J.D. Stigter

Technical Communique: Optimal parametric sensitivity control of a fed-batch reactor

The paper presents a method to derive an optimal parametric sensitivity controller for optimal estimation of a set of parameters in an experiment. The method is demonstrated for a fed batch bio-reactor case study for optimal estimation of the saturation constant Ks and, albeit intuitively, the parameter combination μmaxX/Y where μmax is the maximum growth rate [g/min], Y is the yield coefficient [g/g], and X is the (constant) biomass [g].

A fast algorithm to assess local structural identifiability

The paper presents a novel method for assessing the local structural identifiability question for a general non-linear state-space model. The method is a combination of (i) the application of a singular value decomposition to a parametric output sensitivity matrix that is created by simply integrating the model once and, (ii) a symbolic computation for a reduced model that is guided by the SVD results and allows a confirmation of the conclusions regarding identifiability obtained in the first step. In case there is a lack of identifiability, the symbolic computation quickly results in determination of the exact structure of the nullspace and a suitable re-parametrisation. The method is discussed in detail and applied to three case studies, of which the last two are considerably large, containing 22 and 43 parameters to be identified, respectively.

Test of ACW-gradient optimisation algorithm in computation of an optimal control policy for achieving acceptable nitrate concentration of greenhouse lettuce

The adjustable control-variation weight (ACW)-gradient method proposed by Weinreb [Optimal Control with Multiple Bounded Inputs, Department of Electrical Engineering, Stanford University, Stanford, 1985, p. 148] is put to the test in finding optimal control laws for an optimisation problem with bounds on the inputs and terminal state constraints, presented by Ioslovich and Seginer [Acceptable nitrate concentraion of greenhouse lettuce: an optimal control policy for temperature, plant spacing and nitrate supply, in: Proceedings of the Agricontrol 2000, Wageningen, The Netherlands, IFAC, Wageningen University and Research Centre, Royal Dutch Institute of Engineers, 2000]. By making certain assumptions they derived properties of the solution in an analytic way. Here, it is shown that the numerical ACW-gradient algorithm is capable of finding solutions without making additional assumptions.

Optimization of wildlife management in a large game reserve through waterpoints manipulation: a bio-economic analysis

Surface water is one of the constraining resources for herbivore populations in semi-arid regions. Artificial waterpoints are constructed by wildlife managers to supplement natural water supplies, to support herbivore populations. The aim of this paper is to analyse how a landowner may realize his ecological and economic goals by manipulating waterpoints for the management of an elephant population, a water-dependent species in the presence of water-independent species. We develop a theoretical bio-economic framework to analyse the optimization of wildlife management objectives (in this case revenue generation from both consumptive and non-consumptive use and biodiversity conservation), using waterpoint construction as a control variable. The model provides a bio-economic framework for analysing optimization problems where a control has direct effects on one herbivore species but indirect effects on the other. A landowner may be interested only in maximization of profits either from elephant offtake and/or tourism revenue, ignoring the negative effects that could be brought about by elephants to biodiversity. If the landowner does not take the indirect effects of waterpoints into consideration, then the game reserve management, as the authority entrusted with the sustainable management of the game reserve, might use economic instruments such as subsidies or taxes to the landowners to enforce sound waterpoint management.

Network inference via adaptive optimal design.

BackgroundCurrent research in network reverse engineering for genetic or metabolic networks very often does not include a proper experimental and/or input design. In this paper we address this issue in more detail and suggest a method that includes an iterative design of experiments based, on the most recent data that become available. The presented approach allows a reliable reconstruction of the network and addresses an important issue, i.e., the analysis and the propagation of uncertainties as they exist in both the data and in our own knowledge. These two types of uncertainties have their immediate ramifications for the uncertainties in the parameter estimates and, hence, are taken into account from the very beginning of our experimental design.FindingsThe method is demonstrated for two small networks that include a genetic network for mRNA synthesis and degradation and an oscillatory network describing a molecular network underlying adenosine 3’-5’ cyclic monophosphate (cAMP) as observed in populations of Dyctyostelium cells. In both cases a substantial reduction in parameter uncertainty was observed. Extension to larger scale networks is possible but needs a more rigorous parameter estimation algorithm that includes sparsity as a constraint in the optimization procedure.ConclusionWe conclude that a careful experiment design very often (but not always) pays off in terms of reliability in the inferred network topology. For large scale networks a better parameter estimation algorithm is required that includes sparsity as an additional constraint. These algorithms are available in the literature and can also be used in an adaptive optimal design setting as demonstrated in this paper.

Assessing local structural identifiability for environmental models

The local structural identifiability problem is investigated for the general case and demonstrated for a well-known microbial degradation model that includes 13 unknown parameters and 3 additional states. We address the identifiability question using a novel algorithm that can be used for large models with many parameters to be identified. A key ingredient in the analysis is the application of a singular value decomposition of the normalized parametric output sensitivity matrix that is obtained through a simple model integration. The SVD results are further analysed and verified in a complementary symbolic computation. It is especially the swiftness and accuracy of the suggested method that we consider to be a substantial advantage in comparison to existing methods for a structural identifiability analysis. The method also opens, in a natural way, the analysis of (parametric) uncertainty in general, and this is demonstrated in more detail in the results section. A novel algorithm to assess local structural identifiability of non-linear state-space models is applied.The concept Identifiability Signature is introduced.Both practical and theoretical identifiability are investigated for a microbial degradation model.Re-parametrisations of the model are presented for various sensor combinations.

Optimal Greenhouse Climate Control for Achieving Specified Lettuce Nitrate Concentration

Abstract A mathematical formulation of a realistic optimal greenhouse open-loop control problem for achieving a specified lettuce nitrate concentration is expounded. Like many complex agricultural and (bio)chemical optimal control problems, this problem consisted of non-linear differential algebraic equations, affected by high frequency changing uncontrollable inputs, possibly conflicting path constraints and end-constraints. By reformulating the problem into a problem with isoperimetric constraints in order to deal properly with the path constraints it was cast in a form suitable for a numerical solution with the ACW-gradient optimisation. The optimisation was successful, as is shown in an example.

Optimization of net returns from wildlife consumptive and non-consumptive uses by game reserve management

Landowners and game reserve managers are often faced with the decision whether to undertake consumptive (such as hunting) and/or non-consumptive (such as tourism) use of wildlife resources on their properties. Here a theoretical model was used to examine cases where the game reserve management allocated the amount of land devoted to hunting (trophy hunting) and tourism, based on three scenarios: (1) hunting is separated from tourism but wildlife is shared; (2) hunting and tourism co-exist; and (3) hunting and tourism are separated by a fence. The consumptive and non-consumptive uses are not mutually exclusive; careful planning is needed to ensure that multiple management objectives can be met. Further, the analysis indicates that the two uses may be undertaken in the same area. Whether they are spatially, or temporally separated depends on the magnitude of the consumptive use. When consumptive use is not dominant, the two are compatible in the same shared area, provided the wildlife population is sufficiently large.

NUMERICAL STATIC STATE FEEDBACK LAWS FOR CLOSED-LOOP SINGULAR OPTIMAL CONTROL

Singular and non-singular control trajectories of agricultural and (bio) chemical processes may need to be recalculated from time to time for use in closed-loop optimal control, because of unforeseen changes in state values and noise. This is time consuming. As an alternative, in this paper, numerical, nonlinear, static state feedback laws are developed for optimal control on the singular arc that can be applied in closed-loop without the need for iteration. The efficacy of these laws is demonstrated in an example.