Data-Driven Robust Finite-Iteration Learning Control for MIMO Nonrepetitive Uncertain Systems.

This work considers three main problems related to fast finite-iteration convergence (FIC), nonrepetitive uncertainty, and data-driven design. A data-driven robust finite-iteration learning control (DDRFILC) is proposed for a multiple-input-multiple-output (MIMO) nonrepetitive uncertain system. The proposed learning control has a tunable learning gain computed through the solution of a set of linear matrix inequalities (LMIs). It warrants a bounded convergence within the predesignated finite iterations. In the proposed DDRFILC, not only can the tracking error bound be determined in advance but also the convergence iteration number can be designated beforehand. To deal with nonrepetitive uncertainty, the MIMO uncertain system is reformulated as an iterative incremental linear model by defining a pseudo partitioned Jacobian matrix (PPJM), which is estimated iteratively by using a projection algorithm. Further, both the PPJM estimation and its estimation error bound are included in the LMIs to restrain their effects on the control performance. The proposed DDRFILC can guarantee both the iterative asymptotic convergence with increasing iterations and the FIC within the prespecified iteration number. Simulation results verify the proposed algorithm.

Data-Driven Dynamic Internal Model Control.

A data-driven dynamic internal model control (D 3 IMC) scheme is proposed for unknown nonlinear nonaffine systems bypassing modeling steps. Different from the traditional internal model constructed by either a first-principle or an identified model, a dynamic internal model (DIM) is developed in this work using I/O data where a compact form dynamic linearization approach is introduced for addressing the nonlinearity and nonaffine structure. Then, the D 3 IMC is proposed with both a nominal control algorithm and an uncertainty compensation control algorithm. The former can quickly respond to the feedback errors and the latter can compensate the model-plant mismatch and external disturbances. Meanwhile, the adaptive parameter updating law in the proposed D 3 IMC method inherits the robustness against uncertainties. A nominal D 3 IMC is also designed without including the compensator when there is no exogenous disturbance since the adaptive mechanism can handle system uncertainty. Further, the results are extended and a full-form dynamic linearization-based D 3 IMC is developed to address control of nonlinear systems with more complex dynamics. All the proposed D 3 IMC methods are data-driven without need of an explicit model, and thus they are significant extensions from the traditional model-based IMC. Simulation study verifies the results.

Data-Driven Indirect Iterative Learning Control.

In this work, a data-driven indirect iterative learning control (DD-iILC) is presented for a repetitive nonlinear system by taking a proportional-integral-derivative (PID) feedback control in the inner loop. A linear parametric iterative tuning algorithm for the set-point is developed from an ideal nonlinear learning function that exists in theory by utilizing an iterative dynamic linearization (IDL) technique. Then, an adaptive iterative updating strategy of the parameter in the linear parametric set-point iterative tuning law is presented by optimizing an objective function for the controlled system. Since the system considered is nonlinear and nonaffine with no available model information, the IDL technique is also used along with a strategy similar to the parameter adaptive iterative learning law. Finally, the entire DD-iILC scheme is completed by incorporating the local PID controller. The convergence is proved by applying contraction mapping and mathematical induction. The theoretical results are verified by simulations on a numerical example and a permanent magnet linear motor example.

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.

Sampled-Data Model-Free Adaptive Control for Nonlinear Continuous-Time Systems.

This work aims at presenting a new sampled-data model-free adaptive control (SDMFAC) for continuous-time systems with the explicit use of sampling period and past input and output (I/O) data to enhance control performance. A sampled-data-based dynamical linearization model (SDDLM) is established to address the unknown nonlinearities and nonaffine structure of the continuous-time system, which all the complex uncertainties are compressed into a parameter gradient vector that is further estimated by designing a parameter updating law. By virtue of the SDDLM, we propose a new SDMFAC that not only can use both additional control information and sampling period information to improve control performance but also can restrain uncertainties by including a parameter adaptation mechanism. The proposed SDMFAC is data-driven and thus overcomes the problems caused by model-dependence as in the traditional control design methods. The simulation study is performed to demonstrate the validity of the results.

