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This article proposes three novel time‐varying policy iteration algorithms for finite‐horizon optimal control problem of continuous‐time affine nonlinear systems. We first propose a model‐based time‐varying policy iteration algorithm. The method considers time‐varying solutions to the Hamiltonian–Jacobi–Bellman equation for finite‐horizon optimal control. Based on this algorithm, value function approximation is applied to the Bellman equation by establishing neural networks with time‐varying weights. A novel update law for time‐varying weights is put forward based on the idea of iterative learning control, which obtains optimal solutions more efficiently compared to previous works. Considering that system models may be unknown in real applications, we propose a partially model‐free time‐varying policy iteration algorithm that applies integral reinforcement learning to acquiring the time‐varying value function. Moreover, analysis of convergence, stability, and optimality is provided for every algorithm. Finally, simulations for different cases are given to verify the convenience and effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

For a class of linear discrete‐time‐invariant systems repetitively operated in a finite time length, an iterative correction algorithm is exploited to identify the system Markov parameters with multi‐operation inputs and outputs in obeying a criterion, of which the time order of the corrector is adaptive to the time order of the controller. Interactively, an adaptive iterative learning control is architected which composes the compensator with the approximated Markov parameters and the tracking error in sequentially minimizing a quadratic objective function of the tracking error and the compensation. Algebraic manipulation achieves that the Markov parameters correction error is monotonically declining without any step parameter selection. Further, a rigorous derivation clarifies that the time order of the learning compensator must agree to the relative degree of the system and the tracking error is linearly monotonously convergent if the Markov parameters correction error falls into an allowable range. Inspiringly, the methods and results release the confinement to both the correction and the learning ratios. In addition, a smaller learning ratio factor tolerates a larger Markov parameters correction error. Numerical experiments support the significance and the validity. [ABSTRACT FROM AUTHOR]

Output reference tracking can be improved by iteratively learning from past data to inform the design of feedforward control inputs for subsequent tracking attempts. This process is called iterative learning control (ILC). This article develops a method to apply ILC to systems with nonlinear discrete‐time dynamical models with unstable inverses (i.e., discrete‐time nonlinear nonminimum phase models). This class of systems includes piezoactuators, electric power converters, and manipulators with flexible links, which may be found in nanopositioning stages, rolling mills, and robotic arms, respectively. As these devices may be required to execute fine transient reference tracking tasks repetitively in contexts such as manufacturing, they may benefit from ILC. Specifically, this article facilitates ILC of such systems by presenting a new ILC synthesis framework that allows combination of the principles of Newton's root finding algorithm with stable inversion, a technique for generating stable trajectories from unstable models. The new framework, called invert‐linearize ILC (ILILC), is validated in simulation on a cart‐and‐pendulum system with model error, process noise, and measurement noise. Where preexisting Newton‐based ILC diverges, ILILC with stable inversion converges, and does so in less than one third the number of trials necessary for the convergence of a gradient‐descent‐based ILC technique used as a benchmark. [ABSTRACT FROM AUTHOR]

In this work, an adaptive iterative learning control (AILC) method is designed for a class of parametric discrete‐time nonlinear systems with random initial condition, unknown time‐varying input gain and multiple time‐iteration‐varying factors including multiple unknown time‐iteration‐varying parameters and unknown time‐iteration‐varying external disturbance. The iteration‐varying factors can be generated by virtue of multiple iteration‐varying high‐order internal models, respectively, where iteration‐varying high‐order internal model means it has iteration‐varying order or coefficients. Moreover, the parameter updating law is designed based on the recursive least squares algorithm. Using the designed AILC based on iteration‐varying high‐order internal model, the learning convergence in the iteration domain is guaranteed through rigorous theoretical analysis under Lyapunov theory. Finally, two simulation examples are given to demonstrate that the proposed scheme is effective. [ABSTRACT FROM AUTHOR]

This work investigates robust monotonic convergent iterative learning control (ILC) for uncertain linear systems in both time and frequency domains, and the ILC algorithm optimizing the convergence speed in terms of l2 norm of error signals is derived. First, it is shown that the robust monotonic convergence of the ILC system can be established equivalently by the positive definiteness of a matrix polynomial over some set. Then, a necessary and sufficient condition in the form of sum of squares for the positive definiteness is proposed, which is amendable to the feasibility of linear matrix inequalities. Based on such a condition, the optimal ILC algorithm that maximizes the convergence speed is obtained by solving a set of convex optimization problems. Moreover, the order of the learning function can be chosen arbitrarily so that the designers have the flexibility to decide the complexity of the learning algorithm. [ABSTRACT FROM AUTHOR]

