Optimal mean-variance control for discrete-time linear systems with Markovian jumps and multiplicative noises

In this paper, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noises under two criteria. The first one is an unconstrained mean-variance trade-off performance criterion along the time, and the second one is a minimum variance criterion along the time with constraints on the expected output. We present explicit conditions for the existence of an optimal control strategy for the problems, generalizing previous results in the literature. We conclude the paper by presenting a numerical example of a multi-period portfolio selection problem with regime switching in which it is desired to minimize the sum of the variances of the portfolio along the time under the restriction of keeping the expected value of the portfolio greater than some minimum values specified by the investor. (C) 2011 Elsevier Ltd. All rights reserved.

Trichogramma pretiosum parasitism and dispersal capacity: a basis for developing biological control programs for soybean caterpillars

In order to succeed in biological control programs, not only is it crucial to understand the number of natural enemies to be released but also on how many sites per area this releasing must be performed. These variables might differ deeply among egg parasitoid species and crops worked. Therefore, these trials were carried out to evaluate the parasitism (%) in eggs of Anticarsia gemmatalis and Pseudoplusia includens after the release of different densities of the egg parasitoid Trichogramma pretiosum. Field dispersal was also studied, in order to determine appropriate recommendations for the release of this parasitoid in soybean fields. The regression analysis between parasitism (%) and densities of the parasitoid indicated a quadratic effect for both A. gemmatalis and P. includens. The maximum parasitism within 24 h after the release was reached with densities of 25.6 and 51.2 parasitoids per host egg, respectively, for the two pests. Parasitism of T. pretiosum in eggs of P. includens decreased linearly as the distance of the pest eggs from the parasitoid release sites increased. For P. includens, the mean radius of T. pretiosum action and the area of parasitoid dispersal in the soybean crop were 8.01 m and 85.18 m(2), respectively. We conclude that for a successful biological control program of lepidopteran pests using T. pretiosum in soybean fields, a density of 25.6 parasitoids per host egg, divided into 117 sites per hectare, should be used.

Improved low-voltage-ride-through capability of fixed-speed wind turbines using decentralised control of STATCOM with energy storage system

The design and implementation of a new control scheme for reactive power compensation, voltage regulation and transient stability enhancement for wind turbines equipped with fixed-speed induction generators (IGs) in large interconnected power systems is presented in this study. The low-voltage-ride-through (LVRT) capability is provided by extending the range of the operation of the controlled system to include typical post-fault conditions. A systematic procedure is proposed to design decentralised multi-variable controllers for large interconnected power systems using the linear quadratic (LQ) output-feedback control design method and the controller design procedure is formulated as an optimisation problem involving rank-constrained linear matrix inequality (LMI). In this study, it is shown that a static synchronous compensator (STATCOM) with energy storage system (ESS), controlled via robust control technique, is an effective device for improving the LVRT capability of fixed-speed wind turbines.

A new approach for modeling and control of nonlinear systems via norm-bounded linear differential inclusions

A systematic approach to model nonlinear systems using norm-bounded linear differential inclusions (NLDIs) is proposed in this paper. The resulting NLDI model is suitable for the application of linear control design techniques and, therefore, it is possible to fulfill certain specifications for the underlying nonlinear system, within an operating region of interest in the state-space, using a linear controller designed for this NLDI model. Hence, a procedure to design a dynamic output feedback controller for the NLDI model is also proposed in this paper. One of the main contributions of the proposed modeling and control approach is the use of the mean-value theorem to represent the nonlinear system by a linear parameter-varying model, which is then mapped into a polytopic linear differential inclusion (PLDI) within the region of interest. To avoid the combinatorial problem that is inherent of polytopic models for medium- and large-sized systems, the PLDI is transformed into an NLDI, and the whole process is carried out ensuring that all trajectories of the underlying nonlinear system are also trajectories of the resulting NLDI within the operating region of interest. Furthermore, it is also possible to choose a particular structure for the NLDI parameters to reduce the conservatism in the representation of the nonlinear system by the NLDI model, and this feature is also one important contribution of this paper. Once the NLDI representation of the nonlinear system is obtained, the paper proposes the application of a linear control design method to this representation. The design is based on quadratic Lyapunov functions and formulated as search problem over a set of bilinear matrix inequalities (BMIs), which is solved using a two-step separation procedure that maps the BMIs into a set of corresponding linear matrix inequalities. Two numerical examples are given to demonstrate the effectiveness of the proposed approach.