scholarly journals Remarks on the state convergence of nonlinear systems given any Lp input

2006 ◽  
Author(s):  
Bayu Jayawardhana
Keyword(s):  
Nonlinear Systems ◽  
The State

scholarly journals Event-Triggering State and Fault Estimation for a Class of Nonlinear Systems Subject to Sensor Saturations

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1242
Author(s):  
Cong Huang ◽  
Bo Shen ◽  
Lei Zou ◽  
Yuxuan Shen
Keyword(s):  
Nonlinear Systems ◽  
Difference Equations ◽  
Estimation Error ◽  
Upper Bounds ◽  
The State ◽  
Fault Estimation ◽  
Triggering Mechanism ◽  
Transmission Frequency ◽  
Current Transmission ◽  
Event Triggering

This paper is concerned with the state and fault estimation issue for nonlinear systems with sensor saturations and fault signals. For the sake of avoiding the communication burden, an event-triggering protocol is utilized to govern the transmission frequency of the measurements from the sensor to its corresponding recursive estimator. Under the event-triggering mechanism (ETM), the current transmission is released only when the relative error of measurements is bigger than a prescribed threshold. The objective of this paper is to design an event-triggering recursive state and fault estimator such that the estimation error covariances for the state and fault are both guaranteed with upper bounds and subsequently derive the gain matrices minimizing such upper bounds, relying on the solutions to a set of difference equations. Finally, two experimental examples are given to validate the effectiveness of the designed algorithm.

scholarly journals Ellipsoidal and Gaussian Kalman Filter Model for Discrete-Time Nonlinear Systems

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1168 ◽  
Author(s):  
Ligang Sun ◽  
Hamza Alkhatib ◽  
Boris Kargoll ◽  
Vladik Kreinovich ◽  
Ingo Neumann
Keyword(s):  
Kalman Filter ◽  
Nonlinear Systems ◽  
State Estimation ◽  
Discrete Time ◽  
Probability Distributions ◽  
Nonlinear Problems ◽  
The State ◽  
Filter Model ◽  
Highly Nonlinear ◽  
Correction Step

In this paper, we propose a new technique—called Ellipsoidal and Gaussian Kalman filter—for state estimation of discrete-time nonlinear systems in situations when for some parts of uncertainty, we know the probability distributions, while for other parts of uncertainty, we only know the bounds (but we do not know the corresponding probabilities). Similarly to the usual Kalman filter, our algorithm is iterative: on each iteration, we first predict the state at the next moment of time, and then we use measurement results to correct the corresponding estimates. On each correction step, we solve a convex optimization problem to find the optimal estimate for the system’s state (and the optimal ellipsoid for describing the systems’s uncertainty). Testing our algorithm on several highly nonlinear problems has shown that the new algorithm performs the extended Kalman filter technique better—the state estimation technique usually applied to such nonlinear problems.

scholarly journals Prediction-Based Control for Nonlinear Systems with Input Delay

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
I. Estrada-Sánchez ◽  
M. Velasco-Villa ◽  
H. Rodríguez-Cortés
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Input Signal ◽  
Lyapunov Functional ◽  
The State ◽  
Constant Time Delay ◽  
Change Of Variable ◽  
Lipschitz Systems ◽  
Suitable Change ◽  
Prediction Strategy

This work has two primary objectives. First, it presents a state prediction strategy for a class of nonlinear Lipschitz systems subject to constant time delay in the input signal. As a result of a suitable change of variable, the state predictor asymptotically provides the value of the state τ units of time ahead. Second, it proposes a solution to the stabilization and trajectory tracking problems for the considered class of systems using predicted states. The predictor-controller convergence is proved by considering a complete Lyapunov functional. The proposed predictor-based controller strategy is evaluated using numerical simulations.

scholarly journals Tracking Control Based on Recurrent Neural Networks for Nonlinear Systems with Multiple Inputs and Unknown Deadzone

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
J. Humberto Pérez-Cruz ◽  
José de Jesús Rubio ◽  
E. Ruiz-Velázquez ◽  
G. Solís-Perales
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Exponential Convergence ◽  
Broad Class ◽  
Tracking Error ◽  
The State ◽  
Control Law ◽  
Reference Trajectory ◽  
Uncertain Dynamics ◽  
The Difference

