Gholam Reza Rezaei; Tahereh Binazadeh; Behrouz Safarinejadian
Abstract
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 ...
Read More
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.
R. Hajmohammadi; H. NasiriSoloklo; M.M. Farsangi
Abstract
In this paper, an optimal control of quadratic performance index with nonlinear constrained is presented. The sine-cosine wavelet operational matrix of integration and product matrix are introduced and applied to reduce nonlinear differential equations to the nonlinear algebraic equations. Then, the ...
Read More
In this paper, an optimal control of quadratic performance index with nonlinear constrained is presented. The sine-cosine wavelet operational matrix of integration and product matrix are introduced and applied to reduce nonlinear differential equations to the nonlinear algebraic equations. Then, the Newton-Raphson method is used for solving these sets of algebraic equations. To present ability of the proposed method, two classes, first order system and second order system, are considered. The obtained results show that the proposed method offers improved performance. In this paper, an optimal control of quadratic performance index with nonlinear constrained is presented. The sine-cosine wavelet operational matrix of integration and product matrix are introduced and applied to reduce nonlinear differential equations to the nonlinear algebraic equations. Then, the Newton-Raphson method is used for solving these sets of algebraic equations. To present ability of the proposed method, two classes, first order system and second order system, are considered. The obtained results show that the proposed method offers improved performance
