Stochastic Control

In the present study a multi-objective optimization design criterion for linear viscous elastic vibration control devices has been proposed. More in detail, the problem of an isolator device for the vibration control of a single rigid mass have been analysed. The analysis has been carried out by adopting a stochastic approach, by assuming that the excitations acting on the base of the protected systems are stationary stochastic coloured processes. In the multi-objective optimization problems two antithetic objectives are considered: the maximization of control strategy performance, expressed in stochastic terms by means of the reduction of transmitted acceleration in the protected systems, and the limitation in stochastic terms of the displacement of the vibrations control device. The design variables are the mechanical characteristics - frequency and damping ratio- of the device. In order to perform the stochastic multi-objective optimization, the non dominated sorting genetic algorithm in its second version (NSGA-II) has been adopted, which supplies the Pareto set and the corresponding optimum design variables for different system and input configurations. The sensitivity analysis carried out has showed that the optimum solution (i.e. the maximization of control strategy, expressed in terms of reduction of the response of the main system, and the limitation of the device displacement) is reached, in the two analysed problems, by adopting different strategies, in function of input and system characterization. These strategies act by varying the optimum frequency and damping ratio of the device differently, in function of the allowable performance. The novelty of the proposed method is in using a multi-dimensional criterion for the design. Nowadays, this is a very important issue in modern Technical Codes [20], in which several performance requirements, which often can conflict each others, are fixed. In these situations, the designer must select the design variables which make available all objectives and the use of a multi-dimension criterion is very useful in this context. The validation of the proposed method is demonstrated by developing two applications, in which several parameters involved have been changed. Therefore, results attained by the proposed method can be utilised in order to support the designers in the definition of possible structural solutions in vibration control strategy by using linear viscous-elastic devices In this work we studied stochastic harvest problem, where the biomass dynamics was described by stochastic logarithmic growth model with fractional Brownian motion. Since the data used for the fishery management are not accurate, to maintain existing of the population we proposed to use the risk aversion coefficient for fish stock and added not only control but also state constraints. This formulation of optimal harvest problem could not be solved by classical methods and required some additional transformations. We used fractional filtration and got the integral object equation, which did not contain stochastic term. As a result stochastic optimization problem was changed to non-random one. Using maximum principle we got necessary optimality conditions, which were used for numerical solution of the North-East Arctic cod fishery problem to set suitable harvest levels. We hope that to improve the quality of proposed methodology time-varying parameters model can be used as a control object. This requires new parametric identification method from one side and better understanding of economics and biological development of the exploitable ecosystem from the other one In this chapter, stochastic models based on SDEs for LTF, STF, and ad hoc wireless channels are derived. These models are useful in capturing nodes mobility and environmental changes in mobile wireless networks. The SDE models described allow viewing the wireless channel as a dynamical system, which shows how the channel evolves in time and space. These models take into consideration the statistical and time variations in wireless communication environments. The dynamics are captured by a stochastic state space model, whose parameters are determined by approximating the deterministic DPSD. Inphase and quadrature components of the channel and their statistics are derived from the proposed models. The state space models have been used to verify the effect of fading on a transmitted signal in wireless fading networks. In addition, since these models are represented in state space form, they allow well-developed tools of estimation and identification to be applied to this class of problems. The advantage of using SDE methods is due to computational simplicity because estimation and identification algorithms can be performed recursively and in real time