Derivative-free optimization techniques are widely used for solving optimization problems. The

focus in this work is given to some variants of Nelder-Mead and particle swarm methods to tackle two

unconstrained optimization problems originated from optimal control, namely the pole assignment problem for

discrete and continuous-time positive systems. we present the Nelder-Mead and Particle Swarm optimization

methods to solve problems. Moreover comparing our results with benchmarks in the literature.

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In this work, we consider Nelder-Mead method to tackle the output

feedbackeigenvalue assignment problem for discrete–time control

systems. First, we reformulate this problem as a constrained minimization

problem. Then by applying apenalty-method approach we find a local

solution to the problem using Nelder-Meadmethod. The performance of

the method is illustrated through some test problemsfrom the literature.

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In this paper, the discrete–time periodic static output feedback control design problem is considered. A

hybrid conjugate gradient methods are analyzed and studied to tackle an equivalent optimization problem of this

optimal control problem. Finally, the proposed algorithms are tested numerically through several test problems

from the benchmark collection.

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In this article, we consider the output feedback eigenvalue assignment problem for

continuous and discrete–time control systems. This problem is formulated as unconstrained matrix optimization problems and tackled by the Nelder–Mead simplex

method and particle swarm optimization method. The two methods are extended to

compute the approximate solutions of the eigenvalue assignment problem for the particular cases of decentralized and periodic control systems. The performance of the

methods is demonstrated numerically on several test problems from the benchmark

collection [22] as well as other test examples from the system and control literature.

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Te output feedback eigenvalue assignment problem for discrete-time systems is considered. Te problem is formulated frst as

an unconstrained minimization problem, where a three-term nonlinear conjugate gradient method is proposed to fnd a local

solution. In addition, a cut to the objective function is included, yielding an inequality constrained minimization problem, where a

logarithmic barrier method is proposed for fnding the local solution. Te conjugate gradient method is further extended to tackle

the eigenvalue assignment problem for the two cases of decentralized control systems and control systems with time delay. Te

performance of the methods is illustrated through various test examples.