P-type Iterative Learning Control Research Articles

Robust PD-Type Iterative Learning Control of Discrete Linear Repetitive Processes in the Finite Frequency Domain

This paper studies a robust iterative learning control design for discrete linear repetitive processes in the finite frequency domain. Firstly, the state-space model of the iterative learning process is deduced. Then the dynamic performance condition of the control system in the finite frequency domain is derived by combining it with the stability theory of discrete linear repetitive processes. The system performances in the finite frequency domain are then transformed into the corresponding solutions of the linear matrix inequality by using the generalised KYP lemma. Finally, an integrated state feedback PD-type iterative learning control strategy is proposed. The robust control problem with norm-bounded uncertainty and convex polyhedral uncertainty are also considered in this paper. The simulation of the injection velocity in injection molding verified that the proposed methods in this paper are more effective than the P-type state feedback iterative learning control algorithm.

Kernel-based auto-associative P-type iterative learning control strategy

In order to accelerate the convergence speed of iterative learning control (ILC), taking the P-type learning algorithm as an example, a correction algorithm with kernel-based autoassociative is proposed for the linear system. The learning mechanism of human brain associative memory is introduced to the traditional ILC. The control value of the subsequent time is pre-corrected with the current time information by association in each iterative learning process. The learning efficiency of the whole system is improved significantly with the proposed algorithm. Through the rigorous analysis, it shows that under this new designed ILC scheme, the uniform convergence of the state tracking error is guaranteed. Numerical simulations illustrate the effectiveness of the proposed associative control scheme and the validity of the conclusion.

Contraction Mapping-Based Robust Convergence of Iterative Learning Control With Uncertain, Locally Lipschitz Nonlinearity

This paper studies the output tracking control problems for multiple-input, multiple-output (MIMO) locally Lipschitz nonlinear (LLNL) systems subject to iterative operation and uncertain, iteration-varying external disturbances and initial conditions. Under the assumption of a linear, P-type iterative learning control (ILC) update law, a double-dynamics analysis (DDA) approach is proposed to show the convergence of the ILC process in the presence of the locally Lipschitz nonlinearities and iteration-varying uncertainties. The DDA approach results in a contraction mapping-based convergence condition that guarantees both: 1) the boundedness of all system trajectories and 2) the robust convergence of the output tracking error. Further, a basic system relative degree condition is given that provides a necessary and sufficient (NAS) guarantee of the convergence of the ILC process. As a corollary, it is noted that in the absence of iteration-varying uncertainties, the results likewise provide an NAS convergence guarantee for MIMO LLNL systems. The simulations are presented to illustrate the ideas.

Iterative learning control algorithm for optimal path industrial manipulator

In this paper, a two-degree-of-freedom manipulator is taken as the research object, and the relevant dynamic model is established, the iterative learning controller is designed, and the trajectory tracking control of the manipulator is carried out by using the iterative learning control algorithm. Iterative learning control (ILC) has a better control effect on a two-degree-of-freedom manipulator with repetitive motion characteristics for its non-linear system. In the case of disturbance, a PD-type iterative learning control law is designed. With the increasing number of iterations of the system, the required correction interval is shortened by modifying the gain matrix in real time in the interval, so as to accelerate the convergence speed. The simulation results show that the convergence speed of PD-type ILC is faster than that of P-type ILC, and the convergence effect of PD-type ILC with disturbance is better than that of traditional disturbance-type ILC. The industrial robot system is guaranteed to have good dynamic performance.

Integrated predictive iterative learning control based on updating reference trajectory for point-to-point tracking

A novel control technique is proposed by combining iterative learning control (ILC) and model predictive control (MPC) with updating-reference trajectory for point-to-point tracking problem of batch process. In this paper, a batch-to-batch updating-reference trajectory, which passes through the desired points, is firstly designed as the tracking trajectory within a batch. The updating control law consists of P-type ILC part and MPC part, in which P-type ILC part can improve the performance by learning from previous executions and MPC part is used to suppress the model perturbations and external disturbances. Convergence properties of the integrated predictive iterative learning control (IPILC) are analyzed theoretically, and the sufficient convergence conditions of output tracking error are also derived for a class of linear systems. Comparing with other point-to-point tracking control algorithms, the proposed algorithm can perform better in robustness. Furthermore, updating-reference relaxes the constraints for system outputs, and it may lead to faster convergence and more extensive range of application than those of fixed-reference control algorithms. Simulation results on typical systems show the effectiveness of the proposed algorithm.

