Trajectory enclosures for nonlinear systems with uncertain initial conditions and parameters

2012 ◽  
Author(s):  
E. August ◽  
J. Lu ◽  
H. Koeppl
Keyword(s):  
Nonlinear Systems ◽  
Initial Conditions

APPLICATION OF INFORMATION TECHNOLOGY FOR MODELING THE CONTROL DYNAMICS OF A NUCLEAR REACTOR ZONING ON THE VERTICAL AXIS

2021 ◽  
Vol 5 ◽  
pp. 45-56
Author(s):  
Valery Severyn ◽  
◽  
Elena Nikulina ◽  
Keyword(s):  
Information Technology ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Control Systems ◽  
Nuclear Reactor ◽  
Initial Conditions ◽  
Control Object ◽  
Vertical Axis ◽  
Integration Methods ◽  
Systems Of Differential Equations

The structure of information technology for modeling control systems, which includes a block of systems models, a module of integration methods and other program elements, is considered. To analyze the dynamics of control of a nuclear reactor, programs of mathematical models of a WWER-1000 nuclear reactor of the V-320 series and its control systems in the form of nonlinear systems of differential equations in the Cauchy form have been developed. For the integration of nonlinear systems of differential equations, an algorithm of the system method of the first degree is presented. A mathematical model of a WWER-1000 reactor as a control object with division into zones along the vertical axis in relative variables of state is considered, the values of the constant parameters of the model and the initial conditions corresponding to the nominal mode are given. Using information technology for ten zones of the reactor, the system integration method was used to simulate the dynamics of control of a nuclear reactor. Graphs of neutron and thermal processes in the reactor core, as well as changes in the axial offset when the reactor load is dumped under the influence of the movement of absorbing rods and an increase in the concentration of boric acid, are plotted. The analysis of dynamic processes of reactor control is carried out. The programs of integration methods and models of the WWER-1000 reactor of the V-320 series are included in the information technology to optimize the maneuvering modes of the reactor.

Functional Representation of Nonlinear Systems, Interpolation and Lagrange Expansion for Functionals

1966 ◽  
Vol 88 (2) ◽  
pp. 429-436 ◽  
Author(s):  
D. Gorman ◽  
J. Zaborszky
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Initial Conditions ◽  
Analytic Representation ◽  
Input Output ◽  
The Third ◽  
Functional Representation ◽  
Lagrange Expansion ◽  
Functional Representations ◽  
Measured Input

The paper consists principally of three parts. In the first, an original analytic representation is introduced for systems where differential equations are available. In the second, the structure of the functional is analyzed with nonzero initial conditions. The third introduces functional representations for systems described by past measured input-output records.

scholarly journals Global Asymptotic Stabilization Control for a Class of Nonlinear Systems with Dynamic Uncertainties

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Jiangbo Yu ◽  
Jizhong Wang ◽  
Zhongcai Zhang
Keyword(s):  
Nonlinear Systems ◽  
Controller Design ◽  
Initial Conditions ◽  
Design Procedure ◽  
Control Law ◽  
Asymptotic Stabilization ◽  
Control Approach ◽  
Global Asymptotic Stabilization ◽  
Stabilization Control ◽  
Dynamic Uncertainties

This paper is concerned with the global asymptotic stabilization control problem for a class of nonlinear systems with input-to-state stable (ISS) dynamic uncertainties and uncertain time-varying control coefficients. Unlike the existing works, the ISS dynamic uncertainty is characterized by the uncertain supply rates. By using the backstepping control approach, a systematic controller design procedure is developed. The designed control law can guarantee that the system states are asymptotically regulated to the origin from any initial conditions and the other signals are bounded in closed-loop systems. Moreover, it is shown that, under some additional conditions, a linear control law can be designed by the proposed methodology. The simulation example demonstrates its effectiveness.

scholarly journals Almost Disturbance Decoupling for a Class of Fractional-Order Nonlinear Systems with Zero Dynamics

