scholarly journals Indefinite LQ Problem for Irregular Singular Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Qingxiang Fang ◽  
Jigen Peng ◽  
Feilong Cao
Keyword(s):  
Optimal Control ◽  
Riccati Equation ◽  
State Feedback ◽  
Closed Loop ◽  
Singular Systems ◽  
Algebraic Riccati Equation ◽  
Closed Loop System ◽  
State Pair ◽  
Lq Problem ◽  
Control State

The indefinite LQ problem for irregular singular systems is investigated. Under some general conditions, the optimal control-state pair is obtained by solving an algebraic Riccati equation. The optimal control is synthesized as state feedback. All the finite poles of the closed-loop system are located on the left-half complex plane. An example is given to show the validity of the proposed conclusion.

scholarly journals Singular LQ Problem for Irregular Singular Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Qingxiang Fang ◽  
Baolin Zhang ◽  
Jun-e Feng
Keyword(s):  
Optimal Control ◽  
Control Method ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Free State ◽  
Algebraic Riccati Equation ◽  
Equivalence Transformation ◽  
State Pair ◽  
Lq Problem ◽  
Control State

This paper is concerned with the singular LQ problem for irregular singular systems with persistent disturbances. The full information feedback control method is employed to achieve the optimal control. By restricted system equivalence transformation, the system state is decomposed into free state and restricted state and the input is decomposed into free input and forced input. Some sufficient conditions for the unique existence of optimal control-state pair are derived and these conditions are all described unitedly with matrix rank equalities. The optimal control-state pair can be explicitly formulated via solving an algebraic Riccati equation and a Sylvester equation. Moreover, under the optimal control-state pair, the resulting system has no free state.

scholarly journals StochasticH∞Control for Discrete-Time Singular Systems with State and Disturbance Dependent Noise

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Yong Zhao ◽  
Xiushan Jiang ◽  
Weihai Zhang
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Closed Loop ◽  
Singular Systems ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Mean Square ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Theoretical Results

This paper is concerned with the stochasticH∞state feedback control problem for a class of discrete-time singular systems with state and disturbance dependent noise. Two stochastic bounded real lemmas (SBRLs) are proposed via strict linear matrix inequalities (LMIs). Based on the obtained SBRLs, a state feedbackH∞controller is presented, which not only guarantees the resulting closed-loop system to be mean square admissible but also satisfies a prescribedH∞performance level. A numerical example is finally given to illustrate the effectiveness of the proposed theoretical results.

Sensitivity Reduction of Constraint Forces and Position Control for Mechanical Descriptor Systems

1997 ◽  
Vol 119 (2) ◽  
pp. 286-289
Author(s):  
Dan-chi Jiang ◽  
Wei-Yong Yan ◽  
K. L. Teo
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Position Control ◽  
Design Procedure ◽  
Descriptor Systems ◽  
Algebraic Riccati Equation ◽  
Systematic Design ◽  
Closed Loop System ◽  
Constraint Forces ◽  
Constrained System

This paper deals with the position and force control for mechanical systems with holonomic constraints. Our concern is the design of a feedback controller such that the closed-loop system has a satisfactory transient response and is less sensitive to various types of disturbances. Using an appropriate transformation, the constrained system is converted into an unconstrained system of lower order. Then, an H∞, control problem involving the reduced system is formulated. In the case of state feedback, a systematic design procedure for solving the problem is presented, where the key step is the solution of an algebraic Riccati equation. An example is given to illustrate the effectiveness of the proposed method.

Robust H∞ State Feedback Control With Regional Pole Constraints: An Algebraic Riccati Equation Approach

1998 ◽  
Vol 120 (2) ◽  
pp. 289-292 ◽  
Author(s):  
Zidong Wang
Keyword(s):  
Riccati Equation ◽  
State Feedback ◽  
Closed Loop ◽  
Controller Design ◽  
State Feedback Control ◽  
Algebraic Riccati Equation ◽  
Equation Approach ◽  
Parameter Uncertainties ◽  
Realization Problem ◽  
Loop Matrix

This paper focuses on the controller design for uncertain linear continuous-time systems with H∞ norm and circular pole constraints and addresses the following multiobjective simultaneous realization problem: designing a state feedback controller such that the closed-loop system, for all admissible parameter uncertainties, simultaneously satisfies the prespecified H∞ norm constraint on the transfer function from disturbance input to output and the prespecified circular pole constraint on the closed-loop matrix. An effective, algebraic, modified Riccati equation approach is developed to solve this problem. The existence conditions, as well as the analytical expression of desired controllers, are derived. A numerical example is provided to show the directness and effectiveness of the present approach.

