Decentralized control for spacecraft formation in elliptic orbits

2018 ◽  
Vol 90 (1) ◽  
pp. 166-174
Author(s):  
Baolin Wu ◽  
Xibin Cao
Keyword(s):  
Formation Control ◽  
Cost Control ◽  
Guaranteed Cost Control ◽  
Control Law ◽  
Content Type ◽  
Spacecraft Formation ◽  
Elliptic Orbits ◽  
Control Scheme ◽  
Guaranteed Cost ◽  
Relative Measurements

Purpose This paper aims to address the problem of formation control for spacecraft formation in elliptic orbits by using local relative measurements. Design/methodology/approach A decentralized formation control law is proposed to solve the aforementioned problem. The control law for each spacecraft uses only its relative state with respect to the neighboring spacecraft it can sense. These relative states can be acquired by local relative measurements. The formation control problem is converted to n stabilization problems of a single spacecraft by using algebraic graph theories. The resulting relative motion model is described by a linear time-varying system with uncertain parameters. An optimal guaranteed cost control scheme is subsequently used to obtain the desired control performance. Findings Numerical simulations show the effectiveness of the proposed formation control law. Practical implications The proposed control law can be considered as an alternative to global positioning system-based relative navigation and control system for formation flying missions. Originality/value The proposed decentralized formation control architecture needs only local relative measurements. Fuel consumption is considered by using an optimal guaranteed cost control scheme.

Guaranteed Cost Control of State-Delay System Based on the Equivalent-Input-Disturbance Approach

2016 ◽  
Vol 20 (2) ◽  
pp. 246-253
Author(s):  
Fang Gao ◽  
◽  
Min Wu ◽  
Jinhua She ◽  
Pan Yu ◽  
...  
Keyword(s):  
Linear Matrix Inequality ◽  
Cost Control ◽  
Guaranteed Cost Control ◽  
Delay System ◽  
Linear Matrix ◽  
Control Law ◽  
Matrix Inequality ◽  
State Delay ◽  
Input Disturbance ◽  
Guaranteed Cost

This paper considers a guaranteed cost control problem for state-delay systems with exogenous disturbances for a proper plant. The equivalent-input-disturbance (EID) approach is extended to be able to handle a state-delay system. A new control law is constructed that incorporates an EID estimate in order to ensure a satisfactory control performance. A stability condition for the closed-loop system is provided in terms of a linear matrix inequality, using the Lyapunov function method. Furthermore, a guaranteed cost control state feedback control law and a state observer are designed, based on the linear matrix inequality (LMI). Two numerical examples are provided to demonstrate the validity of the method.

Reliable Guaranteed Cost Control for Uncertain Time-Lag Systems of Actuator Failures

2010 ◽  
Vol 439-440 ◽  
pp. 960-965
Author(s):  
Wang Ping Lu ◽  
Hai Dong Xu ◽  
Shao Yi Li ◽  
Ling Tao
Keyword(s):  
Cost Control ◽  
Time Lag ◽  
Guaranteed Cost Control ◽  
Linear Matrix ◽  
Control Law ◽  
Matrix Inequality ◽  
Actuator Failures ◽  
Guaranteed Cost ◽  
Uncertain Time ◽  
Designing Method

Focusing on a type of uncertain continual time-lag systems, study on the designing problems of law in reliable guaranteed cost feedback control when actuators are in fault condition of continuous-gain. Apply of the processing method of linear matrix inequality, derived out the condition that reliable guaranteed cost exist, and give out the parameterized representation of all the reliable guaranteed cost control law. In this foundation, we can further obtained the designing method of optimal reliable guaranteed cost control law.

Inverse Problem for Linear Systems Containing Uncertain Parameters

1973 ◽  
Vol 95 (1) ◽  
pp. 17-23 ◽  
Author(s):  
S. P. Panda
Keyword(s):  
Inverse Problem ◽  
Dynamic Programming ◽  
Iterative Method ◽  
Linear Systems ◽  
Cost Control ◽  
Guaranteed Cost Control ◽  
Control Law ◽  
Deterministic System ◽  
Uncertain Parameters ◽  
Guaranteed Cost

The concept of fuzzy dynamic programming and of guaranteed cost control initiated by Chang is applied to the inverse problem of guaranteed cost control for linear systems containing uncertain parameters. Obtained, for a class of linear systems with uncertain parameters, is a frequency-domain criterion which, analogous to that for the deterministic system, is sufficient for the control law to be of guaranteed cost type. The author presents an iterative method which, if convergent, enables one to solve the inverse problem for the general linear systems.

scholarly journals State Feedback Guaranteed Cost Repetitive Control for Uncertain Discrete-Time Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-16
Author(s):  
Wentao Chen ◽  
Yechun Lin ◽  
Qingping Wu
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Cost Control ◽  
Repetitive Control ◽  
Guaranteed Cost Control ◽  
State Feedback Control ◽  
Control Law ◽  
Discrete Time Systems ◽  
Guaranteed Cost ◽  
Time Systems

This paper considers the problem of guaranteed cost repetitive control for uncertain discrete-time systems. The uncertainty in the system is assumed to be norm-bounded and time-varying. The objective is to develop a novel design method so that the closed-loop repetitive control system is quadratically stable and a certain bound of performance index is guaranteed for all admissible uncertainties. The state feedback control technique is used in the paper. While for the case that the states are not measurable, an observer-based control scheme is adopted. Sufficient conditions for the existence of guaranteed cost control law are derived in terms of linear matrix inequality (LMI). The control and observer gains are characterized by the feasible solutions to these LMIs. The optimal guaranteed cost control law is obtained efficiently by solving an optimization problem with LMI constraints using existing convex optimization algorithms. A simulation example is provided to illustrate the validity of the proposed method.

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