Class Of Nonlinear Discrete Systems Research Articles

Optimal distributed filtering for nonlinear saturated systems with random access protocol and missing measurements: The uncertain probabilities case

The saturated-constrained distributed filtering problem is discussed for a class of discrete nonlinear systems with random access protocol (RAP) and missing measurements (MMs) under uncertain missing probabilities (UMPs). In order to prevent data congestions, the RAP is adopted to regulate the information transmission, where only one sensor is scheduled to have the communication right and transmit the information at each time step through a shared network. In addition, the phenomenon of MMs is considered, in which the UMPs are characterized by means of the nominal means and error bounds. The main purpose of this paper is to design a distributed filter under saturation constraint such that, for both RAP and MMs under UMPs, there exists an upper bound (UB) matrix of filtering error covariance and the corresponding distributed filter gain is constructed to minimize the trace of the received UB matrix by resorting to the matrix simplifying technique. Besides, the filtering algorithm performances are discussed regarding the boundedness and monotonicity of the presented distributed filtering scheme from the mathematical perspective. Finally, some comparisons are provided to illustrate the validity of the proposed time-varying distributed filtering algorithm.

A framework for 3D tracking of frontal dynamic objects in autonomous cars

Both recognition and 3D tracking of frontal dynamic objects are crucial problems in an autonomous vehicle, while depth estimation as an essential issue becomes a challenging problem using a monocular camera. Since both camera and objects are moving, the issue can be formed as a structure from motion (SFM) problem. In this paper, to elicit features from an image, the YOLOv3 approach is utilized beside an OpenCV tracker. Subsequently, to obtain the lateral and longitudinal distances, a nonlinear SFM model is considered alongside a state-dependent Riccati equation (SDRE) filter and a newly developed observation model. Additionally, a switching method in the form of switching estimation error covariance is proposed to enhance the robust performance of the SDRE filter. The stability analysis of the presented filter is conducted on a class of discrete nonlinear systems. Furthermore, the ultimate bound of estimation error caused by model uncertainties is analytically obtained to investigate the switching significance. Simulations are reported to validate the performance of the switched SDRE filter. Finally, real-time experiments are performed through a multi-thread framework implemented on a Jetson TX2 board, while radar data is used for the evaluation.

Design of Sliding-Mode-Based Control for Nonlinear Systems With Mixed-Delays and Packet Losses Under Uncertain Missing Probability

This paper is coped with the robust sliding-mode-based control problem for a class of discrete nonlinear systems in the presence of mixed-delays and packet losses with uncertain missing probability. Both the time-varying state delays and the infinite distributed state delays are considered. Also, the data packet losses are modeled by a Bernoulli distributed stochastic variable with uncertain missing probability and an update rule is employed to characterize the signal transmitted to controller side. A sliding function is first constructed and the desired stochastic mean-square stability of sliding motion is ensured by providing a sufficient condition based on the matrix inequality technique. Besides, a new discrete SMC strategy is designed to guarantee that the state trajectories are driven onto the bounded band of predesigned sliding surface and maintain them therein during subsequent time. Finally, the effectiveness of the developed sliding-mode control technique is verified by some simulations with comparative results.

Distributed Finite-Horizon Extended Kalman Filtering for Uncertain Nonlinear Systems.

In this paper, the state estimation problem is investigated for a class of discrete nonlinear systems via sensor networks. A novel robust distributed extended Kalman filter, which can handle norm-bounded uncertainties in both the system model and its Taylor series expansion, is developed with ensured estimation performance. The filter is distributed in the sense that for each sensor, only its own measurements and its neighbors' information are utilized to optimize the upper bound of the estimation error covariance. Besides, a sufficient condition for the proposed algorithm is derived, which is simple and user-friendly since it depends on the property of the original nonlinear system instead of the estimation error covariance calculated at every step. Finally, the simulation results are presented to demonstrate the effectiveness of the filtering algorithm.

Distributed finite time cubature information filtering with unknown correlated measurement noises

This paper addresses the distributed state estimation problem for a class of discrete nonlinear system over sensor networks subject to unknown correlated measurement noises. Firstly, under the condition of network connectivity, a novel communication protocol is developed to ensure every sensor node can gather the information distributed throughout the network within finite communication time. Then a fully distributed estimator is designed by periodically fusing the local information and neighbor’s information according to the covariance intersection fusion strategy. Theoretically, it is proved that the distributed estimator in each sensor node is stable with the exponentially bounded estimation error in mean square. Finally, some numerous simulations are performed to illustrate the practical effectiveness and superiority of the proposed state estimator.

