Enhanced Stability Criteria of Network-Based Load Frequency Control of Power Systems with Time-Varying Delays

The stability problem for load frequency control (LFC) of power systems with two time-varying communication delays is studied in this paper. The one-area and two-area LFC systems are considered, respectively, which are modeled as corresponding linear systems with additive time-varying delays. An improved stability criterion is proposed via a modified Lyapunov-Krasovskii functional (LKF) approach. Firstly, an augmented LKF consisting of delay-dependent matrices and some single-integral items containing time-varying delay information in two different delay subintervals is constructed, which makes full use of the coupling information between the system states and time-varying delays. Secondly, the novel negative definite inequality equivalent transformation lemma is used to transform the nonlinear inequality to the linear matrix inequality (LMI) equivalently, which can be easily solved by the MATLAB LMI-Toolbox. Finally, some numerical examples are presented to show the improvement of the proposed approach.

The optimality principle for second-order discrete and discrete-approximate inclusions

This paper deals with the necessary and sufficient conditions of optimality for the Mayer problem of second-order discrete and discrete-approximate inclusions. The main problem is to establish the approximation of second-order viability problems for differential inclusions with endpoint constraints. Thus, as a supplementary problem, we study the discrete approximation problem and give the optimality conditions incorporating the Euler-Lagrange inclusions and distinctive transversality conditions. Locally adjoint mappings (LAM) and equivalence theorems are the fundamental principles of achieving these optimal conditions, one of the most characteristic properties of such approaches with second-order differential inclusions that are specific to the existence of LAMs equivalence relations. Also, a discrete linear model and an example of second-order discrete inclusions in which a set-valued mapping is described by a nonlinear inequality show the applications of these results.

Smoothing Approximation to the New Exact Penalty Function with Two Parameters

In this paper, we propose a new non-smooth penalty function with two parameters for nonlinear inequality constrained optimization problems. And we propose a twice continuously differentiable function which is smoothing approximation to the non-smooth penalty function and define the corresponding smoothed penalty problem. A global solution of the smoothed penalty problem is proved to be an approximation global solution of the non-smooth penalty problem. Based on the smoothed penalty function, we develop an algorithm and prove that the sequence generated by the algorithm can converge to the optimal solution of the original problem.

A Physical Model-Based Observer Framework for Nonlinear Constrained State Estimation Applied to Battery State Estimation

Future electrified autonomous vehicles demand higly accurate knowledge of their system states to guarantee a high-fidelity and reliable control. This constitutes a challenging task—firstly, due to rising complexity and operational safeness, and secondly, due to the need for embedded service oriented architecture which demands a continuous development of new functionalities. Based on this, a novel model based Kalman filter framework is outlined in this publication, which enables the automatic incorporation of multiphysical Modelica models into discrete-time estimation algorithms. Additionally, these estimation algorithms are extended with nonlinear inequality constraint handling functionalities. The proposed framework is applied to a constrained nonlinear state of charge lithium-ion cell observer and is validated with experimental data.

Global existence of solutions to nonlinear Volterra integral equations

A new method is given for proving the global existence of the solution to nonlinear Volterra integral equations. A bound on the solution is derived. The results are based on a nonlinear inequality proved by the author earlier.