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.

Data-Driven Adaptive Iterative Learning Bipartite Consensus for Heterogeneous Nonlinear Cooperation-Antagonism Networks.

Heterogeneous dynamics, strongly nonlinear and nonaffine structures, and cooperation-antagonism networks are considered together in this work, which have been considered as challenging problems in the output consensus of multiagent systems. A heterogeneous linear data model (LDM) is presented to accommodate the nonlinear nonaffine structure of the heterogeneous agent. It also builds an I/O dynamic relationship of the agents along the iteration-dimensional direction to make it possible to learn control experience from previous iterations to improve the transient consensus performance. Then, an adaptive update algorithm is developed for the estimation of the uncertain parameters of the LDM to compensate for the unknown heterogeneous dynamics and model structures. To address the problem of cooperation and antagonism, an adaptive learning consensus protocol is proposed considering two signed graphs, which are structurally balanced and unbalanced, respectively. The learning gain can be regulated using the proposed adaptive updating law to enhance the adaptability to the uncertainties. With rigorous analysis, the bipartite consensus is proven in the case that the graph is structurally balanced, and the convergence of the agent output to zero is also proven in the case that the graph is unbalanced in its structure. The presented bipartite consensus method is data-based without the use of any explicit model information. The theoretical results are demonstrated through simulations.

Quantitative Data-Driven Adaptive Iterative Learning Control: From Trajectory Tracking to Point-to-Point Tracking.

This article reconsiders the data quantization problem in iterative learning control (ILC) for nonlinear nonaffine systems from four aspects: 1) use of available additional control knowledge; 2) different tracking tasks; 3) adaptation to uncertainties; and 4) data-driven design and analysis framework. An iterative linear data model (iLDM) is established first to represent the nonlinear nonaffine system for subsequent control algorithm design and analysis under a data-driven framework. A quantitative data-driven adaptive ILC (QDDAILC) is then developed using quantized tracking errors based on the nonlifted iLDM and, thus, additional available input information from previous time instants can be utilized to improve control performance. The parameter estimation derived from an adaptive updating law makes the learning gain of the QDDAILC adjustable, therefore improving the robustness to uncertainties. Due to the coupled dynamics among inputs and tracking errors, a new double-dynamics analysis method is introduced besides the contraction mapping principle to show error convergence. A quantized data-driven adaptive point-to-point ILC (QDDAPTPILC) is further presented using partial quantized measurements at the specified instants for multi-intermediate-point tracking. Simulation examples verify theoretical results and illustrate that the QDDAPTPILC outperforms the QDDAILC for multi-intermediate-point tracking tasks because it removes the unnecessary constraints.

Spatial Linear Dynamic Relationship of Strongly Connected Multiagent Systems and Adaptive Learning Control for Different Formations.

This article addresses an important problem of how to improve the learnability of an intelligent agent in a strongly connected multiagent network. A novel spatial-dimensional linear dynamic relationship (SLDR) is developed to formulate the spatial dynamic relationship of an agent with respect to all the related agents. The obtained SLDR virtually exists in the computer to describe the input-output (I/O) relationship in the spatial domain and an iterative adaptation mechanism is developed to update the SLDR using I/O information to show real-time dynamical behavior of multiagent systems with nonrepetitive initial states. Subsequently, an SLDR-based adaptive iterative learning control (SLDR-AILC) is presented with rigorous analysis for iteration-variant formation control targets. Not only the 3-D dynamic behavior of the multiagent network but also the control protocols of the communicated agents are incorporated in the learning mechanism and thus strong learnability of the proposed SLDR-AILC is achieved to improve control performance. The proposed SLDR-AILC is a data-driven scheme where no explicit model structure is needed. Simulations with strongly connected topologies verify the theoretical results.