Data‐driven adaptive terminal sliding mode control with prescribed performance

AbstractWe propose a novel data‐driven model‐free adaptive terminal sliding mode control (SMC) for a class of discrete nonlinear systems with perturbations in which tracking error constraints are taken into account in improving tracking accuracy. The goal of this design is that the tracking error trajectory is maintained within the prescribed convergence region which is defined by the performance function, while the disturbances exist. In explaining the advantage of this proposed control scheme, at first, by theoretical calculation, it is proved theoretically that the quasi‐sliding mode can be achieved in a limited time under the specified tracking performance. Furthermore, comparative investigation results are given to validate the effectiveness of the proposed control scheme. Simulation results show that the proposed strategy is superior to model‐free adaptive control, model‐free adaptive terminal SMC, and data‐driven adaptive SMC with prescribed performance control algorithms in terms of tracking accuracy and response speed, which demonstrates the efficiency of the proposed scheme.

Robust model predictive control of discrete nonlinear systems with time delays and disturbances via T–S fuzzy approach

In this paper, robust fuzzy model predictive control of a class of nonlinear discrete systems subjected to time delays and persistent disturbances is investigated. Based on the modeling method of delay difference inclusions, nonlinear discrete time-delay systems can be represented by T–S fuzzy systems comprised of piecewise linear delay difference equations. Moreover, Lyapunov–Razumikhin function (LRF), instead of Lyapunov–Krasovskii functional (LKF), is employed for time-delay systems due to its ability to reflect system original state space and its advantages in controller synthesis and computation. The robust positive invariance and input-to-state stability with respect to disturbance under such circumstances are investigated. A robust constraint set is adopted that the system state is converged to this set round the desired point. In addition, the controller synthesis conditions are derived by solving a set of matrix inequalities. Simulation results show that the proposed approach can be successfully applied to the well-known continuous stirred tank reactor (CSTR) systems subjected to time delay.

On the Robust Stabilization of One Class of Nonlinear Discrete Systems

We study the problem of robust linear stabilization of a family of nonlinear discrete control systems with uncertainties and nonlinearly dependent control. We establish sufficient conditions for the robust stabilization and synthesize linear regulators of state engaged in the robust stabilization. The obtained necessary conditions for the robust stabilization are close to sufficient.

Sliding Mode-Like Fuzzy Logic Control With Adaptive Boundary Layer for Multiple-Variable Discrete Nonlinear Systems

AbstractMore serious chattering emerges in discrete systems of sliding mode control. The paper presents a sliding mode-like fuzzy logic control design, which eliminates the chattering, for a class of discrete nonlinear systems with multiple variables. First, the boundary layer is self-tuned on-line, and then, the chattering free is obtained. Consequently, the fuzzy logic control (FLC) is designed to approximate the sliding mode control (SMC) with boundary layer self-tuning. Finally, the performance of the robustness, chattering free, and adaption are verified by the simulation results.

Fault Detection and Diagnosis for a Class of Nonlinear Systems with Decentralized Event-triggered Transmissions

In this paper, the fault detection and diagnosis problems are considered for a class of discrete nonlinear systems with decentralized event-triggered measurement transmissions. Each sensor determines, according to certain triggering rules, whether to transmit the present measurement to remote filters based on only locally available information. A set of filters is designed where each filter aims to jointly estimate the system states and a specific possible fault. Upper bounds of the estimation error covariances are obtained in the simultaneous presence of the linearization errors and decentralized event-triggered transmissions, and then the filter gains are calculated to minimize such bounds. The filters are designed in a recursive way and thus the algorithm is applicable for online implementation. When a fault is detected, the filter with the least residual is regarded as the one corresponding to the actual fault and its output can be seen as the states and fault estimation. The effectiveness of the proposed method is illustrated by a simulation example.

Nonlinear generalized predictive control based on online least squares support vector machines

For a class of nonlinear discrete systems with unknown parameters, an adaptive direct generalized predictive control method based on online least squares support vector machines (OLS–SVM) is proposed. In the method, the OLS–SVM is used to design the controller directly, and an improved projection algorithm based on the tracking error is introduced to adjust the weights of the OLS–SVM adaptively, so the inverse matrix is avoided in the process of online real-time control. It is proved that the proposed method can make the tracking error converge to a small neighborhood of the origin. Simulation results have shown the correctness and effectiveness of the proposed method.

