Optimal control of nonlinear systems represented by differential algebraic equations

An iterative procedure is described for solving nonlinear optimal control problems subject to differential algebraic equations. The procedure iterates on an integrated modified simplified model based problem with parameter updating in such a manner that the correct solution of the original nonlinear problem is achieved.

A new approach for the solution of the optimal set-point tracking problem for nonlinear systems

In this paper, a discrete time dynamic integrated system optimisation and parameter estimation algorithm is applied to the solution of the nonlinear tracking optimal control problem. A version of the algorithm with a linear-quadratic model-based problem is developed and implemented in software. The algorithm implemented is tested with simulation examples.

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.

Global climate change and soil carbon stocks: predictions from two contrasting models for the turnover of organic carbon in soil

Enhanced release of CO2 to the atmosphere from soil organic carbon as a result of increased temperatures may lead to a positive feedback between climate change and the carbon cycle, resulting in much higher CO2 levels and accelerated lobal warming. However, the magnitude of this effect is uncertain and critically dependent on how the decomposition of soil organic C (heterotrophic respiration) responds to changes in climate. Previous studies with the Hadley Centre’s coupled climate–carbon cycle general circulation model (GCM) (HadCM3LC) used a simple, single-pool soil carbon model to simulate the response. Here we present results from numerical simulations that use the more sophisticated ‘RothC’ multipool soil carbon model, driven with the same climate data. The results show strong similarities in the behaviour of the two models, although RothC tends to simulate slightly smaller changes in global soil carbon stocks for the same forcing. RothC simulates global soil carbon stocks decreasing by 54 GtC by 2100 in a climate change simulation compared with an 80 GtC decrease in HadCM3LC. The multipool carbon dynamics of RothC cause it to exhibit a slower magnitude of transient response to both increased organic carbon inputs and changes in climate. We conclude that the projection of a positive feedback between climate and carbon cycle is robust, but the magnitude of the feedback is dependent on the structure of the soil carbon model.

On the determinants of optimal border enforcement

We extend the current immigration-enforcement literature by incorporating both the practice of people smuggling and a role for non-wage income into a two-country, dynamic general equilibrium model. We use the model economy to examine three questions. First, how does technological progress in the smuggling industry affect the level of migration and capital accumulation for a given level of enforcement? Second, do changes in border enforcement affect the level of migration, capital accumulation, and smuggling activity? Third, is the optimal level of enforcement sensitive to technological progress in the smuggling industry? We show that the government chooses to devote resources to border enforcement only if the deterrent effect on smugglers is large enough. Otherwise, it is not worth taxing host-country natives as the taxes paid will more than offset any income gain resulting from fewer migrants.

Photochemical cross-linking of plastically compressed collagen gel produces an optimal scaffold for corneal tissue engineering

The experiments were designed to use photochemically cross-linked plastically compressed collagen (PCPCC) gel to support corneal epithelial cells. A plastically compressed collagen (PCC) scaffold was photo cross-linked by UVA in the presence of riboflavin to form a biomaterial with optimal mechanical properties. The breaking force, rheology, surgical suture strength, transparency, ultrastructure, and cell-based biocompatibility were compared between PCPCC and PCC gels. The breaking force increased proportionally with an increased concentration of riboflavin. The stress required to reach breaking point of the PCPCC scaffolds was over two times higher compared to the stress necessary to break PCC scaffolds in the presence of 0.1% riboflavin. Rheology results indicated that the structural properties of PCC remain unaltered after UVA cross-linking. The PCC gels were more easily broken than PCPCC gels when sutured on to bovine corneas. The optical density values of PCPCC and PCC showed no significant differences (p > 0.05). SEM analyses showed that the collagen fibres within the PCPCC gels were similar in morphology to PCC gels. No difference in cell-based biocompatibility was seen between the PCPCC and PCC scaffolds in terms of their ability to support the ex vivo expansion of corneal epithelial cells or their subsequent differentiation evidenced by similar levels of cytokeratin 14. In conclusion, PCPCC scaffold is an optimal biomaterial for use in therapeutic tissue engineering of the cornea.