This paper deals with the problem of trajectory tracking for a broad class of uncertain nonlinear systems with multiple inputs each one subject to an unknown symmetric deadzone. On the basis of a model of the deadzone as a combination of a linear term and a disturbance-like term, a continuous-time recurrent neural network is directly employed in order to identify the uncertain dynamics. By using a Lyapunov analysis, the exponential convergence of the identification error to a bounded zone is demonstrated. Subsequently, by a proper control law, the state of the neural network is compelled to follow a bounded reference trajectory. This control law is designed in such a way that the singularity problem is conveniently avoided and the exponential convergence to a bounded zone of the difference between the state of the neural identifier and the reference trajectory can be proven. Thus, the exponential convergence of the tracking error to a bounded zone and the boundedness of all closed-loop signals can be guaranteed. One of the main advantages of the proposed strategy is that the controller can work satisfactorily without any specific knowledge of an upper bound for the unmodeled dynamics and/or the disturbance term.

State Feedback and Output Feedback Control of Polynomial Nonlinear Systems Using Fractional Lyapunov Functions

2007 ◽  
Author(s):  
Qian Zheng ◽  
Fen Wu
Keyword(s):  
Feedback Control ◽  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Output Feedback ◽  
Lyapunov Functions ◽  
State Feedback ◽  
The State ◽  
State Feedback Control ◽  
Feedback Gain ◽  
Variation Rate

In this paper, we will study the state feedback control problem of polynomial nonlinear systems using fractional Lyapunov functions. By adding constraints to bound the variation rate of each state, the general difficulty of calculating derivative of nonquadratic Lyapunov function is effectively overcome. As a result, the state feedback conditions are simplified as a set of Linear Matrix Inequalities (LMIs) with polynomial entries. Computationally tractable solution is obtained by Sum-of-Squares (SOS) decomposition. And it turns out that both of the Lyapunov matrix and the state feedback gain are state dependent fractional matrix functions, where the numerator as well as the denominator can be polynomials with flexible forms and higher nonlinearities involved in. Same idea is extended to a class of output dependent nonlinear systems and the stabilizing output feedback controller is specified as polynomial of output. Synthesis conditions are similarly derived as using constant Lyapunov function except that all entries in LMIs are polynomials of output with derivative of output involved in. By bounding the variation rate of output and gridding on the bounded interval, the LMIs are solvable by SOS decomposition. Finally, two examples are used to materialize the design scheme and clarify the various choices on state boundaries.

scholarly journals Learning Output Reference Model Tracking for Higher-Order Nonlinear Systems with Unknown Dynamics

Algorithms ◽  
2019 ◽  
Vol 12 (6) ◽  
pp. 121 ◽  
Author(s):  
Mircea-Bogdan Radac ◽  
Timotei Lala
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Reference Model ◽  
The State ◽  
State Transitions ◽  
Practical Implementation ◽  
General Function ◽  
State Action ◽  
Model Free ◽  
Continuous State

This work suggests a solution for the output reference model (ORM) tracking control problem, based on approximate dynamic programming. General nonlinear systems are included in a control system (CS) and subjected to state feedback. By linear ORM selection, indirect CS feedback linearization is obtained, leading to favorable linear behavior of the CS. The Value Iteration (VI) algorithm ensures model-free nonlinear state feedback controller learning, without relying on the process dynamics. From linear to nonlinear parameterizations, a reliable approximate VI implementation in continuous state-action spaces depends on several key parameters such as problem dimension, exploration of the state-action space, the state-transitions dataset size, and a suitable selection of the function approximators. Herein, we find that, given a transition sample dataset and a general linear parameterization of the Q-function, the ORM tracking performance obtained with an approximate VI scheme can reach the performance level of a more general implementation using neural networks (NNs). Although the NN-based implementation takes more time to learn due to its higher complexity (more parameters), it is less sensitive to exploration settings, number of transition samples, and to the selected hyper-parameters, hence it is recommending as the de facto practical implementation. Contributions of this work include the following: VI convergence is guaranteed under general function approximators; a case study for a low-order linear system in order to generalize the more complex ORM tracking validation on a real-world nonlinear multivariable aerodynamic process; comparisons with an offline deep deterministic policy gradient solution; implementation details and further discussions on the obtained results.

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