General Nonlinear Discrete-time Systems Research Articles

A multi-observer based estimation framework for nonlinear systems under sensor attacks

For general discrete-time nonlinear systems, we address the state estimation problem under sensor attacks. We provide a general estimation scheme, built around the idea of sensor redundancy and multi-observers, capable of reconstructing the system state in spite of sensor attacks and noise, for a large class of nonlinear plants and observers. This scheme has been proposed by others for linear systems and here we propose a unifying framework for a much larger class of nonlinear systems.

A Set-Membership Approach to Event-Triggered Filtering for General Nonlinear Systems Over Sensor Networks

This paper is concerned with the distributed set-membership filtering problem for a class of general discrete-time nonlinear systems under event-triggered communication protocols over sensor networks. To mitigate the communication burden, each intelligent sensing node broadcasts its measurement to the neighboring nodes only when a predetermined event-based media-access condition is satisfied. According to the interval mathematics theory, a recursive distributed set-membership scheme is designed to obtain an ellipsoid set containing the target states of interest via adequately fusing the measurements from neighboring nodes, where both the accurate estimate on Lagrange remainder and the event-based media-access condition are skillfully utilized to improve the filter performance. Furthermore, such a scheme is only dependent on neighbor information and local adjacency weights, thereby fulfilling the scalability requirement of sensor networks. In addition, an optimization algorithm is developed to minimize the trace of the estimated ellipsoid set, and the effect from the adopted event-triggered threshold is thoroughly discussed as well. Finally, a simulation example is utilized to illustrate the usefulness of the proposed distributed set-membership filtering scheme.

Extended State Observer-Based Data-Driven Iterative Learning Control for Permanent Magnet Linear Motor With Initial Shifts and Disturbances

In this paper, an extended state observer-based data-driven iterative learning control [extended state observer (ESO)-based DDILC] is developed for a permanent magnet linear motor (PMLM). The PMLM is formulated mathematically by using a general nonlinear discrete-time system with consideration of exogenous disturbances. Then, a new iterative dynamic linearization (IDL) is proposed to equivalently reformulate the nonlinear PMLM system with a linear input-output incremental form involving iteration-varying initial states and disturbances. The concept of ESO is introduced into iteration direction to iteratively estimate the random initial states and disturbances as well as their corresponding partial derivatives by considering all of them as a whole extended state. The proposed ESO-based DDILC scheme contains a learning control algorithm and a gradient parameter updating algorithm obtained from two distinct objective functions, respectively. Moreover, the proposed method is data-driven and no explicit model is involved. Theoretical analysis shows the robustness of the proposed method in the presence of iteration-varying initial shifts and disturbances. The simulation on PMLM is conducted to confirm the validity and applicability of the ESO-based DDILC.

Stability Analysis of Discrete-Time Infinite-Horizon Optimal Control With Discounted Cost

We analyze the stability of general nonlinear discrete-time systems controlled by an optimal sequence of inputs that minimizes an infinite-horizon discounted cost. First, assumptions related to the controllability of the system and its detectability with respect to the stage cost are made. Uniform semiglobal and practical stability of the closed-loop system is then established, where the adjustable parameter is the discount factor. Stronger stability properties are thereupon guaranteed by gradually strengthening the assumptions. Next, we show that the Lyapunov function used to prove stability is continuous under additional conditions, implying that stability has a certain amount of nominal robustness. The presented approach is flexible and we show that robust stability can still be guaranteed when the sequence of inputs applied to the system is no longer optimal but near-optimal. We also analyze stability for cost functions in which the importance of the stage cost increases with time, opposite to discounting. Finally, we exploit stability to derive new relationships between the optimal value functions of the discounted and undiscounted problems, when the latter is well-defined.

Policy Gradient Adaptive Dynamic Programming for Data-Based Optimal Control.

The model-free optimal control problem of general discrete-time nonlinear systems is considered in this paper, and a data-based policy gradient adaptive dynamic programming (PGADP) algorithm is developed to design an adaptive optimal controller method. By using offline and online data rather than the mathematical system model, the PGADP algorithm improves control policy with a gradient descent scheme. The convergence of the PGADP algorithm is proved by demonstrating that the constructed Q -function sequence converges to the optimal Q -function. Based on the PGADP algorithm, the adaptive control method is developed with an actor-critic structure and the method of weighted residuals. Its convergence properties are analyzed, where the approximate Q -function converges to its optimum. Computer simulation results demonstrate the effectiveness of the PGADP-based adaptive control method.

Compensation of time-varying input delay for discrete-time nonlinear systems

Summary We consider general discrete-time nonlinear systems (of arbitrary nonlinear growth) with time-varying input delays and design an explicit predictor feedback controller to compensate the input delay. Such results have been achieved in continuous time, but only under the restriction that the delay rate is bounded by unity, which ensures that the input signal flow does not get reversed, namely, that old inputs are not felt multiple times by the plant (because on such subsequent occasions, the control input acts as a disturbance). For discrete-time systems, an analogous restriction would be that the input delay is non-increasing. In this work, we do not impose such a restriction. We provide a design and a global stability analysis that allow the input delay to be arbitrary (containing intervals of increase, decrease, or stagnation) over an arbitrarily long finite period of time. Unlike in the continuous-time case, the predictor feedback law in the discrete-time case is explicit. We specialize the result to linear time-invariant systems and provide an explicit estimate of the exponential decay rate. Carefully constructed examples are provided to illustrate the design and analytical challenges. Copyright © 2015 John Wiley & Sons, Ltd.

Adaptive Controller Design for a Class of Discrete Nonlinear Systems

In this paper, we have discussed the adaptive controller problem for a class of nonlinear discrete systems. Firstly, the general nonlinear discrete-time system is transformed into a new form which is more suitable for adaptive controller design. Based on the new model, the observer is proposed to estimate the unavailable states. The adaptive controller is designed to track the desired trajectory.

Optimal Iterative Learning Control for Nonlinear Discrete-Time Systems

In this paper, the problem about optimal iterative learning control of general nonlinear discrete-time systems has been studied. Based on the sufficient conditions of the existence of optimal iterative learning control in general nonlinear discrete-time systems, in view of the practical application, propose an approximate iterative algorithm, and prove the approximate iterative control restraining to the optimum control.

Output regulation of the general nonlinear discrete-time system

With the use of centre manifold and dynamic system theory, the necessary and sufficient conditions are obtained for the solvabilities of the output regulator problems for the general nonlinear discrete-time system. This work generalizes and refines the corresponding results by Isidori and Byrnes on the affine nonlinear continuous-time system.

On the stability of receding horizon control of nonlinear discrete-time systems

In this paper, we give sufficient conditions that guarantee the existence of the receding horizon control and the stability of the feedback system. The controlled system is a general nonlinear discrete-time system. Local and global stability are studied separately, giving rise to two sets of sufficient conditions. The context is that of regulation and tracking with internal model control scheme.

Identification of non-linear processes using reciprocal multiquadric functions

In this paper radial basis function (RBF) networks are used to model general non-linear discrete-time systems. In particular, reciprocal multiquadric functions are used as activation functions for the RBF networks. A stepwise regression algorithm based on orthogonalization and a series of statistical tests is employed for designing and training of the network. The identification method yields non-linear models, which are stable and linear in the model parameters. The advantages of the proposed method compared to other radial basis function methods and backpropagation neural networks are described. Finally, the effectiveness of the identification method is demonstrated by the identification of two non-linear chemical processes, a simulated continuous stirred tank reactor and an experimental pH neutralization process.