructing compensators based on their models. The initial state error of such a system is also considered, a modified initial state learning strategy is proposed to ensure the initial state error tends to a prescribed level with the increasing of iterations. By fully analyzing the properties of the APIM, the convergence conditions with respect to the input error, the state error, and the tracking error along the iteration domain are given. The simulation and experimental results are provided to demonstrate strong robustness and excellent tracking accuracy with the proposed model-free compensation learning control scheme.

Data-driven set-point learning control with ESO and RBFNN for nonlinear batch processes subject to nonrepetitive uncertainties

This paper proposes an extended state observer (ESO) based data-driven set-point learning control (DDSPLC) scheme for a class of nonlinear batch processes with a priori P-type feedback control structure subject to nonrepetitive uncertainties, by only using the process input and output data available in practice. Firstly, the unknown process dynamics is equivalently transformed into an iterative dynamic linearization data model (IDLDM) with a residual term. A radial basis function neural network is adopted to estimate the pseudo partial derivative information related to IDLDM, and meanwhile, a data-driven iterative ESO is constructed to estimate the unknown residual term along the batch direction. Then, an adaptive set-point learning control law is designed to merely regulate the set-point command of the closed-loop control structure for realizing batch optimization. Robust convergence of the output tracking error along the batch direction is rigorously analyzed by using the contraction mapping approach and mathematical induction. Finally, two illustrative examples from the literature are used to validate the effectiveness and advantage of the proposed design.

Repetitive process based indirect-type iterative learning control for batch processes with model uncertainty and input delay

This paper develops an indirect iterative learning control scheme for batch processes with time-varying uncertainties, input delay, and disturbances. In this paper, a predictor based on a state observer is designed to estimate the future state and to compensate for the input delay. Then a feedback controller based on the estimated state and the set-point error is used to track the specified reference trajectory, where, of the options available, a robust H∞ controller is designed in the presence of time-varying uncertainties and load disturbances. Then a proportional plus derivative type iterative learning control law is designed. An injection molding process model demonstrates the new method’s effectiveness, and a comparison with a direct-type design is given.

Deep Reinforcement Learning Control of Fully-Constrained Cable-Driven Parallel Robots

Cable-driven parallel robots (CDPRs) have complex cable dynamics and working environment uncertainties, which bring challenges to the precise control of CDPRs. This paper introduces the reinforcement learning to offset the negative effect on control performance of CDPRs resulting from the uncertainties. The problem of controller design for CDPRs in the framework of deep reinforcement learning is investigated. A learning based control algorithm is proposed to compensate for uncertainties due to cable elasticity, mechanical friction, etc. A basic control law is given for the nominal model, and a Lyapunov-based deep reinforcement learning control law is designed. Moreover, the stability of the closed-loop tracking system under the reinforcement learning algorithm is proved. Both simulation and experiments validate the effectiveness and advantages of the proposed control algorithm.

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.

Robust exponential stability analysis of switched systems under switching boundary mismatch

AbstractSwitching boundary is an integral part of the switched system, but the existing literature on switched systems does not focus on the system under switching boundary mismatch. In this article, the switching boundary mismatch is considered, and the control strategy based on observation algorithm is designed for the state dependent switched system. By implementing the proposed strategy, the system can realize robust exponential stability and track the desired trajectory. Since the switching boundary mismatch is unmeasurable, an observation algorithm is designed. Combining the observation algorithm and iterative learning control law, the new control strategy can be derived. According to the Lyapunov stability theory and mode dependent average dwell time method, the robust exponential stability conditions of the closed‐loop system based on linear matrix inequalities are given. The mode dependent average dwell time of each subsystem can be solved simultaneously. Finally, simulations have been taken to verify the designed strategy can render the closed‐loop system achieve robust exponential stability and can track the desired trajectory.

High-order model-free adaptive iterative learning control

In this paper, a high-order model-free adaptive iterative learning control (HOMFAILC) scheme is proposed for nonlinear non-affine discrete-time systems. The main feature of the proposed HOMFAILC is that not only the control input iterative learning law is designed with higher-order algorithms but also the parameter iterative adaptive updating law has the similar forms. Using additional control knowledge in both the iterative learning control law and the parameter estimation law, the control performance of the proposed HOMFAILC can be improved consequently. Furthermore, the similar structure in the control law and parameter updating law can also help to achieve a better control performance. The convergence is proved with rigorous mathematical analysis. Simulation study shows the effectiveness of the proposed HOMFAILC.

Repetitive process based design of PD-type iterative learning control laws for batch processes with time-delays

This paper uses linear matrix inequality techniques and the Kalman-Yakubovich-Popov lemma to design an iterative learning control law for a class of batch processes with state delays. The design procedure is based on the stability theory for repetitive processes, a class of 2D systems. A numerical example illustrates the new design and demonstrates that the design has advantages compared to the existing alternatives.

Deep reinforcement learning for active control of a three-dimensional bluff body wake

The application of deep reinforcement learning (DRL) to train an agent capable of learning control laws for pulsed jets to manipulate the wake of a bluff body is presented and discussed. The work has been performed experimentally at a value of the Reynolds number Re∼105 adopting a single-step approach for the training of the agent. Two main aspects are targeted: first, the dimension of the state, allowing us to draw conclusions on its effect on the training of the neural network; second, the capability of the agent to learn optimal strategies aimed at maximizing more complex tasks identified with the reward. The agent is trained to learn strategies that minimize drag only or minimize drag while maximizing the power budget of the fluidic system. The results show that independently on the definition of the reward, the DRL learns forcing conditions that yield values of drag reduction that are as large as 10% when the reward is based on the drag minimization only. On the other hand, when also the power budget is accounted for, the agent learns forcing configurations that yield lower drag reduction (5%) but characterized by large values of the efficiency. A comparison between the natural and the forced conditions is carried out in terms of the pressure distribution across the model's base. The different structure of the wake that is obtained depending on the training of the agent suggests that the possible forcing configuration yielding similar values of the reward is local minima for the problem. This represents, to the authors' knowledge, the first application of a single-step DRL in an experimental framework at large values of the Reynolds number to control the wake of a three-dimensional bluff body.

