We consider the problem of optimal control of vibrating structures and we analyse the solution provided by collocated semiactive decentralised damping devices. We mainly consider the ℋ_∞ criterion and we first study the case of constant dampers, showing that in the case of a single damper the performance is a quasi-convex function of friction so there is a single local minimum which is a global one. The case of multiple dampers does not exhibit this feature and time-expensive computations may be required. Secondly, we consider the case in which dampers may be tuned on line, and in particular the case in which they work in a switching on–off mode. We propose a state-switching feedback control strategy, which outperforms the constant damping approach with the optimal static gain performance as an upper bound. For large distributed flexible structures, state feedback is unrealistic and so we propose a stochastic strategy based on a Markov-jump criterion for which the transition probability are not assigned but designed to optimise average performance, with guaranteed asymptotic stability. Finally, we show that the same result provided for the ℋ_∞ case holds for the ℋ₂ and the l ₁ criteria.

In this paper it is shown that the controller design methodology recently introduced by the authors to stabilize non-globally feedback linearizable triangular systems solves the long-standing problem of transient stabilization of multimachine power systems with non-negligible transfer conductances. The 3n-dimensional (aggregated) model of the n-generator system, with lossy transmission lines, nonlinear loads and excitation control, is considered. A nonlinear dynamic state-feedback control law that ensures, under some conditions on the physical parameters, global asymptotic stability of the operating point is constructed. To the best of the authors' knowledge only existence results-with the restrictive assumption of uniform inertia generators-are available to date for this problem. Simulation results of the New England benchmark system illustrate the performance of the proposed controller.

One of the main requirements in the design of structures made of functionally graded materials is their best response when used in an actual environment. This optimum behaviour may be achieved by searching for the optimal variation of the mechanical and physical properties along which the material compositionally grades. In the works available in the literature, the solution of such an optimization problem usually is obtained by searching for the values of the so called heterogeneity factors (characterizing the expression of the property variations) such that an objective function is minimized. Results, however, do not necessarily guarantee realistic structures and may give rise to unfeasible volume fractions if mapped into a micromechanical model. This paper is motivated by the confidence that a more intrinsic optimization problem should a priori consist in the search for the constituents’ volume fractions rather than tuning parameters for prefixed classes of property variations. Obtaining a solution for such a class of problem requires tools borrowed from dynamic optimization theory. More precisely, herein the so-called Pontryagin Minimum Principle is used, which leads to unexpected results in terms of the derivative of constituents’ volume fractions, regardless of the involved micromechanical model. In particular, along this line of investigation, the optimization problem for axisymmetric bodies subject to internal pressure and for which plane elasticity holds is formulated and analytically solved. The material is assumed to be functionally graded in the radial direction and the goal is to find the gradation that minimizes the maximum equivalent stress. A numerical example on internally pressurized functionally graded cylinders is also performed. The corresponding solution is found to perform better than volume fraction profiles commonly employed in the literature.

Material property variation in non-homogeneous internally pressurized thick-walled cylinders is investigated within the context of dynamic programming theory. The material is assumed to be linear, elastic, isotropic, and functionally graded in the radial direction. Based on the plane stress hypothesis, a state space formulation is given and the optimal control problem is stated and solved by means of Pontryagin’s Principle for different objective functionals. Optimal Young’s modulus distribution is found to be piecewise linear along the radial domain. A brief digression on the possible existence of switching points is addressed. Finally, a numerical example is performed within a special class of derived optimal solutions, showing promising results in terms of equivalent stress reduction with respect to the most used variations in literature.