P-type Iterative Learning Control with Initial State Learning for One-sided Lipschitz Nonlinear Systems

In this paper, the problem of iterative learning control is considered for a class of one-sided Lipschitz nonlinear systems. For such nonlinear systems, open-loop and closed-loop P-type learning algorithms with initial state learning are adopted, respectively. Furthermore, the convergence conditions of the P-type learning algorithms are established. It is shown that both algorithms can guarantee the system output converges to the desired one on the whole time interval. A numerical example is constructed to illustrate the effectiveness of the proposed learning algorithms.

An Iterative Learning Control Algorithm With Gain Adaptation for Stochastic Systems

This paper proposes an iterative learning control (ILC) algorithm with gain adaptation for discrete-time stochastic systems. The algorithm is based on Kesten's accelerated stochastic approximation (SA) algorithm. The gain adaptation uses only tracking error information, and, hence, is a data-driven adaptation approach. If stochastic noises account for a small proportion of the tracking error, the learning gain matrix remains constant with a high probability. If stochastic noises dominate the tracking error, the learning gain matrix is decreasing. Therefore, the new ILC algorithm converges more quickly than existing SA-based algorithms. In addition, the classic P-type ILC law for noise-free systems is a special case of the new ILC algorithm. The behaviors of the proposed ILC algorithm are demonstrated through examples.

Consensus control via iterative learning for distributed parameter models multi-agent systems with time-delay

Most of the available results of iterative learning control (ILC) are that solve the consensus problem of lumped parameter models multi-agent systems. This paper considers the consensus control problem of distributed parameter models multi-agent systems with time-delay. By using the knowledge between neighboring agents, considering time-delay problem in the multi-agent systems, a distributed P-type iterative learning control protocol is proposed. The consensus error between any two agents in the sense of L2 norm can converge to zero after enough iterations based on proposed ILC law. And then we extend these conclusions to Lipschitz nonlinear case. Finally, the simulation result shows the effectiveness of the control method.

Robust Model-Free Adaptive Iterative Learning Control for Vibration Suppression Based on Evidential Reasoning.

Through combining P-type iterative learning (IL) control, model-free adaptive (MFA) control and sliding mode (SM) control, a robust model-free adaptive iterative learning (MFA-IL) control approach is presented for the active vibration control of piezoelectric smart structures. Considering the uncertainty of the interaction among actuators in the learning control process, MFA control is adopted to adaptively adjust the learning gain of the P-type IL control in order to improve the convergence speed of feedback gain. In order to enhance the robustness of the system and achieve fast response for error tracking, the SM control is integrated with the MFA control to design the appropriate learning gain. Real-time feedback gains which are extracted from controllers construct the basic probability functions (BPFs). The evidence theory is adopted to the design and experimental investigations on a piezoelectric smart cantilever plate are performed to validate the proposed control algorithm. The results demonstrate that the robust MFA-IL control presents a faster learning speed, higher robustness and better control performance in vibration suppression when compared with the P-type IL control.

Iterative learning radial basis function neural networks control for unknown multi input multi output nonlinear systems with unknown control direction

In this paper, an iterative learning radial basis function neural-networks (RBF NN) control algorithm is developed for a class of unknown multi input multi output (MIMO) nonlinear systems with unknown control directions. The proposed control scheme is very simple in the sense that we use just a P-type iterative learning control (ILC) updating law in which an RBF neural network term is added to approximate the unknown nonlinear function, and an adaptive law for the weights of RBF neural network is proposed. We chose the RBF NN because it has universal approximation capabilities and can approximate any continuous function. In addition, among the advantages of our controller scheme is the fact that it is applicable to deal with a class of nonlinear systems without the need to satisfy the global Lipschitz continuity condition and we assume, only, that the unstructured uncertainty is norm-bounded by an unknown function. Another advantage of the proposed controller and unlike other works on ILC, we do not need any prior knowledge of the control directions for MIMO nonlinear system. Thus, the Nussbaum-type function is used to solve the problem of unknown control directions. In order to prove the asymptotic stability of the closed-loop system, a Lyapunov-like positive definite sequence is used, which is shown to be monotonically decreasing under the control design scheme. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed control scheme.

