scholarly journals Finite-Horizon Optimal Control of Discrete-Time Switched Linear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Qixin Zhu ◽  
Guangming Xie
Keyword(s):  
Optimal Control ◽  
Control Systems ◽  
Discrete Time ◽  
Finite Horizon ◽  
Linear Control ◽  
Linear Control Systems ◽  
Control Input ◽  
Optimal Switching ◽  
Control Laws ◽  
Control Factors

Finite-horizon optimal control problems for discrete-time switched linear control systems are investigated in this paper. Two kinds of quadratic cost functions are considered. The weight matrices are different. One is subsystem dependent; the other is time dependent. For a switched linear control system, not only the control input but also the switching signals are control factors and are needed to be designed in order to minimize cost function. As a result, optimal design for switched linear control systems is more complicated than that of non-switched ones. By using the principle of dynamic programming, the optimal control laws including both the optimal switching signal and the optimal control inputs are obtained for the two problems. Two examples are given to verify the theory results in this paper.

scholarly journals On Existence of Stabilizing Switching Laws within a Class of Unstable Linear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Sendren Sheng-Dong Xu ◽  
Chih-Chiang Chen
Keyword(s):  
Control Systems ◽  
Linear Systems ◽  
Switched Systems ◽  
The Other ◽  
Linear Control ◽  
Linear Control Systems ◽  
Problem Statement ◽  
Theoretical Derivation ◽  
Control Laws ◽  
Numerical Examples

The equivalence of two conditions, condition (3) and condition (4) stated in Problem Statement section, regarding the existence of stabilizing switching laws between two unstable linear systems first appeared in (Feron 1996). Although Feron never published this result, it has been referenced in almost every survey on switched systems; see, for example, (Liberzon and Morse 1999). This paper proposes another way to prove the equivalence of two conditions regarding the existence of stabilizing switching laws between two unstable linear systems. One is effective for theoretical derivation, while the other is implementable, and a class of stabilizing switching laws have been explicitly constructed by Wicks et al. (1994). With the help of the equivalent relation, a condition for the existence of controllers and stabilizing switching laws between two unstabilizable linear control systems is then proposed. Then, the study is further extended to the issue concerning the construction of quadratically stabilizing switching laws among unstable linear systems and unstabilizable linear control systems. The obtained results are employed to study the existence of control laws and quadratically stabilizing switching laws within a class of unstabilizable linear control systems. The numerical examples are illustrated and simulated to show the feasibility and effectiveness of the proposed methods.

scholarly journals Canonical forms for positive discrete-time linear control systems

2000 ◽  
Vol 310 (1-3) ◽  
pp. 49-71 ◽  
Author(s):  
Rafael Bru ◽  
Sergio Romero ◽  
Elena Sánchez
Keyword(s):  
Control Systems ◽  
Discrete Time ◽  
Linear Control ◽  
Linear Control Systems ◽  
Canonical Forms ◽  
Time Linear

Stability Analysis of Finite-Level Quantized Discrete-Time Linear Control Systems

2010 ◽  
Vol 16 (3) ◽  
pp. 258-271 ◽  
Author(s):  
Carlos E. de Souza ◽  
Daniel F. Coutinho ◽  
Minyue Fu
Keyword(s):  
Stability Analysis ◽  
Control Systems ◽  
Discrete Time ◽  
Linear Control ◽  
Linear Control Systems ◽  
Time Linear

LMI-based linear anti-windup for discrete time linear control systems

2006 ◽  
Author(s):  
Marco Massimetti ◽  
Luca Zaccarian ◽  
Tingshu Hu ◽  
Andrew R. Teel
Keyword(s):  
Control Systems ◽  
Discrete Time ◽  
Linear Control ◽  
Linear Control Systems ◽  
Time Linear

scholarly journals Controllability Properties and Invariance Pressure for Linear Discrete-Time Systems

2021 ◽  
Author(s):  
Fritz Colonius ◽  
João A. N. Cossich ◽  
Alexandre J. Santana
Keyword(s):  
Control Systems ◽  
Discrete Time ◽  
Linear Control ◽  
Linear Control Systems ◽  
Hyperbolic Case ◽  
Discrete Time Systems ◽  
Control Set ◽  
Time Systems ◽  
Invariance Pressure

AbstractFor linear control systems in discrete time controllability properties are characterized. In particular, a unique control set with nonvoid interior exists and it is bounded in the hyperbolic case. Then a formula for the invariance pressure of this control set is proved.

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