AILC for Rigid-Flexible Coupled Manipulator System in Three-Dimensional Space with Time-Varying Disturbances and Input Constraints

In this paper, an adaptive iterative learning control (AILC) law is developed for two-link rigid-flexible coupled manipulator system in three-dimensional (3D) space with time-varying disturbances and input constraints. Based on the Hamilton’s principle, a dynamic model of a manipulator system is established. The conditional equation that is coupled by ordinary differential equations and partial differential equations is derived. In order to achieve high-precision tracking of the revolving angles and vibration suppression of the elastic part, the iterative learning control law based on the disturbance observer is considered in the process of the design controller. The composite Lyapunov energy function is proposed to prove that the angle errors and elastic deformation can eventually converge to zero with the increase of the number of iterations. Ultimately, the simulation results to rigid-flexible coupled manipulator system are given to prove the convergence of the control objectives under the adaptive iterative learning control law.

Practical design of a time-varying iterative learning control law using fuzzy logic

Iterative Learning Control (ILC) is an intelligent control algorithm that can effectively handle a tracking error in any system that operates in a repetitive manner. In practice, it is hardly possible to implement a single gain learning control law to improve the tracking performance due to the existence of large transient growth. To prevent the growth, this paper proposes a time-varying learning control design using the unique concept of fuzzy logic control to track the desired trajectory as well as the desired control input signal. The proposed control design is developed on both serial and parallel ILC configurations. The two configurations are initially constructed and implemented on a robotic manipulator with the use of a single gain learning control law. To avoid bad transients, the gain adjustment mechanism based on fuzzy logic control is introduced to vary the learning gain in each time step for enhancing the robustness of the system. According to the simulation and experiment on a robotic manipulator, both ILC structures with the proposed mechanism achieve the desired learning performance without bad transients.

Simple Learning-Based Robust Trajectory Tracking Control of a 2-DOF Helicopter System

Stabilization and tracking control of Unmanned Aircraft Systems (UASs) such as helicopters in a complex environment with system uncertainties, unknown disturbances, and noise is a challenging task; therefore, to compensate for system uncertainties and unknown disturbances, this paper presents a trajectory tracking control strategy for a 2-DOF (degree of freedom) helicopter system testbed by employing a gradient descent-based simple learning control law that minimizes the cost function corresponding to desired closed-loop error dynamics of the nonlinear system under control. In addition, to ensure the stability of the closed-loop nonlinear system, further analysis is provided. The learning capability of the designed controller makes it suitable to take system uncertainties and unknown disturbances into account. The results of computer simulations and real-time experiment using the Quanser AERO helicopter are included to demonstrate the effectiveness of the designed control strategy.

A Fuzzy System Based Iterative Learning Control for Nonlinear Discrete-Time Systems with Iteration-Varying Uncertainties

In this paper, we consider an iterative learning control problem for a class of unknown discrete-time nonlinear systems with iteration-varying initial error, iteration-varying system parameters, iteration-varying external disturbance, iteration-varying desired output, and iteration-varying control direction. These iteration-varying uncertainties are not required to take any particular structure such as the high-order internal model and only need to satisfy certain boundedness conditions. We propose an iterative learning control law with an adaptive iteration-varying fuzzy system to overcome all the uncertainties and achieve the learning control objective. Furthermore, we present a sufficient condition for designing adaptive gains and prove the convergence of the learning error to a small value as the trial number is large enough. Finally, we use two simulation examples to demonstrate all the theoretical results.

A Novel Fast Iterative Learning Control for Linear Discrete Systems with Parametric Disturbance and Measurement Noise

Precise industrial control technology is constantly in need of accurate and strong control. Error convergence for a typical linear system is very minimal when using a conventional iterative learning control strategy. This study develops a quick iterative learning control law to address this issue. We have presented a new PD iterative learning control approach which is basically grounded on backward error and control parameter rectification for a class of linear discrete time-invariant (LDTI) systems. We have deliberated the repetitive system, which has constraint disturbance and measurement noise. First, we have developed a form of the faster learning law along with a full explanation of the algorithm’s control factor generation process. And then, using the vector method in conjunction with the theory of spectral radius, sufficient conditions for the algorithm’s convergence are introduced for parameter estimation with no noise, parameter uncertainty but excluding the noise, parameter uncertainty with small perturbations, and noise in four different scenarios. Eventually, results show that convergence depends on the control law’s learning factor, the correction term, the factor of association, and the learning interval. Ultimately, the simulation results indicate that suggested approach has a faster error convergence as compared with classical PD algorithm.

Finite difference based iterative learning control with initial state learning for a class of fractional order two‐dimensional continuous‐discrete linear systems

SummaryThis article presents a PI‐type iterative learning control (ILC) law with initial state learning for a class of () fractional order two‐dimensional (2D) linear systems. First, by using backward difference method, the finite difference approximation of the fractional order derivative is obtained, which leads to globally order accuracy. Then, a PI‐ILC law is constructed at the nodes and the convergence analysis of the iterative scheme is proved. A linear matrix inequality‐based sufficient condition is derived to guarantee that the tracking error is asymptotically convergent. The obtained convergence condition is fractional order dependent. Most of the classical ILC conditions for fractional order one‐dimensional linear systems fall into the special cases of this article. Finally, the simulation results show the effectiveness of the proposed control method.