State estimation for a class of discrete nonlinear systems with randomly occurring uncertainties and distributed sensor delays

In this paper, the state estimation problem is investigated for a class of discrete nonlinear systems with randomly occurring uncertainties and distributed sensor delays. The norm-bounded uncertainties enter into the system in a randomly way, and such randomly occurring uncertainties (ROUs) obey certain Bernoulli distributed white noise sequence with known conditional probability. By constructing a new Lyapunov–Krasovskii functional, sufficient conditions are proposed to guarantee the convergence of the estimation error for all discrete time-varying delays, ROUs and distributed sensor delays. Subsequently, the explicit form of the estimator parameter is derived by solving two linear matrix inequalities (LMIs) which can be easily tested by using standard numerical software. Finally, a simulation example is given to illustrate the feasibility and effectiveness of the proposed estimation scheme.

Convergence of PD-Type Iterative Learning Control of Nonlinear Discrete Systems and its Robustness

Abstract: For the control problem of nonlinear discrete systems, this paper describes the status of current research and analyzes the advantages and disadvantages of open-loop and closed-loop iterative learning controller. A class of nonlinear discrete systems will be extended to the general nonlinear discrete systems. To the general nonlinear discrete systems, a open-closed-loop PD-type iterative learning controller which based on current and last output error instead of last output error only is proposed. It makes use of information on system operation more fully and accurately. Besides, based on norm of λ and mathematical induction, its sufficient condition for convergence is given. In order to test its robustness, a simulation is done in the case of a persistent interference. Simulation results show that it is efficient.

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.

Stability in the domain of nonlinear difference inclusions1

The problem of establishing the sufficient conditions for robust stability in a given domain is considered for the class of nonlinear discrete systems described by a difference inclusion. The nonlinear function of the system cannot be represented in a quasilinear form, and only nonlinear constraints are specified for its values. Examples of constructive testing of the sufficient stability conditions are presented.

H∞ Observer Design for a Class of Nonlinear Discrete Systems

In this paper, the problem of observing the state of a class of discrete nonlinear system is addressed. The design of the observer is dealt with using H∞ performance techniques, taking into account disturbance and noise attenuation. The result is an LMI optimization problem that can be solved by standard optimization techniques. A design strategy is proposed based on the available disturbances information.

About the Stability and Positivity of a Class of Discrete Nonlinear Systems of Difference Equations

This paper investigates stability conditions and positivity of the solutions of a coupled set of nonlinear difference equations under very generic conditions of the nonlinear real functions which are assumed to be bounded from below and nondecreasing. Furthermore, they are assumed to be linearly upper bounded for sufficiently large values of their arguments. These hypotheses have been stated in 2007 to study the conditions permanence.

Robust H∞ observer for nonlinear discrete systems with time delay and parameter uncertainties

The robust H∞ observer design problem is studied for a class of nonlinear discrete systems with time delay and uncertainties. The nonlinearities are assumed to satisfy global Lipschitz conditions which appear in both the dynamics and the measured output equation. The problem addressed is to design a nonlinear observer such that, for all the admissible uncertainties, the dynamics of the observer error is globally exponentially stable and has a prescribed H∞ performance. A linear matrix inequality approach is developed and a sufficient condition is obtained to design the nonlinear robust H∞ observer. Specifically, the convergent rate of the error state can be estimated by the initial condition and time delay of the system. Furthermore, robust H∞ observer designs for linear (or bilinear) discrete systems with time delay and uncertainties can be obtained directly. Finally, the effectiveness of the proposed observer design is illustrated through two numerical examples.

On the Maximal Output Admissible Set for a Class of Nonlinear Discrete Systems

Consider the nonlinear discrete system x(i + 1) = A(x(i)x(i), i ≥ 0, where A is a nonlinear map such that A(x) is a real matrix for every x ∈ Rn, the output function is supposed to be y(i) = Cx(i), i ≥ 0. Given a constraint set Ω ⊂ Rp, an initial state x(0) is said to be output admissible if the resulting output signal (y(i))i satisfies the condition y(i) ∈ Ω for every integer i ≥ 0. In this paper we propose a theoretical and algorithmic studying of the set of all possible such initial states. The case of discrete delayed systems is also considered. The second part of the paper is devoted to the characterization of the output admissible initial states corresponding to a continuous-time nonlinear system with discrete output.

Domain of attraction of nonlinear discrete systems with delays

In this paper, we obtain the methods to determine the domain of exponential attraction of a class of nonlinear discrete systems with delays. Examples are given to show the applicability of the proposed approach.