Spatially interconnected systems (SISs) are formed by a chain of subsystems or units with the same or similar structure, all of which directly interact with their neighbors. For robust tracking of SISs subject to both polytopic uncertainty and external disturbances, a PD‐type iterative learning control (ILC) algorithm integrated with real‐time output feedback is proposed in the absence of accurate state measurement. By lifting along the spatial variable, the SISs are first transformed into an equivalent one‐dimensional (1D) state‐space model. Then, the transformed 1D system, together with the learning law, is reformulated as an equivalent discrete repetitive process model. Based on the Lyapunov theory, sufficient conditions in terms of bilinear matrix inequalities (BMIs) are established to ensure the robust stability of the resulting ILC system along the trial. To circumvent computation problem of BMIs, a two‐stage heuristic approach is developed to derive ILC gains iteratively. Finally, the validity of the proposed method is verified by the comparative simulation of temperature distribution model of the metal rod. [ABSTRACT FROM AUTHOR]

Summary: For linear continuous multiple‐input multiple‐output systems with vector relative degree, which operate repetitively with an input‐driven motion and a following autonomous motion over a finite time interval, this article proposes an iteratively moving average operator (IMAO) based D‐type iterative learning control (ILC) method to address the iteratively varying input trail lengths and random initial state shifts. The proposed ILC algorithm has a rectifying action to random initial state shifts at the designed initial time interval. From the terminal time of rectifying action to the end of control input, it makes the ILC tracking error convergent into a bounded range, the bound of which is proportional to the initial state shifts. Specifically, as the initial state shifts remain fixed, the ILC tracking error can be driven to zero at the relevant time interval along the iteration axis. An example manifests the validity of the proposed IMAO based D‐type ILC algorithm. [ABSTRACT FROM AUTHOR]

Summary: Most existing iterative learning control algorithms are designed to improve tracking performance with respect to a given trajectory over a fixed time period. In this article, we design two iterative learning‐based economic model predictive controllers for repetitive tasks where no target trajectory is available. The controller is able to search for suboptimal trajectories with good performance by exploiting information from previous experience. Compared with existing works, the objective function is not assumed to be positive definite so it is not limited to the tracking problem but can represent more general economic performance index. The controller can learn from the previous closed‐loop trajectory, resulting in a performance which is guaranteed to be no worse than the previous one. Under some standard assumptions in model predictive control, the recursive feasibility of the algorithms is ensured. We show that the fixed operation time algorithm can guarantee that the performance is no worse than the previous iteration even without the dissipative assumption. By allowing the operation time to vary, the flexible operation time algorithm can balance the operation time and the system performance if dissipative assumption is satisfied. For both algorithms, each iteration is guaranteed to be completed within a uniformly bounded time duration. [ABSTRACT FROM AUTHOR]

Summary: This article deals with the problem of iterative learning control algorithm for a class of nonlinear parabolic distributed parameter systems (DPSs) with iteration‐varying desired trajectories. Here, the variation of the desired trajectories in the iteration domain is described by a high‐order internal model. According to the characteristics of the systems, the high‐order internal model‐based P‐type learning algorithm is constructed for such nonlinear DPSs, and furthermore, the corresponding convergence theorem of the presented algorithm is established. It is shown that the output trajectory can converge to the desired trajectory in the sense of (L2,λ)‐norm along the iteration axis within arbitrarily small error. Finally, a simulation example is given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a novel high-order optimal terminal iterative learning control (high-order OTILC) is proposed via a data-driven approach for nonlinear discrete-time systems with unknown orders in the input and output. The objective is to track the desired values at the endpoint of the operation cycle. The terminal tracking errors over more than one previous iterations are used to enhance the high-order OTILC's performance with faster convergence. From rigor of the analysis, the monotonic convergence of the terminal tracking error is proved along the iteration direction. More importantly, the condition for a high-order OTILC to outperform the low-order ones is first established by this work. The learning gain is not fixed but iteratively updated by using the input and output (I/O) data, which enhances the flexibility of the proposed controller for modifications and expansions. The proposed method is data-driven in which no explicit models are used except for the input and output data. The applications to a highly nonlinear continuous stirred tank reactor and a highly nonlinear fed-batch fermentater demonstrate the effectiveness of the proposed high-order OTILC design. [ABSTRACT FROM AUTHOR]

SUMMARY Based on recent papers that have demonstrated that robust iterative learning control can be based on parameter optimization using either the inverse plant or gradient concepts, this paper presents a unification of these ideas for discrete-time systems that not only retains the convergence properties and the robustness properties derived in previous papers but also permits the inclusion of filters in the input update formula and a detailed analysis of the effect of non-minimum-phase dynamics on algorithm performance in terms of a 'plateauing' or 'flat-lining' effect in the error norm evolution. Although the analysis is in the time domain, the robustness conditions are expressed as frequency domain inequalities. The special case of a version of the inverse algorithm that can be used to construct a robust stable anti-causal inverse non-minimum-phase plant is presented and analysed in detail. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]