Optimal discrete-time control for non-linear cascade systems

In this paper we develop an optimality-based framework for designing controllers for discrete-time nonlinear cascade systems. Specifically, using a nonlinear-nonquadratic optimal control framework we develop a family of globally stabilizing backstepping-type controllers parameterized by the cost functional that is minimized. Furthermore, it is shown that the control Lyapunov function guaranteeing closed-loop stability is a solution to the steady-state Bellman equation for the controlled system and thus guarantees both optimality and stability

KEYLINK: a new soil model including soil structure and soil fauna as key drivers

Recent improvements in understanding and modelling of the soil and SOM are not yetimplemented into existing ecosystem models (review: Vereecken et al. 2016). Manyecosystem models do not represent any structure of the soil (with only one organic and onemineral layer), although it is clear that humidity and temperature profile are of high importance,and cannot be simulated without soil structure. Moreover, physical accessibility of SOM is animportant determinant of its stability (besides chemical recalcitrance). Although the importanceof soil fauna as ‘engineers’ on soil structure is well-documented, this is seldom represented inecosystem level models (Barot et al. 2007). The important role of other faunal foodweb agents(Bengtsson et al. 1996) is completely ignored in ecosystem models, although functionaldiversity of the foodweb is of major importance for a well-functioning soil. It is also clear thatthe importance of EM fungi was not recognized in the older soil models, while recent researchsuggests their importance both as main components of older SOM and as networks betweentrees that exchange both C and nutrients (Averill & Hawkes 2016).At the same time, many very detailed models exist that require too many data forimplementation into ecosystem models or are difficult to parameterize but offer interestinginsights into soil functioning. In ecosystem models the representation of the soil needs to berelatively simple, fast in calculations and requiring only limited input.Within COST actions KEYSOM and BIOLINK a new integrative soil model ‘KEYLINK’ wasdeveloped that is simple enough for inclusion into existing ecosystem models, yet includes thenewest insights concerning:- Main soil fauna ‘agents’ divided into functional groups: engineers, fungivores,predators….- Main drivers: water – t – structure –pH – litter quality- Main processes: SOM stabilization, decay, nutrient & water uptak