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Xiaoping Liu ◽  
Yajing Zhao ◽  
Caiyun Wang ◽  
Huanqing Wang ◽  
Yucheng Zhou
Keyword(s):  
Nonlinear Systems ◽  
Fractional Order ◽  
Initial Conditions ◽  
Design Method ◽  
Tracking Error ◽  
Lyapunov Stability Theory ◽  
External Disturbances ◽  
Output Tracking ◽  
Almost Disturbance Decoupling ◽  
Disturbance Decoupling

The problem of almost disturbance decoupling is addressed for fractional-order nonlinear systems. A new definition for the norm is proposed to describe the effect of disturbances on the output tracking error for fractional-order systems. Based on the Lyapunov stability theory and the backstepping design method, a tracking controller is constructed to make the output tracking error converge to zero without external disturbances and to attenuate the effect of disturbances on the tracking error at zero initial conditions. In order to validate these theoretical results, a numerical example and two practical examples are given.

Parameter identifiability of nonlinear systems: the role of initial conditions

Automatica ◽  
2003 ◽  
Vol 39 (4) ◽  
pp. 619-632 ◽  
Author(s):  
Maria Pia Saccomani ◽  
Stefania Audoly ◽  
Leontina D'Angiò
Keyword(s):  
Nonlinear Systems ◽  
Initial Conditions ◽  
Parameter Identifiability

What Could Be Worse than the Butterfly Effect?

2008 ◽  
Vol 38 (4) ◽  
pp. 519-547 ◽  
Author(s):  
Robert C. Bishop
Keyword(s):  
Nonlinear Systems ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Classical Mechanics ◽  
Physical Systems ◽  
Physics Community ◽  
Sensitive Dependence ◽  
Classical Models ◽  
In The Beginning

Our understanding of classical mechanics (CM) has undergone significant growth in the latter half of the twentieth century and in the beginning of the twenty-first. This growth has much to do with the explosion of interest in the study of nonlinear systems in contrast with the focus on linear systems that had colored much work in CM from its inception. For example, although Maxwell and Poincaré arguably were some of the first to think about chaotic behavior, the modern study of chaotic dynamics traces its beginning to the pioneering work of Edward Lorenz (1963). This work has yielded a rich variety of behavior in relatively simple classical models that was previously unsuspected by the vast majority of the physics community (see Hilborn 2001). Chaos is a property of nonlinear systems that is usually characterized by sensitive dependence on initial conditions (SDIC). In CM the behavior of simple physical systems is described using models (such as the harmonic oscillator) that capture the main features of the systems in question (Giere 1988).

scholarly journals A Novel Method of Prescribed Constraint Control Without Initial Condition of Nonlinear Systems

2021 ◽  
Author(s):  
Hui Liu ◽  
Xiaohua Li ◽  
Xiaoping Liu
Keyword(s):  
Nonlinear Systems ◽  
Control Strategy ◽  
Control Method ◽  
Actuator Saturation ◽  
Initial Conditions ◽  
Setting Time ◽  
Tracking Error ◽  
Initial Condition ◽  
Constraint Control ◽  
Performance Constraint

Abstract A novel constraint control strategy without initial condition of constrained variables is investigated based on backstepping technique for nonlinear systems. In this paper, the novel constraint control strategy is presented for a class of strict-feedback nonlinear systems with actuator saturation and external disturbances by using a nonlinear mapping and a novel performance constraint function. In this control strategy, there are two prescribed constraint functions, the design of these functions is not related to the initial conditions of the constrained variables. Unlike the existing constraint control method without initial condition, the proposed method gives a new solution. It can guarantee that the constraint variable gets into a prescribed constraint region from any initial value no later than a setting time. And the setting time is a design parameter, it can be set arbitrarily. A prescribed performance constraint tracking controller is designed in this paper. It can make that the tracking error of the nonlinear system is constrained to a given region no later than the given setting time, and the transient and steady state performance of the system are ensured. Finally, the proposed method is compared with the existing method, the effectiveness and superiority of the proposed method are demonstrated by two practical examples.

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