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In this paper, we develop a new hybrid conjugate gradient method that inherits the features of the Liu and Storey (LS), Hestenes and Stiefel (HS), Dai and Yuan (DY) and Conjugate Descent (CD) conjugate gradient methods. The new method generates a descent direction independently of any line search and possesses good convergence properties under the strong Wolfe line search conditions. Numerical results show that the proposed method is robust and efficient.

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We consider digital input-constrained adaptive and non-adaptive output feedback control for a class of nonlinear systems which arise as models for controlled exothermic chemical reactors. Our objective is set-point control of the temperature of the reaction, with pre-specified asymptotic tracking accuracy set by the designer. Our approach is based on -tracking controllers, but in a context of piecewise constant sampled-data output feedbacks and possibly adapted sampling periods. The approach does not require any knowledge of the systems parameters, does not invoke an internal model, is simple in its design, copes with noise corrupted output measurements, and requires only a feasibility assumption in terms of the reference temperature and the input constraints.

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