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Abstract: We consider a switched-capacitor DC/DC power converter with variable switching instants. The determination of optimal switching instants giving low output ripple and strong load regulation is posed as a non-smooth dynamic optimization problem. By introducing a set of auxiliary differential equations and applying a time-scaling transformation, we formulate an equivalent optimization problem with semi-infinite constraints. Existing algorithms can be applied to solve this smooth semi-infinite optimization problem. The existence of an optimal solution is also established. For illustration, the optimal switching instants for a practical switched-capacitor DC/DC power converter are determined using this approach. [Copyright &y& Elsevier]

Abstract: In this work, we consider the well-posedness of state-based switched systems in the sense of piecewise classical solutions which commonly arise in the control of hybrid systems. We give some necessary and sufficient conditions for the well-posedness of this class of systems. These results can be used as tools for excluding the bimodal system having a Zeno state. [Copyright &y& Elsevier]

In this article, we consider a class of optimal control problems involving dynamical systems described by impulsive integrodifferential equations. First, we approximate the integral kernel of the integral equation by a finite expansion of the shifted Chebyshev polynomial. Through this process, the optimal control problem is approximated by a sequence of optimal control problems involving only impulsive ordinary differential equations. Each of them can be viewed as a nonlinear optimization problem. For each of these approximated problems, the gradient formula of the cost functional can be derived and hence can be solved by many efficient optimization techniques. Consequently, the optimal control software, MISER, is applicable for the purpose. Then, we present some convergence results showing the relationship between the sequence of the optimal controls of the approximated problems and that of the original problem. Finally, a numerical example is presented to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we investigate a class of parabolic differential equations of neutral type, and obtain some sufficient conditions of the oscillation for such equations satisfying two kinds of boundary value conditions. [Copyright &y& Elsevier]

Abstract: In this paper, we establish several oscillatory criteria for even order neutral differential equations with distributed deviating arguments, which generalize and improve some known results. [Copyright &y& Elsevier]

Abstract: In this paper, we consider an interesting identification problem where an unknown phenomenon is to be identified by the trajectory of an impulsive differential equation. The system coefficients, the locations of the switching time points, and the heights of the jumps at these time points are to be determined such that the summation of the least square errors of the trajectory of the impulsive system and the phenomenon over the observed time points is minimized. This becomes an interesting dynamical optimization problem. We develop an efficient computational method for solving this dynamical optimization problem. Our approach first is to use the control parameterization enhancing transform to convert this dynamical optimization problem into an equivalent optimal parameter selection problem, where the varying time points are being mapped into fixed time points. Then, the gradient formula of the cost function is derived. Thus, this optimal parameter selection problem can be solved as a mathematical programming problem. For illustration, a numerical example is solved by using the proposed method. [Copyright &y& Elsevier]

In this paper, the control parametrization enhancing technique (CPET) is applied to obtain numerical solution to a special class of ordinary differential equations where the right-hand side has state dependent discontinuities. Switching locations corresponding to these discontinuities can be calculated exactly and conveniently. Illustrative examples are provided to demonstrate the novel technique. [ABSTRACT FROM AUTHOR]

Abstract: In this work, we investigate the properties of a class of quadratic infinite programs where the objective is a quadratic functional of integral type and the feasible region is a subset of the infinite dimensional space . We first derive a dual problem of the primal problem to demonstrate that there is no duality gap between them. Then we prove that the objective function depends continuously on the design function. Two existence theorems for this kind of optimization problem are presented. These theoretical results may prove useful in the design of efficient algorithms for this class of infinite programming problem. [Copyright &y& Elsevier]