Data-Driven Adaptive Consensus Learning From Network Topologies.

The problem of consensus learning from network topologies is studied for strongly connected nonlinear nonaffine multiagent systems (MASs). A linear spatial dynamic relationship (LSDR) is built at first to formulate the dynamic I/O relationship between an agent and all the other agents that are communicated through the networked topology. The LSDR consists of a linear parametric uncertain term and a residual nonlinear uncertain term. Utilizing the LSDR, a data-driven adaptive learning consensus protocol (DDALCP) is proposed to learn from both time dynamics of agent itself and spatial dynamics of the whole MAS. The parametric uncertainty and nonlinear uncertainty are estimated through an estimator and an observer respectively to improve robustness. The proposed DDALCP has a strong learning ability to improve the consensus performance because time dynamics and network topology information are both considered. The proposed consensus learning method is data-driven and has no dependence on the system model. The theoretical results are demonstrated by simulations.

Event-Triggered ILC for Optimal Consensus at Specified Data Points of Heterogeneous Networked Agents With Switching Topologies.

In this article, the optimal consensus problem at specified data points is considered for heterogeneous networked agents with iteration-switching topologies. A point-to-point linear data model (PTP-LDM) is proposed for heterogeneous agents to establish an iterative input-output relationship of the agents at the specified data points between two consecutive iterations. The proposed PTP-LDM is only used to facilitate the subsequent controller design and analysis. In the sequel, an iterative identification algorithm is presented to estimate the unknown parameters in the PTP-LDM. Next, an event-triggered point-to-point iterative learning control (ET-PTPILC) is proposed to achieve an optimal consensus of heterogeneous networked agents with switching topology. A Lyapunov function is designed to attain the event-triggering condition where only the control information at the specified data points is available. The controller is updated in a batch wise only when the event-triggering condition is satisfied, thus saving significant communication resources and reducing the number of the actuator updates. The convergence is proved mathematically. In addition, the results are also extended from linear discrete-time systems to nonlinear nonaffine discrete-time systems. The validity of the presented ET-PTPILC method is demonstrated through simulation studies.

Data-Driven Terminal Iterative Learning Consensus for Nonlinear Multiagent Systems With Output Saturation.

This article considers the problem of finite-time consensus for nonlinear multiagent systems (MASs), where the nonlinear dynamics are completely unknown and the output saturation exists. First, the mapping relationship between the output of each agent at the terminal time and the control input is established along the iteration domain. By using the terminal iterative learning control method, two novel distributed data-driven consensus protocols are proposed depending on the input and output saturated data of agents and its neighbors. Then, the convergence conditions independent of agents' dynamics are developed for the MASs with fixed communication topology. It is shown that the proposed data-driven protocol can guarantee the system to achieve two different finite-time consensus objectives. Meanwhile, the design is also extended to the case of switching topologies. Finally, the effectiveness of the data-driven protocol is validated by a simulation example.

Event-Triggered Nonlinear Iterative Learning Control.

An event-triggered nonlinear iterative learning control (ET-NILC) method is presented for repetitive nonaffine and nonlinear systems that have 2-D dynamic behavior along both time and iteration directions. Based on the virtual linear data model, the ET-NILC method is proposed by designing an event triggering condition based on the Lyapunov-like stability analysis conducted along the iteration direction. The learning gain function of ET-NILC is nonlinear and updated by designing an iterative learning parameter estimation law to enhance the robustness. From the perspective of the time dynamics, the proposed ET-NILC is a feedforward control and the event-triggering condition can be verified offline using tracking errors, event triggering errors, and the estimated parameters together. Moreover, the proposed ET-NILC is a data-driven scheme since it merely uses I/O data for the design. The results are also extended to repetitive multiple-input-multiple-output (MIMO) nonaffine nonlinear systems using the property of input-to-state stability as the basic mathematical tool. The convergence of the proposed ET-NILC methods is proved. Several simulations illustrate the effectiveness of the proposed methods.

