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Content available remote The p-Factor Method for Nonlinear Optimization
We present the main concept and results of the p-regularity theory (also known as p-factor analysis of nonlinear mappings) applied to nonlinear optimization problems. The approach is based on the construction of p-factor operator. The main result of this theory gives a detailed description of the structure of the zero set of irregular nonlinear mappings. Applications include a new numerical method for solving nonlinear optimization problems and p- order necessary and sufficient optimality conditions. We substantiate the rate of convergence of p-factor method.
We consider the following problems. Given a discrete-time linear system, find, if possible, linear state-feedback control laws such that the corresponding closed-loop system trajectory is positive whenever the initial state is positive. This problem is called the feedback holdability problem. If, in addition, the requirement of non-negativity is imposed on controls, the problem is a positive feedback holdability problem. In the paper, necessary and sufficient conditions for feedback and positive feedback holdability are established in a form of systems of linear inequalities and a procedure for computing the set of all state-feedback controllers that make the closed-loop system holdable is proposed. The relation between controllability and holdability is also treated. Feedback and positive feedback holdability of the class of positive systems is considered as well.
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