Optimal fuzzy iterative learning control based on artificial bee colony for vibration control of piezoelectric smart structures

Combining P-type iterative learning (IL) control, fuzzy logic control and artificial bee colony (ABC) algorithm, a new optimal fuzzy IL controller is designed for active vibration control of piezoelectric smart structures. In order to accelerate the learning speed of feedback gain, the fuzzy logic controller is integrated into the ANSYS finite element (FE) models by using APDL (ANSYS Parameter Design Language) approach to adjust adaptively the learning gain of P-type IL control. For improving the performance and robustness of the fuzzy logic controller as well as diminishing human intervention in the operation process, ABC algorithm is used to automatically identify the optimal configurations for values in fuzzy query table, fuzzification parameters and defuzzification parameters, and the main program of ABC algorithm is operated in MATLAB. The active vibration equations are driven from the FE equations for the dynamic response of a linear elastic piezoelectric smart structure. Considering the vibrations generated by various external disturbances, the optimal fuzzy IL controller is numerically investigated for a clamped piezoelectric smart plate. Results demonstrate that the proposed control approach makes the feedback gain has a fast learning speed and performs excellent in vibration suppression. This is demonstrated in the results by comparing the new control approach with the P-type IL control.

Iterative consensus control for a class of nonlinear MIMO multi-agent systems with data dropout

Consider frequent data dropout phenomena of measurements due to communication channel failure. The consensus tracking problem for a class of nonlinear MIMO multi-agent systems (MAS) with data dropouts is addressed in this paper. The phenomena of data dropout is described by an introduced random variable, which is defined with a Bernoulli sequence valued 0/1. Moreover, the situation which only part of the agents can access the desired trajectory information also take into account. Based on the random variable, a modified distributed P-type iterative learning control algorithm with data drops is proposed. In addition, the identical initialization condition of classic iterative learning control (ILC) is released as well. Then, the theoretical analysis of the system convergence condition is given by using the contraction mapping method and supermom norm technical. As a result, the proposed ILC algorithm can guaranteed the system convergence with data dropout in a finite time. Finally, an illustrative example is presented to demonstrate the perfect tracking performance and the effectiveness of the scheme.

Accelerated Iterative Learning Control of Speed Ripple Suppression for a Seeker Servo Motor

To suppress the speed ripple of a permanent magnet synchronous motor in a seeker servo system, we propose an accelerated iterative learning control with an adjustable learning interval. First, according to the error of current iterative learning for the system, we determine the next iterative learning interval and conduct real-time correction on the learning gain. For the learning interval, as the number of iterations increases, the actual interval that needs correction constantly shortens, accelerating the convergence speed. Second, we analyze the specific structure of the controller while applying reasonable assumptions pertaining to its condition. Using the λ-norm, we analyze and apply our mathematical knowledge to obtain a strict mathematical proof on the P-type iterative learning control and obtain the condition of convergence for the controller. Finally, we apply the proposed method for periodic ripple inhibition of the torque rotation speed of the permanent magnet synchronous motor and establish the system model; we use the periodic load torque to simulate the ripple torque of the synchronous motor. The simulation and experimental results indicate the effectiveness of the method.

ILC with Initial State Learning for Fractional Order Linear Distributed Parameter Systems

This paper presents a second order P-type iterative learning control (ILC) scheme with initial state learning for a class of fractional order linear distributed parameter systems. First, by analyzing the control and learning processes, a discrete system for P-type ILC is established, and the ILC design problem is then converted to a stability problem for such a discrete system. Next, a sufficient condition for the convergence of the control input and the tracking errors is obtained by introducing a new norm and using the generalized Gronwall inequality, which is less conservative than the existing one. Finally, the validity of the proposed method is verified by a numerical example.

