Optimal control of a class of discrete–continuous non-linear systems — decomposition and hierarchical structure

A technique is derived for solving a non-linear optimal control problem by iterating on a sequence of simplified problems in linear quadratic form. The technique is designed to achieve the correct solution of the original non-linear optimal control problem in spite of these simplifications. A mixed approach with a discrete performance index and continuous state variable system description is used as the basis of the design, and it is shown how the global problem can be decomposed into local sub-system problems and a co-ordinator within a hierarchical framework. An analysis of the optimality and convergence properties of the algorithm is presented and the effectiveness of the technique is demonstrated using a simulation example with a non-separable performance index.

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.

Genetic algorithms for optimal control of beer fermentation

This paper uses genetic algorithms to optimise the mathematical model of a beer fermentation process that operates in batch mode. The optimisation is based in adjusting the temperature profile of the mixture during a fixed period of time in order to reach the required ethanol levels but considering certain operational and quality restrictions.

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.

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.

‘Leger est aprendre mes fort est arendre’: wool, debt, and the dispersal of Pipewell Abbey (1280-1330)

It has long been known that English Cistercian monasteries often sold their wool in advance to foreign merchants in the late thirteenth century. The abbey of Pipewell in Northamptonshire features in a number of such contracts with Cahorsin merchants. This paper looks again at these contracts in the context of over 200 other such agreements found in the governmental records. Why did Pipewell descend into penury over this fifty year period? This case study demonstrates that the promise of ready cash for their most valuable commodity led such abbots to make ambitious agreements – taking on yet more debt to service existing creditors – that would lead to their eventual bankruptcy.