scholarly journals A New Finite-Time Bounded Control of Stochastic Itô Systems with (x,u,v)-Dependent Noise: Different Quadratic Function Approach

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Zhiguo Yan ◽  
Zhongwei Lin
Keyword(s):  
Finite Time ◽  
Stochastic Systems ◽  
Quadratic Function ◽  
Function Approach ◽  
Control Input ◽  
Matrix Inequalities ◽  
Bounded Control ◽  
Linear Stochastic Systems ◽  
Nonlinear Matrix ◽  
Finite Time Boundedness

This paper addresses the finite-time bounded control problem of linear stochastic systems with state, control input, and external disturbance-dependent noise ((x,u,v)-dependent noise for short). The notion of finite-time boundedness of linear stochastic systems is first introduced. Then a different quadratic function approach is proposed to give a sufficient condition for finite-time boundedness of such a class of systems, and its superiority to common quadratic approach is shown. Moreover, the finite-time bounded controller design problem is studied and two sufficient conditions for the existence of state and output feedback controllers are presented in terms of nonlinear matrix inequalities. An algorithm is given for solving the obtained nonlinear matrix inequalities. Finally, an example is employed to illustrate the effectiveness of our obtained results.

scholarly journals Finite-Time H2/H∞ Control for Linear Itô Stochastic Systems with x,u,v-Dependent Noise

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Zhiguo Yan ◽  
Shiyu Zhong ◽  
Xingping Liu
Keyword(s):  
Optimization Algorithm ◽  
Finite Time ◽  
Performance Index ◽  
State Feedback ◽  
Closed Loop ◽  
Stochastic Systems ◽  
Transient Performance ◽  
Closed Loop Systems ◽  
Linear Stochastic Systems ◽  
Finite Time Boundedness

This paper deals with the problem of the H2/H∞ control based on finite-time boundedness for linear stochastic systems. The motivation for investigating this problem comes from one observation that the H2/H∞ control does not involve systems’ transient performance. To express this problem clearly, a concept called finite-time H2/H∞ control is introduced. Moreover, state feedback and observer-based finite-time H2/H∞ controllers are designed, which guarantee finite-time boundedness, H2 performance index, and H∞ performance index of the closed-loop systems. Furthermore, an optimization algorithm on the finite-time H2/H∞ control is presented to obtain the minimum values of the H2 index and H∞ index. Finally, we use an example to show the validity of the obtained results.

scholarly journals Bounded finite-time stabilization of the prey – predator model via Korobov’s controllability function

2021 ◽  
Vol 21 (1) ◽  
pp. 76-87
Author(s):  
Abdon E. Choque-Rivero ◽  
◽  
Fernando Ornelas-Tellez ◽  
Keyword(s):  
Equilibrium Point ◽  
Finite Time ◽  
Control Input ◽  
Bounded Control ◽  
Physical Restriction ◽  
Simulation Results ◽  
Finite Time Stabilization ◽  
Predator Model ◽  
Control Methodology ◽  
Predator System

The problem of finite-time stabilization for a Leslie-Gower prey – predator system through a bounded control input is solved. We use Korobov’s controllability function. The trajectory of the resulting motion is ensured for fulfilling a physical restriction that prey and predator cannot achieve negative values. For this purpose, a certain ellipse depending on given data and the equilibrium point of the considered system is constructed. Simulation results show the effectiveness of the proposed control methodology.

Design the finite-time H∞ resilient filter of a class of switched systems with uncertain parameters

2017 ◽  
Vol 40 (9) ◽  
pp. 2756-2764 ◽  
Author(s):  
Qilong Ai ◽  
Chengcheng Ren ◽  
Jun Dong ◽  
Shuping He
Keyword(s):  
Dynamic Systems ◽  
Finite Time ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Error Dynamic ◽  
Finite Time Boundedness ◽  
Error Dynamics

This paper is concerned with the problem of finite-time H∞ resilient filtering for a class of switch systems. The filtering error dynamics is constructed based on the H∞ resilient filter. The objective is to design a filter such that the finite-time H∞ gain from the unknown input to an estimation error is minimized or guaranteed to be less than or equal to a prescribed value. By selecting the proper multiple Lyapunov function and using the average dwell-time approach, sufficient conditions are obtained for the existence of the desired H∞ resilient filter, which also guarantee the finite-time boundedness of the filtering error dynamic systems. The design criteria are proposed in the form of linear matrix inequalities and then described as an optimization algorithm. Finally, a numerical example is employed to illustrate the effectiveness of the developed techniques.

scholarly journals Robust Finite-TimeH∞Control for Linear Time-Varying Descriptor Systems with Jumps

