Dynamic integrated system optimization and parameter estimation for discrete time optimal control of nonlinear systems

An algorithm for solving nonlinear discrete time optimal control problems with model-reality differences is presented. The technique uses Dynamic Integrated System Optimization and Parameter Estimation (DISOPE), which achieves the correct optimal solution in spite of deficiencies in the mathematical model employed in the optimization procedure. A version of the algorithm with a linear-quadratic model-based problem, implemented in the C+ + programming language, is developed and applied to illustrative simulation examples. An analysis of the optimality and convergence properties of the algorithm is also presented.

Hierarchical control and optimisation of the Tennessee Eastman process

Based on integrated system optimisation and parameter estimation a method is described for on-line steady state optimisation which compensates for model-plant mismatch and solves a non-linear optimisation problem by iterating on a linear - quadratic representation. The method requires real process derivatives which are estimated using a dynamic identification technique. The utility of the method is demonstrated using a simulation of the Tennessee Eastman benchmark chemical process.

Optimal control of nonlinear differential algebraic equation systems

A novel iterative procedure is described for solving nonlinear optimal control problems subject to differential algebraic equations. The procedure iterates on an integrated modified linear quadratic model based problem with parameter updating in such a manner that the correct solution of the original non-linear problem is achieved. The resulting algorithm has a particular advantage in that the solution is achieved without the need to solve the differential algebraic equations . Convergence aspects are discussed and a simulation example is described which illustrates the performance of the technique. 1. Introduction When modelling industrial processes often the resulting equations consist of coupled differential and algebraic equations (DAEs). In many situations these equations are nonlinear and cannot readily be directly reduced to ordinary differential equations.

German open ended funds: was there a valuation problem?

In late 2005, a number of German open ended funds suffered significant withdrawals by unit holders. The crisis was precipitated by a long term bear market in German property investment and the fact that these funds offered short term liquidity to unit holders but had low levels of liquidity in the fund. A more controversial suggestion was that the crisis was exacerbated by a perception that the valuations of the fund were too infrequent and inaccurate. As units are priced by reference to these valuations with no secondary market, the valuation process is central to the process. There is no direct evidence that these funds were over-valued but there is circumstantial evidence and this paper examines the indirect evidence of the process to see whether the hypothesis that valuation is an issue for the German funds holds any credibility. It also discusses whether there is a wider issue for other funds of this nature or whether it is a parochial problem confined to Germany. The conclusions are that there is reason to believe that German valuation processes make over-valuation in a recession more likely than in other countries and that more direct research into the German valuation system is required to identify the issues which need to be addressed to make the valuation system more trusted.

Ω-results for Beurling's zeta function and lower bounds for the generalised Dirichlet divisor problem

In this paper we study generalised prime systems for which the integer counting function NP(x) is asymptotically well behaved, in the sense that NP(x)=ρx+O(xβ), where ρ is a positive constant and . For such systems, the associated zeta function ζP(s) is holomorphic for . We prove that for , for any ε>0, and also for ε=0 for all such σ except possibly one value. The Dirichlet divisor problem for generalised integers concerns the size of the error term in NkP(x)−Ress=1(ζPk(s)xs/s), which is O(xθ) for some θ<1. Letting αk denote the infimum of such θ, we show that .