a b s t r a c tThe experimental validation of a real-time optimization (RTO) strategy for the optimal operation of a solid oxide fuel cell (SOFC) stack is reported in this paper. Unlike many existing studies, the RTO approach presented here utilizes the constraint-adaptation methodology, which assumes that the optimal operating point lies on a set of active constraints and then seeks to satisfy those constraints in practice via the addition of a correction term to each constraint function. These correction terms, also referred to as "modifiers", correspond to the difference between predicted and measured constraint values and are updated at each steady-state iteration, thereby allowing the RTO to iteratively meet the optimal operating conditions of an SOFC stack despite significant plant-model mismatch. The effects of the filter parameters used in the modifier update and of the RTO frequency on the general performance of the algorithm are also investigated.

Obtaining a reliable gradient estimate for an unknown function when given only its discrete measurements is a common problem in many engineering disciplines. While there are many approaches to obtaining an estimate of a gradient, obtaining lower and upper bounds on this estimate is an issue that is often overlooked, as rigorous bounds that are not overly conservative usually require additional assumptions on the function that may either be too restrictive or impossible to verify. In this work, we try to make some progress in this direction by considering four general structural assumptions as a means of bounding the function gradient in a rigorous likelihood sense. After proposing an algorithm for calculating these bounds, we compare their accuracy and precision across different scenarios in an extensive numerical study.

The subject of real-time, steady-state optimization under significant uncertainty is addressed in this paper. Specifically, the use of constraint-adaptation schemes is reviewed, and it is shown that, in general, such schemes cannot guarantee process feasibility over the relevant input space during the iterative process. This issue is addressed via the design of a feasibility-guaranteeing input filter, which is easily derived through the use of a Lipschitz bound on the plant behavior. While the proposed approach works to guarantee feasibility for the singleconstraint case, early sub-optimal convergence is noted for cases with multiple constraints. In this latter scenario, some constraint violations must be accepted if convergence to the optimum is desired. An illustrative example is given to demonstrate these points.

Abstract:We investigate the general iterative controller tuning (ICT) problem, where the task is to find a set of controller parameters that optimize some user-defined performance metric when the same control task is to be carried out repeatedly. Following a repeatability assumption on the system, we show that the ICT problem may be formulated as a real-time optimization (RTO) problem, thus allowing for the ICT problem to be solved in the RTO framework, which is both very flexible and comes with strong theoretical guarantees. In particular, we propose the use of a recently released RTO solver and outline a simple procedure for how this solver may be configured to solve ICT problems. The effectiveness of the proposed method is illustrated by successfully applying it to four case studies-two experimental and two simulated-that cover the tuning of model-predictive, general fixed-order and PID controllers, as well as a system of controllers working in parallel.

In this short note, the recently popular modifier-adaptation framework for real-time optimization is discussed in tandem with the well-developed trustregion framework of numerical optimization, and it is shown that the basic version of the former is a simplification of the latter when the problem is unconstrained. This relation is then exploited to propose a globally convergent modifier-adaptation algorithm using already developed trust-region theory. Cases when the two may not be equivalent and extensions to constrained problems are also discussed.

Abstract-A new approach for gradient estimation in the context of real-time optimization under uncertainty is proposed in this paper. While this estimation problem is often a difficult one, it is shown that it can be simplified significantly if an assumption on the local quasiconvexity of the process is made and the resulting constraints on the gradient are exploited. To do this, the estimation problem is formulated as a constrained weighted least-squares problem with appropriate choice of the weights. Two numerical examples illustrate the effectiveness of the proposed method in converging to the true process optimum, even in the case of significant measurement noise.

A gradient-descent method for the run-to-run tuning of MPC controllers is proposed. It is shown that, with an assumption on process repeatability, the MPC tuning parameters may be brought to a locally optimal set. SISO and MIMO examples illustrate the characteristics of the proposed approach.

A new approach to solving a large class of factorable nonlinear programming (NLP) problems to global optimality is presented in this paper. Unlike the traditional strategy of partitioning the decision-variable space employed in many branch-and-bound methods, the proposed approach approximates the NLP problem by a reverse-convex programming (RCP) problem to a controlled precision, with the latter then solved by an enumerative search. To establish the theoretical guarantees of the method, the notion of "RCP regularity" is introduced and it is proven that enumeration is guaranteed to yield a global optimum when the RCP problem is regular. An extended RCP algorithmic framework is then presented and its performance is examined for a small set of test problems.