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Xiaoming Su ◽  
Adiya Bao
Keyword(s):  
Linear Matrix Inequalities ◽  
Finite Time ◽  
Linear Time ◽  
Descriptor Systems ◽  
Feasibility Problem ◽  
Descriptor System ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Finite Time Boundedness

The finite-timeH∞control problem is addressed for uncertain time-varying descriptor system with finite jumps and time-varying norm-bounded disturbance. Firstly, a sufficient condition of finite-time boundedness for the abovementioned class of system is obtained. Then the result is extended to finite-timeH∞for the system. Based on the condition, state feedback controller is designed such that the closed-loop system is finite-time boundedness and satisfiesL2gain. The conditions are given in terms of differential linear matrix inequalities (DLMIs) and linear matrix inequalities (LMIs), and such conditions require the solution of a feasibility problem involving DLMIs and LMIs, which can be solved by using existing linear algorithms. Finally, a numerical example is given to illustrate the effectiveness of the method.

Continuous-Time Feedback Control With Finite-Time Boundedness and H∞ Performance Criteria

2015 ◽  
Author(s):  
Jacob D. Hostettler ◽  
Xin Wang
Keyword(s):  
Feedback Control ◽  
Linear Matrix Inequalities ◽  
Finite Time ◽  
Control Method ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Performance Criteria ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Finite Time Boundedness

For advanced control applications, research into the use of linear matrix inequalities has yielded a notable amount of work in the area of nonlinear systems. Linear Matrix Inequalities can be formed through the application of desired performance criteria to a general system. By proper selection of a Lyapunov energy function, sufficient conditions to satisfy the performance objectives can be realized. The performance criteria, typically chosen for the application, define the objectives associated with the control. This work presents a control method for discrete-time systems with finite-time boundedness and H∞ performance criteria. The design of the controller corresponds to a system existing with bounded model uncertainties, and in the presence of L2 type external disturbances. Through the use of a linear state feedback control, sufficient conditions which guarantee the finite-time stability and H∞ performance objectives are achieved via the solution of a Linear Matrix Inequality. MATLAB application and simulation is carried out using the field oriented control of a permanent magnet synchronous generator in order to effectively demonstrate the effectiveness of this control strategy in the wind energy conversion system application.

Observer-Based Finite-Time Nonfragile Control for Nonlinear Systems With Actuator Saturation

2018 ◽  
Vol 14 (1) ◽  
Author(s):  
R. Sakthivel ◽  
R. Mohana Priya ◽  
Chao Wang ◽  
P. Dhanalakshmi
Keyword(s):  
Finite Time ◽  
Actuator Saturation ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Discrete Time System ◽  
Time Varying Delay ◽  
Control Gain ◽  
Finite Time Boundedness ◽  
Nonfragile Control

This paper considers a design problem of dissipative and observer-based finite-time nonfragile control for a class of uncertain discrete-time system with time-varying delay, nonlinearities, external disturbances, and actuator saturation. In particular, in this work, it is assumed that the nonlinearities satisfy Lipschitz condition for obtaining the required results. By choosing a suitable Lyapunov–Krasovskii functional, a new set of sufficient conditions is obtained in terms of linear matrix inequalities, which ensures the finite-time boundedness and dissipativeness of the resulting closed-loop system. Meanwhile, the solvability condition for the observer-based finite-time nonfragile control is also established, in which the control gain can be computed by solving a set of matrix inequalities. Finally, a numerical example based on the electric-hydraulic system is provided to illustrate the applicability of the developed control design technique.

scholarly journals Finite-TimeH∞Filtering for Singular Stochastic Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Caixia Liu ◽  
Yingqi Zhang ◽  
Huixia Sun
Keyword(s):  
Finite Time ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Time Interval ◽  
Inequality Technique ◽  
Error System ◽  
Singular Stochastic Systems ◽  
Finite Time Boundedness ◽  
Bounded Disturbance ◽  
Linear Matrix Inequality Technique

This paper addresses the problem of finite-timeH∞filtering for one family of singular stochastic systems with parametric uncertainties and time-varying norm-bounded disturbance. Initially, the definitions of singular stochastic finite-time boundedness and singular stochasticH∞finite-time boundedness are presented. Then, theH∞filtering is designed for the class of singular stochastic systems with or without uncertain parameters to ensure singular stochastic finite-time boundedness of the filtering error system and satisfy a prescribedH∞performance level in some given finite-time interval. Furthermore, sufficient criteria are presented for the solvability of the filtering problems by employing the linear matrix inequality technique. Finally, numerical examples are given to illustrate the validity of the proposed methodology.

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