Adjacent-Agent Dynamic Linearization-Based Iterative Learning Formation Control.

The dynamical relationship of the multiple agents' behavior in a networked system is explored and utilized to enhance the control performance of the multiagent formation in this paper. An adjacent-agent dynamic linearization is first presented for nonlinear and nonaffine multiagent systems (MASs) and a virtual linear difference model is built between two adjacent agents communicating with each other. Considering causality, the agents are assigned as parent and child, respectively. Communication is from parent to child. Taking the advantage of the repetitive characteristics of a large class of MASs, an adjacent-agent dynamic linearization-based iterative learning formation control (ADL-ILFC) is proposed for the child agent using 3-D control knowledge from iterations, time instants, and the parent agent. The ADL-ILFC is a data-driven method and does not depend on a first-principle physical model but the virtual linear difference model. The validity of the proposed approach is demonstrated through rigorous analysis and extensive simulations.

3-D Learning-Enhanced Adaptive ILC for Iteration-Varying Formation Tasks.

This paper explores the formation control problem of repetitive nonlinear homogeneous and asynchronous multiagent networks, where the early starting agent is designated as the parent, and the later starting agent with a small delayed time is designated as the child. Moreover, the desired formation reference is allowed to be different from iteration to iteration. A space-dimensional dynamic linearization method is presented to build the linear dynamic relationship between two parent-child agents in a networked system. Then, a 3-D learning-enhanced adaptive iterative learning control (3D-AILC) is proposed by utilizing the additional control information from previous time instants, iterative operations, and parent agents. In other words, the proposed method processes 3-D dynamics to strengthen its learnability, i.e., time dimension, iteration dimension, and space dimension. The desired formation signal is incorporated into the learning control law to compensate its iterative variation to achieve a fast and precise tracking performance. The proposed 3D-AILC is data based and does not use an explicit mechanistic model. The validity of the proposed approach is proven theoretically and tested through simulations as well. Moreover, the proposed method also works well with time-iteration-varying topologies and nonrepetitive uncertainties.

Computationally Efficient Data-Driven Higher Order Optimal Iterative Learning Control.

Based on a nonlifted iterative dynamic linearization formulation, a novel data-driven higher order optimal iterative learning control (DDHOILC) is proposed for a class of nonlinear repetitive discrete-time systems. By using the historical data, additional tracking errors and control inputs in previous iterations are used to enhance the online control performance. From the online data, additional control inputs of previous time instants within the current iteration are utilized to improve transient response. The data-driven property of the proposed method implies that no model information except for the I/O data is utilized. The computational complexity is reduced by avoiding matrix inverse operation in the proposed DDHOILC approach due to the nonlifted linear formulation of the original model. The asymptotic convergence is proved rigorously. Furthermore, the convergence property is analyzed and evaluated via three performance indexes. By elaborately selecting the higher order factors, the higher order learning control law outperforms the lower order one in terms of convergence performance. Simulation results verify the effectiveness of the proposed approach.

Enhanced Data-Driven Optimal Terminal ILC Using Current Iteration Control Knowledge.

In this paper, an enhanced data-driven optimal terminal iterative learning control (E-DDOTILC) is proposed for a class of nonlinear and nonaffine discrete-time systems. A dynamical linearization approach is first developed with iterative operation points to formulate the relationship of system output and input into a linear affine form. Then, an ILC law is constructed with a nonlinear learning gain, which is a function about the system partial derivative with respect to the time-varying control input. In addition, a parameter updating law is designed to estimate the unknown partial derivatives iteratively. The input signals of the proposed E-DDOTILC are time-varying and updated utilizing not only the terminal tracking error of the previous run but also the input signals of the previous time instants in the current iteration. The proposed approach is a data-driven control strategy and only the I/O data are required for the controller design and analysis. The monotonic convergence and effectiveness of the proposed approach is further verified by both the rigorous mathematical analysis and the simulation results.