Optimization of impulsive control systems with intermediate state constraints

In this paper, we consider an optimal impulsive control problem with intermediate state constraints. The peculiarity of the problem consists in a non-standard way of specifying of intermediate constraints. So the constraints must be satisfied for at least one selection of a set-valued solution to the impulsive control system. We prove a theorem for the existence of an optimal control and propose the reduction procedure that transforms the initial optimal control problem with intermediate constraints into a hybrid problem with control parameters. This hybrid problem gives an equivalent description of the optimal impulsive control problem. We discuss a numerical algorithm based on a direct collocation method and give a schema to the corresponding numerical calculations for a test example.

The Relation between Alpha/Beta Oscillations and the Encoding of Sentence induced Contextual Information

Pre-stimulus alpha (8–12 Hz) and beta (16–20 Hz) oscillations have been frequently linked to the prediction of upcoming sensory input. Do these frequency bands serve as a neural marker of linguistic prediction as well? We hypothesized that if pre-stimulus alpha and beta oscillations index language predictions, their power should monotonically relate to the degree of predictability of incoming words based on past context. We expected that the more predictable the last word of a sentence, the stronger the alpha and beta power modulation. To test this, we measured neural responses with magnetoencephalography of healthy individuals during exposure to a set of linguistically matched sentences featuring three levels of sentence context constraint (high, medium and low constraint). We observed fluctuations in alpha and beta power before last word onset, and modulations in M400 amplitude after last word onset. The M400 amplitude was monotonically related to the degree of context constraint, with a high constraining context resulting in the strongest amplitude decrease. In contrast, pre-stimulus alpha and beta power decreased more strongly for intermediate constraints, followed by high and low constraints. Therefore, unlike the M400, pre-stimulus alpha and beta dynamics were not indexing the degree of word predictability from sentence context.

Transfer Function Analysis of Constrained, Distributed Piezoelectric Vibration Energy Harvesting Beam Systems

This paper presents a novel formulation and exact solution of the frequency response function (FRF) of vibration energy harvesting beam systems by the distributed transfer function method (TFM). The method is applicable for coupled electromechanical systems with nonproportional damping, intermediate constraints, and nonclassical boundary conditions, for which the system transfer functions are either very difficult or cumbersome to obtain using available methods. Such systems may offer new opportunities for optimized designs of energy harvesters via parameter tuning. The proposed formulation is also systematic and amenable to algorithmic numerical coding, allowing the system response and its derivatives to be computed by only simple modifications of the parameters in the system operators for different boundary conditions and the incorporation of feedback control principles. Examples of piezoelectric energy harvesters with nonclassical boundary conditions and intermediate constraints are presented to demonstrate the efficacy of the proposed method and its use as a design tool for vibration energy harvesters via tuning of system parameters. The results can also be used to provide benchmarks for assessing the accuracies of approximate techniques.

Eigenfrequencies of generally restrained beams

We deal with the exact determination of eigenfrequencies of a beam with intermediate elastic constraints and generally restrained ends. It is the purpose of this paper to use the calculus of variations to obtain the equations of motion and the natural boundary conditions, and particularly those at the intermediate constraints. Numerical values for the first five natural frequencies are presented in a tabular form for a wide range of values of the restraint parameters. Several particular cases are presented and some of these cases have been compared with those available in the literature.