P-type iterative learning control algorithm for a class of linear singular impulsive systems

This paper is focused on the iterative learning control problem for linear singular impulsive systems. For the purpose of tracking the desired output trajectory, a P-type iterative learning control algorithm is investigated for such system. Based on the fundamental property of singular impulsive systems and the restricted equivalent transformation theory of singular systems, the convergence conditions of the tracking errors for the system are obtained in the sense of λ norm. Finally, the validation of the algorithm is confirmed by a numerical example.

Deterministic Convergence for Learning Control Systems Over Iteration-Dependent Tracking Intervals.

This brief addresses the iterative learning control (ILC) problems for discrete-time systems subject to iteration-dependent tracking time intervals. A modified class of P-type ILC algorithms is proposed by properly defining an available modified output, for which robust convergence analysis is performed with an inductive approach. It is shown that if a persistent full-learning property is ensured, then a necessary and sufficient convergence condition of ILC can be derived to reach the perfect output tracking objective though the tracking time interval is iteration-dependent. That is, the tracking of ILC for iteration-dependent time intervals can be guaranteed in the same deterministic (not stochastic) convergence way as that of traditional ILC over a fixed time interval. Furthermore, the developed tracking results can be extended to admit iteration-dependent uncertainties in initial state and external disturbances. Simulation tests are also included to demonstrate the effectiveness of the modified P-type ILC.

ILC method for solving approximate controllability of fractional differential equations with noninstantaneous impulses

In this paper, we utilize fractional calculus, theory of semigroup and fixed point approach to prove existence and approximate controllability results for a class of fractional differential equations (FDEs) with noninstantaneous impulses by constructing a suitable composite control function, imposing that the associated linear problem is approximately controllable on the terminal subinterval and dividing our global task into many subtasks on each subinterval. Next, we apply P-type iterative learning control (ILC) updating law to generate a sequence of control functions to find a desired control function to guarantee the error between the output and the desired reference trajectories tending to zero via a suitable norm in the sense of uniform convergence. As a result, the limit of the sequence of control functions is the required control to guarantee the above problem is approximately controllable. In addition, a numerical example is illustrated to demonstrate ILC scheme to solve approximate controllability of time fractional impulsive PDEs via tracking the given continuous and discontinuous trajectory.

The convergence of iterative learning control for some fractional system

In this paper, we study the convergence of iterative learning control for some fractional equation. Firstly, by using the Laplace transform and the M-L function, we show the concept of mild solutions. Secondly, by using the Gronwall inequality, we show the sufficient conditions of convergence for the open P-type and the close P-type iterative learning control. At last, we give some examples to illustrate our main results.

Data-Driven Learning Control for Stochastic Nonlinear Systems: Multiple Communication Constraints and Limited Storage.

This paper proposes a data-driven learning control method for stochastic nonlinear systems under random communication conditions, including data dropouts, communication delays, and packet transmission disordering. A renewal mechanism is added to the buffer to regulate the arrived packets, and a recognition mechanism is introduced to the controller for the selection of suitable update packets. Both intermittent and successive update schemes are proposed based on the conventional P-type iterative learning control algorithm, and are shown to converge to the desired input with probability one. The convergence and effectiveness of the proposed algorithms are verified by means of illustrative simulations.

Varying trail lengths-based iterative learning control for linear discrete-time systems with vector relative degree

ABSTRACTIn this article, to tackle with the iteration-varying trail lengths and random initial state shifts, an average operator-based PD-type iterative learning control (ILC) law is firstly presented for linear discrete-time multiple-input multiple-output (MIMO) systems with vector relative degree. The proposed PD-type ILC law includes an initial rectifying action against initial state shifts, and pursues the reference trajectory tracking beyond the initial time points. As special cases of the PD-type ILC law, P-type and D-type ILC laws are then introduced. It is proved that for linear discrete-time MIMO systems with vector relative degree, the three proposed ILC laws can drive the varying trail lengths-based ILC tracking errors to zero in mathematical expectation beyond the initial time points. A numerical example is used to illustrate the effectiveness of the proposed ILC laws.