Deqing Huang

D-type anticipatory iterative learning control for a class of inhomogeneous heat equations

In this paper, a D-type anticipatory iterative learning control (ILC) scheme is applied to the boundary control of a class of inhomogeneous heat equations, where the heat flux at one side is the control input while the temperature measurement at the other side is the control output. By transforming the inhomogeneous heat equation into its integral form and exploiting the properties of the embedded Jacobi Theta functions, the learning convergence of ILC is guaranteed through rigorous analysis, without any simplification or discretization of the 3D dynamics in the time, space as well as iteration domains. The adopted ILC scheme makes full use of the process repetition and deals with state-independent or state-dependent uncertainties. Meanwhile, due to the feedforward characteristic of ILC, the proposed scheme not only makes anticipatory compensation possible to overcome the heat conduction delay in boundary output tracking, but also eliminates the gain margin limitation encountered in feedback control. In the end, an illustrative example is presented to demonstrate the performance of the proposed ILC scheme.

High-Performance Tracking of Piezoelectric Positioning Stage Using Current-Cycle Iterative Learning Control With Gain Scheduling

In this paper, two types of sampled-data current-cycle iterative learning control (ILC) (CILC) schemes are exploited to perform high-performance tracking control for piezoelectric positioning stage systems. The proposed CILC schemes consist of a direct feedback control (FC) loop and an add-on ILC loop and thus can simultaneously deal with repeatable and nonrepeatable components in tracking error. Based on the modeling result of the control system, gain-scheduling technique is further incorporated in the learning filter design of the ILC loop to speed up the learning convergence. In consequence, low tracking error in the time domain and fast convergence speed in the iteration domain are achieved concurrently. In the end, to illustrate the respective characteristics of CILC schemes and verify their superiorities to pure FC or pure ILC, a set of experiments including low-frequency (2 Hz) tracking and high-frequency (100 Hz) tracking is conducted with detailed comparisons among proportional/proportional-plus-integral control, pure ILC with robust design, pure ILC with gain scheduling, and CILC with gain scheduling.

Modeling and Vibration Control for a Nonlinear Moving String With Output Constraint

In this paper, boundary control laws are developed to stabilize the transverse vibration for a nonlinear vertically moving string system. The control system is considered with varying length, varying speed, and the constrained boundary output. Based on the integral-barrier Lyapunov function, the exponential stability is proved with the proposed control without consideration of the disturbance. When the external boundary disturbance is taken into account, the disturbance observer is designed to eliminate its effect. The vibration is regulated and the boundary output always remains in the constrained space by appropriately choosing the control parameters. The control design and the stability analysis are based on the original infinite-dimensional dynamic equations. Extensive numerical examples illustrate the performance of the control system.

An Iterative Learning Control Approach for Linear Systems With Randomly Varying Trial Lengths

This technical note addresses an iterative learning control (ILC) design problem for discrete-time linear systems where the trial lengths could be randomly varying in the iteration domain. An ILC scheme with an iteration-average operator is introduced for tracking tasks with non-uniform trial lengths, which thus mitigates the requirement on classic ILC that all trial lengths must be identical. In addition, the identical initialization condition can be absolutely removed. The learning convergence condition of ILC in mathematical expectation is derived through rigorous analysis. As a result, the proposed ILC scheme is applicable to more practical systems. In the end, two illustrative examples are presented to demonstrate the performance and the effectiveness of the averaging ILC scheme for both time-invariant and time-varying linear systems.

Initial state iterative learning for final state control in motion systems

In this work, an initial state iterative learning control (ILC) approach is proposed for final state control of motion systems. ILC is applied to learn the desired initial states in the presence of system uncertainties. Four cases are considered where the initial position or speed is a manipulated variable and the final displacement or speed is a controlled variable. Since the control task is specified spatially in states, a state transformation is introduced such that the final state control problems are formulated in the phase plane to facilitate spatial ILC design and analysis. An illustrative example is provided to verify the validity of the proposed ILC algorithms.

Coexistence of Limit Cycles and Homoclinic Loops in a SIRS Model with a Nonlinear Incidence Rate

Recently, Ruan and Wang [J. Differential Equations, 188 (2003), pp. 135–163] studied the global dynamics of a SIRS epidemic model with vital dynamics and a nonlinear saturated incidence rate. Under certain conditions they showed that the model undergoes a Bogdanov–Takens bifurcation; i.e., it exhibits saddle-node, Hopf, and homoclinic bifurcations. They also considered the existence of none, one, or two limit cycles. In this paper, we investigate the coexistence of a limit cycle and a homoclinic loop in this model. One of the difficulties is to determine the multiplicity of the weak focus. We first prove that the maximal multiplicity of the weak focus is 2. Then feasible conditions are given for the uniqueness of limit cycles. The coexistence of a limit cycle and a homoclinic loop is obtained by reducing the model to a universal unfolding for a cusp of codimension 3 and studying degenerate Hopf bifurcations and degenerate Bogdanov–Takens bifurcations of limit cycles and homoclinic loops of order 2.

