Duality theorems for convex problems with time delay

In this paper, we examine a class of convex problems of Bolza type, involving a time delay in the state. It encompasses a variety of time-delay problems arising in the calculus of variations and optimal control. A duality analysis is carried out which, among other things, leads to a characterization of minimizers in terms of the Euler-Lagrange inclusion. The results obtained improve in significant respects on what is achievable by techniques previously employed, based on elimination of the time delay by introduction of an infinite-dimensional state space or on the method of steps.     

Generic existence of Lipschitzian solutions of optimal control problems without convexity assumptions

The Tonelli existence theorem in the calculus of variations and its subsequent modifications were established for integrands f which satisfy convexity and growth conditions. In this paper we consider a large class of optimal control problems which is identified with a complete metric space of integrands without convexity assumptions and show that for a generic integrand the corresponding optimal control problem possesses a unique solution and this solution is Lipschitzian.     

Semideterministic Global Optimization Method: Application to a Control Problem of the Burgers Equation

This paper has two objectives. We introduce a new global optimization algorithm reformulating optimization problems in terms of boundary-value problems. Then, we apply this algorithm to a pointwise control problem of the viscous Burgers equation, where the control weight coefficient is progressively decreased. The results are compared with those obtained with a genetic algorithm and an LM-BFGS algorithm in order to check the efficiency of our method and the necessity of using global optimization techniques.     

挖坑机钻头主轴纵向振动系统模型的建立与控制

首先利用弹性杆理论和H am ilton变分原理建立了挖坑机钻头主轴及钻尖在工作过程中由于外激励的作用使钻尖与土壤互相作用而产生纵向振动的动力学模型,同时给出边界条件和初始条件.其次通过把系统外激励函数当作控制变量,利用Banach空间几何性质证明了此系统存在唯一最优控制元.     

Time dependent analysis of finite buffer fluid flows and risk models with a dividend barrier

Based on the matrix-analytic approach to fluid flows initiated by Ramaswami, we develop an efficient time dependent analysis for a general Markov modulated fluid flow model with a finite buffer and an arbitrary initial fluid level at time 0. We also apply this to an insurance risk model with a dividend barrier and a general Markovian arrival process of claims with possible dependencies in successive inter-claim intervals and in claim sizes. We demonstrate the implementability and accuracy of our algorithms through a set of numerical examples that could also serve as test cases for comparing other solution approaches.      

Structure of minimizers in linear-quadratic Bolza problems of optimal control

In this paper, we study intersections of extremals in a linear-quadratic Bolza problem of optimal control. The structure of the inter-sections is described. We show that this structure implies the semipositive definiteness of the quadratic cost functional. In addition, we derive necessary and sufficient conditions for the existence of minimizers.     

On a recursive method for the estimation of unknown parameters of partially observed chaotic systems

We investigate a recently proposed method for on-line parameter estimation and synchronization in chaotic systems. This novel technique has been shown effective to estimate a single unknown parameter of a primary chaotic system with known functional form that is only partially observed through a scalar time series. It works by periodically updating the parameter of interest in a secondary system, with the same functional form as the primary one but no explicit coupling between their dynamic variables, in order to minimize a suitably defined cost function. In this paper, we review the basics of the method, and investigate its robustness and new extensions. In particular, we study the performance of the novel technique in the presence of noise (either observational, i.e., an additive contamination of the observed time series, or dynamical, i.e., a random perturbation of the system dynamics) and when there is a mismatch between the primary and secondary systems. Numerical results, including comparisons with other techniques, are presented. Finally, we investigate the extension of the original method to perform the estimation of two unknown parameters and illustrate its effectiveness by means of computer simulations.     

A locally computed suboptimal control strategy for a class of interconnected systems

In this paper, a locally computed suboptimal control strategy for a class of interconnected systems is introduced. First, optimal statefeedback control equations are derived for a finite-horizon quadratic cost. Then, the control for each subsystem is separated into two portions. The first portion stabilizes the isolated subsystem, and the second portion corresponds to the interactions. To achieve a locally calculable control, an approximation to the optimal control equations is introduced, and two iterative suboptimal control algorithms are developed. In the first algorithm, the initial conditions of subsystems are assumed to be known; in the second algorithm, this information is replaced by statistical distributions. The orders of errors in the iterations of the algorithm and in the suboptimality are given in terms of interconnections. An example with comparisons is also included to show the performance of the approach.     

OPTIMAL INSTAR PARASITIZATION IN A STAGE STRUCTURED HOST-PARASITOID MODEL

A stage structured host-parasitoid model is derived and the equilibria studied. It is shown under what conditions the parasitoid controls an exponentially growing host in the sense that a coexistence equilibrium exists. Furthermore, for host populations whose inherent growth rate is not too large it is proved that in order to minimize the adult host equilibrium level it is necessary that the parasitoids attack only one of the larval stages. It is also proved in this case that the minimum adult host equilibrium level is attained when the parasitoids attack that larval stage which also maximizes the expected number of emerging adult parasitoid per larva at equilibrium. Numerical simulations tentatively indicate that the first conclusion remains in general valid for the model. However, numerical studies also show that it is not true in general that the optimal strategy will maximize the number of emerging adult parasitoid per larva at equilibrium.     

Optimal control of unsteady compressible viscous flows

The control of complex, unsteady flows is a pacing technology for advances in fluid mechanics. Recently, optimal control theory has become popular as a means of predicting best case controls that can guide the design of practical flow control systems. However, most of the prior work in this area has focused on incompressible flow which precludes many of the important physical flow phenomena that must be controlled in practice including the coupling of fluid dynamics, acoustics, and heat transfer. This paper presents the formulation and numerical solution of a class of optimal boundary control problems governed by the unsteady two‐dimensional compressible Navier–Stokes equations. Fundamental issues including the choice of the control space and the associated regularization term in the objective function, as well as issues in the gradient computation via the adjoint equation method are discussed. Numerical results are presented for a model problem consisting of two counter‐rotating viscous vortices above an infinite wall which, due to the self‐induced velocity field, propagate downward and interact with the wall. The wall boundary control is the temporal and spatial distribution of wall‐normal velocity. Optimal controls for objective functions that target kinetic energy, heat transfer, and wall shear stress are presented along with the influence of control regularization for each case. Copyright © 2002 John Wiley & Sons, Ltd.