Optimal Control for Discrete-Time, Linear Fractional-Order Systems with Markovian Jumps

2020 ◽  
Vol 21 ◽  
pp. 291-301
Author(s):  
Viorica M. Ungureanu ◽  
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Discrete Time ◽  
Fractional Order Systems ◽  
Time Linear

Model Predictive Control of General Fractional Order Systems Using a General Purpose Optimal Control Problem Solver: RIOTS

2019 ◽  
Author(s):  
Sina Dehghan ◽  
Tiebiao Zhao ◽  
YangQuan Chen ◽  
Taymaz Homayouni
Keyword(s):  
Optimal Control ◽  
Model Predictive Control ◽  
Fractional Order ◽  
Predictive Control ◽  
Order System ◽  
Problem Solver ◽  
Fractional Order Systems ◽  
Application Process ◽  
Order Model ◽  
Integer Order

Abstract RIOTS is a Matlab toolbox capable of solving a very general form of integer order optimal control problems. In this paper, we present an approach for implementing Model Predictive Control (MPC) to control a general form of fractional order systems using RIOTS toolbox. This approach is based on time-response-invariant approximation of fractional order system with an integer order model to be used as the internal model in MPC. The implementation of this approach is demonstrated to control a coupled MIMO commensurate fractional order model. Moreover, the performance and its application process is compared to examples reported in the literature.

New Conditions and Numerical Checking Method for the Practical Stability of Fractional Order Positive Discrete-Time Linear Systems

2019 ◽  
Vol 20 (3-4) ◽  
pp. 315-323
Author(s):  
Hongli Yang ◽  
Yuexiao Jia
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
The State ◽  
Practical Stability ◽  
Space Systems ◽  
State Matrix ◽  
Numerical Examples ◽  
State Space Systems ◽  
Linear State ◽  
Time Linear

AbstractPractical stability of a fractional order discrete-time linear state-space systems was put up in recent years. It is usually checked by the eigenvalues of the state matrix, some methods have been given during these years. But if the size of the state matrix is large, the computations of eigenvalues can be very onerous. In this paper, some new conditions on practical stability for positive fractional discrete-time linear system are presented. Numerically checking method of practical stability is presented based on the new conditions given in this paper. It is illustrated by the numerical examples that our checking method is effective and true. Compared to the now existing methods, numerically checking method is an attractive method because it’s easily implemented.

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