Optimal iterative learning control design for multi-agent systems consensus tracking

Abstract Under a repeatable operation environment, this paper proposes an iterative learning control scheme that can be applied to multi-agent systems to perform consensus tracking under the fixed communication topology. The agent dynamics are modeled by time-varying nonlinear equations which satisfy the global Lipschitz continuous condition. In addition, the desired consensus trajectory is only accessible to a subset of the followers. By using the concept of the graph dependent matrix norm, the convergence conditions can be specified at the agent level, which depend on a set of eigenvalues that are associated with the communication topology. The results are first derived for homogeneous agent systems and then extended to heterogeneous systems. Next, optimal controller gain design methods are proposed in the sense that the λ -norm of tracking error converges at the fastest rate, which imposes a tightest bounding function for the actual tracking error in the λ -norm analysis framework. In the end, an illustrative example of a group of heterogeneous agents is provided to demonstrate the effectiveness of the proposed design methods.

Iterative learning control design for linear discrete-time systems with multiple high-order internal models

This work is focused on the iterative learning control (ILC) design for linear discrete-time systems with iteration-varying factors, including reference, initial state, and exogenous disturbances. First, multiple high-order internal models (HOIMs) are given for various iteration-varying factors. The reference is generated by an HOIM, and the initial state and the exogenous disturbances ultimately satisfy HOIMs but do not strictly follow HOIMs in finite iteration interval. Then, a new ILC scheme, a special high-order ILC (HO-ILC), is constructed according to an augmented HOIM that is the aggregation of all HOIMs. For simplicity, the case with only iteration-varying reference is first considered, where the asymptotic stability and monotone convergence based ILC design methods are both presented by using the 2-D analysis approach. Next, more iteration-varying factors are further considered. In this situation, the HOIM-based ILC is transformed into a controller design problem of a 2-D Roesser model with non-zero boundary states and disturbances, where the 2-D H ∞ performance is studied. In consequence, an ILC design criterion is presented to achieve perfect tracking and 2-D H ∞ performance. For comparison, the monotone convergence based ILC design method is extended to the situation with more iteration-varying factors. Utilizing information provided by the multiple HOIMs, it is verified that HO-ILC outperforms low-order ILC (LO-ILC) in presence of iteration-varying factors. Meanwhile, the 2-D H ∞ based ILC is shown to be superior to the monotone convergence based ILC. Finally, a microscale robotic deposition system with iteration-varying factors is given to illustrate the advantage of the proposed 2-D H ∞ based ILC.

Iterative learning control of inhomogeneous distributed parameter systems—frequency domain design and analysis

Abstract This paper aims to construct a design and analysis framework for iterative learning control of linear inhomogeneous distributed parameter systems (LIDPSs), which may be hyperbolic, parabolic, or elliptic, and include many important physical processes such as diffusion, vibration, heat conduction and wave propagation as special cases. Owing to the system model characteristics, LIDPSs are first reformulated into a matrix form in the Laplace transform domain. Then, through the determination of a fundamental matrix, the transfer function of LIDPS is precisely evaluated in a closed form. The derived transfer function provides the direct input–output relationship of the LIDPS, and thus facilitates the consequent ILC design and convergence analysis in the frequency domain. The proposed control design scheme is able to deal with parametric and non-parametric uncertainties and make full use of the process repetition, while avoid any simplification or discretization for the 3D dynamics of LIDPS in the time, space, and iteration domains. In the end, two illustrative processes are addressed to demonstrate the efficacy of the proposed iterative learning control scheme.

Adaptive Boundary Iterative Learning Control for an Euler–Bernoulli Beam System With Input Constraint

This paper addresses the vibration control and the input constraint for an Euler–Bernoulli beam system under aperiodic distributed disturbance and aperiodic boundary disturbance. Hyperbolic tangent functions and saturation functions are adopted to tackle the input constraint. A restrained adaptive boundary iterative learning control (ABILC) law is proposed based on a time-weighted Lyapunov–Krasovskii-like composite energy function. In order to deal with the uncertainty of a system parameter and reject the external disturbances, three adaptive laws are designed and learned in the iteration domain. All the system states of the closed-loop system are proved to be bounded in each iteration. Along the iteration axis, the displacements asymptotically converge toward zero. Simulation results are provided to illustrate the effectiveness of the proposed ABILC scheme.