DISTRIBUTED OPTIMIZATION FOR TSOS CONTROL Sample Clauses

DISTRIBUTED OPTIMIZATION FOR TSOS CONTROL. In terms of real-time optimisation techniques, the current state-of-the-art is that optimisation techniques are being activated mostly off-line and use a variety of optimisation methods that fit different assumptions: robust (worst-case) optimisation, stochastic optimisation, and black-box methods optimisation. In the field of robust (or worst-case) optimisation methods, the state-of- the-art focuses on methods for providing robust performance guarantees for convex optimisation problems. For real-time decision-making purposes, the use of robust optimisation methods involving recourse, i.e., modelling the notion that future decisions can be deferred until future information is available, is an area of intensive ongoing research. In particular, it has been shown that the computation of optimal recourse is an NP-hard problem in general [BGGN03]. Therefore, the state-of-the-art research for recourse methods in robust optimisation has focused on the development of sub-optimal methods that are amenable to real-time computation [L03, BBN09] and for which strong system-theoretic properties (i.e., stability when applied repeatedly in closed- loop) can be provided [GKM06, GK09]. The most recent results in this area have focused on providing computational certificates of the degree of sub-optimality incurred by these methods [HGK11, BK11]. Stochastic optimisation focuses on optimizing an expected value criterion subject to constraints. Aside from the need to parameterize policies in the recourse sense discussed above, an additional difficulty relates to the interpretation of constraints. Due to the probabilistic nature of the uncertainty that enters the optimisation, the hard, worst-case constraints used in robust optimisation often turn out to be infeasible. One then has to resort to soft interpretations, such as chance constraints (ensuring that the probability of meeting the constraint is above a certain threshold [LLS05]) and integrated chance constraints (ensuring that the expected value of a constraint function is above a certain threshold [K-HV06]). State-of-the-art research in this area is concerned with obtaining problem formulations that can efficiently be solved by optimisation solvers. Convex problem formulations [BB07, PS09], or, in cases where this is not possible, convex approximations of the non-convex problems [NS06, CKW09]. Optimisation by black-box methods aims to address problems for which efficiently solvable formulations are impossible to obtain...