Optimal Finite-time Control of Positive Linear Discrete-time Systems
This paper considers solving optimization problem for linear discrete time systems such that closed-loop discrete-time system is positive (i.e., all of its state variables have non-negative values) and also finite-time stable. For this purpose, by considering a quadratic cost function, an optimal co...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Shahid Rajaee Teacher Training University
2016-07-01
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| Series: | Journal of Electrical and Computer Engineering Innovations |
| Subjects: | |
| Online Access: | https://jecei.sru.ac.ir/article_620_f4de143f06ffbd964a03f28b69e1518f.pdf |
| Summary: | This paper considers solving optimization problem for linear discrete time systems such that closed-loop discrete-time system is positive (i.e., all of its state variables have non-negative values) and also finite-time stable. For this purpose, by considering a quadratic cost function, an optimal controller is designed such that in addition to minimizing the cost function, the positivity property of the optimal state trajectory of the closed-loop system is also guaranteed. Furthermore, state variables of the closed-loop system converge to the origin in finite steps (finite-time stability). In this regard, the LQR+(positive LQR) problem for the linear discrete time systems is stated. Once, the cost function with finite-time horizon is considered and another time the cost function with infinite-time horizon is assumed. In this regard, two theorems are given and proved which consider the problem of building positive and also optimize of the linear time-varying discrete time systems. Results can also be applied to linear time-invariant discrete time systems. Finally, computer simulations are given to illustrate effective performance of the designed controller and also verify the theoretical results. |
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| ISSN: | 2322-3952 2345-3044 |