In this paper, we mainly concern about nonlinear BSDE which is often used to describe a case of constraint on the wealth of an investor. Unlike the linear case, we can show that under a certain situation, both buyer and seller can create arbitrage opportunities in the derivative market. We utilize a relation between BSDE and PDE in order to obtain the bounds of a solution. As a result, we succeed in establishing a sufficient condition which guarantees the existence of the arbitrage opportunities, and the limitation of the arbitrages as well. In addition, we are able to extend the results to a more general class of models and accomplish in strengthening the comonotonic theorem for BSDEs. Furthermore, by applying the results, we obtain a sufficient condition that ensures the additivity of g-expectation even when a generator of BSDE is nonlinear.
This paper addresses output smoothing control of an electric power system with multiple homes. The notion of home is a unit of small-scale power system closed to consumers. A home consists of local renewable-based energy source, energy storage, load, power conversion circuit, and control system. Output smoothing control aims to regulate the output power of a single home or coupled multiple homes to the outside of it and is expected to reduce the influence of fluctuating renewable sources to the outside, e.g. a commercial distribution grid. In this paper, we propose a batterybased algorithm for the output smoothing control and demonstrate its effectiveness in a practical,residential power system with two homes. In addition to the practical demonstration, by deriving a mathematical model for dynamics of active power flow in the controlled system and analyzing the model numerically and theoretically, we provide a guideline of tuning the feedback gain of the algorithm for a desired control response.
A new algorithm is proposed to estimate parameters of MISO system. The algorithm is an expansion of the previously proposed algorithm by the author for SISO system. Those algorithms use an iterative calculation and they consist of two parts. One part is the estimation of the system parameters using the variances of errors. The other part is the estimation of the variances of errors using the system parameters. The estimation of the system parameters is one of the least squares identification algorithms using eigenvector. The variances of errors are estimated by solving linear simultaneous equations derived from the difference equation of the system. Some simulations show the effectiveness of the proposed method.
The ultimate subject of the present study is concerned with the design of a nonlinear control law with integral compensation for the output voltage of boost converters through the use of their discretized bilinear model. In this first part of the study, we begin with a discretized model of boost converters obtained by rigorously taking account of the switching action in the converters. Since the control input, the duty cycle, is involved in this model in a highly nonlinear fashion,however, designing a discrete-time control law with this model is rather unrealistic. To circumvent this difficulty, we approximate the discretized model and introduce a simplified model, a discretized bilinear model, and discuss its favorable property. We further give a method for experimentally determining the discretized bilinear model through system identification. With an experiment on identifying an actual boost converter, we then discuss the effectiveness of the discretized bilinear model and its identification method. The resulting model will be used for discrete-time control law design to verify effectiveness of the overall scheme of the present study in an accompanying paper.
This paper is concerned with nonlinear control with integral compensation for the output voltage of boost converters through the use of their discretized bilinear model. We first derive a nonlinear state feedback control law through Lyapunov stability theory, where we introduce a Lyapunov function candidate and maximize its decrement at each switching instant under a penalty on the control input. This approach is then modified to incorporate an integral action in the control law,and a method is provided for confirming the closed-loop stability under the modified control law. We next apply the design method of the control law with integral compensation to the identified discretized bilinear model of a boost converter. Finally, we carry out control experiments with the designed control law, through which the effectiveness of the overall scheme of the present study is demonstrated.