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Data-based control design methods most often consist of iterative adjustment of the controller's parameters towards the parameter values which minimize an H2 performance criterion. Typically, batches of input-output data collected from the system are used to feed directly a gradient descent optimization - no process model is used. The convergence to the global minimum of the performance criterion depends on the initial controller parameters, as well as on the size and direction of the steps taken at each iteration. This paper discusses these issues and provides a method for choosing the search direction and the step size at each optimization step so that convergence to the global minimum is obtained with high convergence rate.

The decay of beam-generated Langmuir wave into another Langmuir wave and an ion-acoustic wave is a well-known problem with wide-ranging applications. However, most discussions in the literature are based upon simple one-dimensional approximation. Recently, the present authors carried out a fully self-consistent two-dimensional analysis of the beam-driven Langmuir wave decay problem. The main focus of the present authors' work to date had been on the nonlinear evolution of Langmuir turbulence and its influence on the electrons. Relatively little attention had been paid to the ion-acoustic wave generation. In the present discussion, the focus is placed on the dynamics of ion-acoustic turbulence that results from the decay of beam-generated Langmuir wave. The present analysis considers three electron components, the dense core, a primary beam and a counter-streaming beam. We find that the ion-sound turbulence level sensitively depends on the properties of the counter-streaming beam.

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