Robust optimal operation of continuous catalytic reforming process under feedstock uncertainty

The continuous catalytic regenerative (CCR) reforming process is one of the most significant sources of hydrogen production in the petroleum refining process. However, the fluctuations in feedstock composition and flow rate could significantly affect both product distribution and energy consumption. In this study, a robust deviation criterion based multi-objective optimization approach is proposed to perform the optimal operation of CCR reformer under feedstock uncertainty, with simultaneous maximization of product yields and minimization of energy consumption. Minimax approach is adopted to handle these uncertain objectives, and the Latin hypercube sampling method is then used to calculate these robust deviation criteria. Multi-objective surrogate-based optimization methods are next introduced to effectively solve the robust operational problem with high computational cost. The level diagram method is finally utilized to assist in multi-criteria decision-making. Two robust operational optimization problems with different objectives are solved to demonstrate the effectiveness of the proposed method for robust optimal operation of the CCR reforming process under feedstock uncertainty.     

The robust knapsack problem with queries

We consider robust knapsack problems where item weights are uncertain. We are allowed to query an item to find its exact weight,where the number of such queries is bounded by a given parameter Q. After these queries are made, we need to pack the items robustly, i.e., so that the choice of items is feasible for every remaining possible scenario of item weights.The central question that we consider is: Which items should be queried in order to gain maximum profit? We introduce the notion of query competitiveness for strict robustness to evaluate the quality of an algorithm for this problem, and obtain lower and upper bounds on this competitiveness for interval-based uncertainty. Similar to the study of online algorithms, we study the competitiveness under different frameworks, namely we analyze the worst-case query competitiveness for deterministic algorithms, the expected query competitiveness for randomized algorithms and the average case competitiveness for known distributions of the uncertain input data. We derive theoretical bounds for these different frameworks and evaluate them experimentally. We also extend this approach to Γ-restricted uncertainties introduced by Bertsimas and Sim.Furthermore, we present heuristic algorithms for the problem. In computational experiments considering both the interval-based and the Γ-restricted uncertainty, we evaluate their empirical performance. While the usage of a Γ-restricted uncertainty improves the nominal performance of a solution (as expected), we find that the query competitiveness gets worse.     

A design of a robust discrete-time controller

In this paper, we proposed a robust discrete-time controller. This control system, which is derived from the idea of the normalized plant, does not include plant parameters. Thus, we obtain a control system independent of plant parameters and that has the same structure as a conventional optimal servo control system. Simulation and experimental results show that the proposed method is fairly robust to plant parameter variations and external disturbances.     

Outlier-resistant methods for estimation and model fitting

Least squares is perhaps the most widely used technique for model fitting. In this article, we illustrate the poor performance of least squares when there are spurious values, or outliers, in a sequence of measurements. A brief overview of three well-known classes of robust alternatives to the least-squares mean is presented. For robust regression, a recent proposal called least median squares (LMS) is decribed. LMS regression is compared to least-squares regression in an example involving the estimation of optical fiber geometry. References are provided for software that is available for robust estimation techniques surveyed in this article.     

A delta transform approach to loop gain-phase shaping design of robust digital control systems

This paper addresses the existence of loop gain-phase shaping (LGPS) solutions for the design of robust digital control systems for SISO, minimum-phase, continuous-time processes with parametric uncertainty. We develop the frequency response properties of LGPS for discrete-time systems using the Δ-transform, a transform method that applies to both continuous-time and discrete-time systems. A theorem is presented which demonstrates that for reasonable specifications there always exists a sampling period such that the robust digital control problem has a solution. Finally, we offer a procedure for estimating the maximum feasible sampling period for LGPS solutions to robust digital control problems.     

Design of minimax robust LQG controllers under parameter and noise uncertainties

The problem of design of minimax robust LQG controllers for linear systems with parameter and noise uncertainties is considered in this paper. Necessary and sufficient conditions for converting this problem to a two-person, zero-sum continuous game problem are presented. A simple procedure for design of a suboptimal minimax robust LQG controller, i.e., the LQG controller for least-favourable model, is proposed. Necessary and sufficient conditions for the existence of a saddle point are established. Under these conditions, the controller obtained is exactly the minimax LQG controller. When there does not exist a saddle point, the worst-case error between the controller obtained and the minimax robust LQG controllers under described uncertainties is bounded.     

A novel distributed approach to robust fault detection and identification

In this paper, we propose a novel distributed robust fault detection and identification (RFDI) scheme for a class of nonlinear systems. Firstly, a detection and identification estimator—robust fault tracking approximator (RFTA) is designed for online health monitoring. A novel feature of the RFTA is that it can simultaneously detect and accurately identify the shape and magnitude of the fault and disturbance. Moreover, it takes less online training time compared with the traditional neural network based fault diagnosis schemes. For some distributed systems, a network of distributed estimators is constructed where the RFTA is embedded into each estimator. Then we use consensus filter to filter the outputs of each estimator. One of the most important merits of the consensus filter is that its outputs can dramatically improve the accuracy of fault detection and identification. Next, the stability of the distributed RFDI scheme is rigorously investigated. Finally, two numerical examples are given to illustrate the feasibility and effectiveness of the proposed approach.     

On the binomial confidence interval and probabilistic robust control

The Clopper-Pearson confidence interval has ever been documented as an exact approach in some statistics literature. More recently, such approach of interval estimation has been introduced to probabilistic control theory and has been referred as non-conservative in control community. In this note, we clarify the fact that the so-called exact approach is actually conservative. In particular, we derive analytic results demonstrating the extent of conservatism in the context of probabilistic robustness analysis. This investigation encourages seeking better methods of confidence interval construction for robust control purpose.