Assessment and Future Directions of Nonlinear Model Predictive ...

NMPC for Complex Stochastic Systems 2796.3 Environment ManagementIn [12] a version of stochastic MPC is developed for a problem of investmentdecisions into R&D on alternative sustainable technologies. A stochastic modelis available which describes the effects of R&D expenditure into alternative technologies,on various indicators of sustainability, such as CO 2 emissions and energyuse, over a horizon of 30 years. The objective is to decide on the allocationover time of expenditure into the competing technologies, subject to a budgetaryconstraint. The performance criterion is the probability that a particular indicatorexceeds some threshold value, and the constraints are minimum probabilitiesof other indicators exceeding their threshold values. Here is an application inwhich ‘real-time’ means updating the solution once a year, so that the computationalcomplexity of the MCMC approach is not an issue.There are many other environmental problems, such as water resources management,fishery harvesting policy, atmospheric ozone regulation, river qualitymanagement, etc, that require decision-making over time on the basis of dynamicmodels, under conditions of considerable uncertainty [2]. All of these appear tobe suitable applications of the MCMC approach.6.4 Financial ManagementThe problem of optimal portfolio allocation is often posed as a problem ofstochastic control, and has attracted very sophisticated solutions [6]. This isthe problem of distributing (and re-distributing from time to time) a fixed investmentbudget into various asset classes, so as to maximise the value of theportfolio, or the income, etc [15]. Very approximate, inherently stochastic models,are available for the future trajectory of value appreciation and/or incomefrom each asset class, and constraints may be present, such as a limit on theprobability of losses exceeding some specified value. Update intervals may rangefrom hours to months, depending on the kinds of assets considered. Once again,these problems appear to be amenable to the MCMC approach.7 ConclusionsWe have presented a very powerful and general approach to solving optimisationproblems in the form of maximisation of the expected value of a performancecriterion, subject to satisfying a set of constraints with a prescribed probability.The only essential requirement for implementation of the approach is a modelbasedstochastic simulator. We have argued that the form of the criterion is notrestrictive, and that this approach is applicable to a wide variety of stochasticcontrol problems. Since the approach depends on the availability of a model, andcan be applied repeatedly in real-time, updated by the latest measurements, webelieve that it qualifies to be considered as an MPC method.The two approaches can be contrasted as follows:1. Conventional NMPC typically assumes that disturbances and other sourcesof uncertainty are bounded but otherwise unknown. MCMC requires astochastic description of uncertainty.