Dissipative Control of Singular Systems by Proportional Plus Derivative State Feedback

2012 ◽  
Vol 246-247 ◽  
pp. 826-831
Author(s):  
Shuang Yun Xing ◽  
Xin Jing ◽  
Yang Cao
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Singular Systems ◽  
Uncertain System ◽  
Loop System ◽  
Descriptor Systems ◽  
Control Synthesis ◽  
Closed Loop System ◽  
Dissipative Control ◽  
Derivative Matrix

This article deals with the problem of dissipative control synthesis for a class of descriptor systems with uncertainties in the derivative matrix. Attention is focused on the design of a proportional plus derivative (PD) state feedback, which guarantees that the closed-loop system is robustly stable and strict dissipative. Firstly, a sufficient condition for the closed-loop system is robustly stable and strict dissipative is presented by using a simple idea of changing the problem to the corresponding problem of an augmented uncertain system. Then, a PD controller is constructed by solving LMIs. Finally, a numerical example is given to demonstrate that the proposed method is effective.

The Swing Control of Cranes with Variable Rope Length Based on Linear Time Varying System Theory

2012 ◽  
Vol 461 ◽  
pp. 763-767
Author(s):  
Li Fu Wang ◽  
Zhi Kong ◽  
Xin Gang Wang ◽  
Zhao Xia Wu
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Linear Time ◽  
Feedback Stabilization ◽  
Time Varying ◽  
Closed Loop System ◽  
Overhead Cranes ◽  
Time Varying Systems ◽  
Time Invariant ◽  
Time Invariant System

In this paper, following the state-feedback stabilization for time-varying systems proposed by Wolovich, a controller is designed for the overhead cranes with a linearized parameter-varying model. The resulting closed-loop system is equivalent, via a Lyapunov transformation, to a stable time-invariant system of assigned eigenvalues. The simulation results show the validity of this method.

A Digital Algorithm for Near-Minimum-Time Control of Robot Manipulators

1987 ◽  
Vol 109 (4) ◽  
pp. 320-327 ◽  
Author(s):  
C. K. Kao ◽  
A. Sinha ◽  
A. K. Mahalanabis
Keyword(s):  
Control Algorithm ◽  
State Feedback ◽  
Closed Loop ◽  
Robot Manipulator ◽  
Minimum Time ◽  
State Feedback Control ◽  
Final States ◽  
Closed Loop System ◽  
Time Control ◽  
Digital Algorithm

A digital state feedback control algorithm has been developed to obtain the near-minimum-time trajectory for the end-effector of a robot manipulator. In this algorithm, the poles of the linearized closed loop system are judiciously placed in the Z-plane to permit near-minimum-time response without violating the constraints on the actuator torques. The validity of this algorithm has been established using numerical simulations. A three-link manipulator is chosen for this purpose and the results are discussed for three different combinations of initial and final states.

Global fixed-time stabilization for a class of uncertain high-order nonlinear systems with dead-zone input nonlinearity

2018 ◽  
Vol 41 (7) ◽  
pp. 1888-1895
Author(s):  
Fangzheng Gao ◽  
Yanling Shang ◽  
Yuqiang Wu ◽  
Yanhong Liu
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Closed Loop ◽  
Dead Zone ◽  
Fixed Time ◽  
High Order ◽  
Closed Loop System ◽  
Sign Function ◽  
Input Nonlinearity ◽  
Power Integrator

This paper considers the problem of global fixed-time stabilization for a class of uncertain high-order nonlinear systems. One distinct characteristic of this work is that the system under consideration possesses the dead-zone input nonlinearity. By delicately combining the sign function with a power integrator technique, a state feedback controller is designed such that the states of the resulting closed-loop system converge to the origin within a fixed time. A simulation example is provided to illustrate the effectiveness of the proposed approach.

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