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This paper proposes a new class of real-time optimization schemes to overcome system-model mismatch of uncertain processes. This work's novelty lies in integrating derivative-free optimization schemes and multi-fidelity Gaussian processes within a Bayesian optimization framework. The proposed scheme uses two Gaussian processes for the stochastic system, one emulates the (known) process model, and another, the true system through measurements. In this way, low fidelity samples can be obtained via a model, while high fidelity samples are obtained through measurements of the system. This framework captures the system's behavior in a non-parametric fashion while driving exploration through acquisition functions. The benefit of using a Gaussian process to represent the system is the ability to perform uncertainty quantification in real-time and allow for chance constraints to be satisfied with high confidence. This results in a practical approach that is illustrated in numerical case studies, including a semi-batch photobioreactor optimization problem.

This paper investigates a new class of modifier-adaptation schemes to overcome plant-model mismatch in real-time optimization of uncertain processes. The main contribution lies in the integration of concepts from the areas of Bayesian optimization and derivative-free optimization. The proposed schemes embed a physical model and rely on trust-region ideas to minimize risk during the exploration, while employing Gaussian process regression to capture the plant-model mismatch in a non-parametric way and drive the exploration by means of acquisition functions. The benefits of using an acquisition function, knowing the process noise level, or specifying a nominal process model are illustrated on numerical case studies, including a semi-batch photobioreactor optimization problem.

This paper presents an extension of the recent multi-parametric (mp-)NCO-tracking methodology by Sun et al. [Comput. Chem. Eng. 92:64-77, 2016] for the design of robust multi-parametric controllers for constrained continuous-time linear systems in the presence of uncertainty. We propose a robust-counterpart formulation and solution of multi-parametric dynamic optimization (mp- DO), whereby the constraints are backed-o ff based on a worst-case propagation of the uncertainty using either interval analysis or ellipsoidal calculus and an ancillary linear state feedback. We address the case of additive uncertainty, and we discuss approaches to dealing with multiplicative uncertainty that retain tractability of the mp-NCO-tracking design problem, subject to extra conser- vativeness. In order to assist with the implementation of these controllers, we also investigate the use of data classifiers based on deep learning for approximating the critical regions in continuous-time mp-DO problems, and subsequently searching for a critical region during on-line execution. We illustrate these developments with the case studies of a fluid catalytic cracking (FCC) unit and a chemical reactor cascade.

We present an extension of set-valued integration to enable efficient sensitivity analysis of parameter-dependent ordinary differential equation (ODE) systems, using both the forward and adjoint methods. The focus is on continuous-time set-valued integration, whereby auxiliary ODE systems are derived whose solutions describe high-order inclusions of the parametric trajectories in the form of polynomial models. The forward and adjoint auxiliary ODE systems treat the parameterization error of the original differential variables as a time-varying uncertainty, and propagate the sensitivity bounds forward and backward in time, respectively. This construction enables building on the sensitivity analysis capabilities of state-of-the-art solvers, such as CVODES in the SUNDIALS suite. Several numerical case studies are presented to assess the performance and accuracy of these set-valued sensitivity integrators.

The wastewater treatment industry is undergoing a major shift towards a proactive interest in recovering materials and energy from wastewater streams, driven by both economic incentives and environmental sustainability. With the array of available treatment technologies and recovery options growing steadily, systematic approaches to determining the inherent trade-off between multiple economic and environmental objectives become necessary, namely enviroeconomic optimization. The main objective of this chapter is to present one such methodology based on superstructure modeling and multi-objective optimization, where the main environmental impacts are quantified using life cycle assessment (LCA). This methodology is illustrated with the case study of a municipal wastewater treatment facility. The results show that accounting for LCA considerations early on in the synthesis problem may lead to dramatic changes in the optimal process configuration, thereby supporting LCA integration into decision-making tools for wastewater treatment alongside economical selection criteria.

This paper describes an optimization-based approach to reducing extreme structural loads during rapid or emergency shutdown of multi-megawatt wind turbine generators. The load reduction problem is cast into an optimal control formulation, and a simple, low-order model is developed in order for this optimization problem to be tractable in reasonable time using state-of-the-art numerical methods. To handle the variations in wind speed and turbulence inherent to wind turbine operation as well as the presence of model mismatch, a real-time optimization strategy based on fast sensitivity updates is also considered, whose online computational burden is limited to the repeated solution of quadratic programs that are designed offline. The low-order model and both the open-loop and closed-loop optimal control strategies are validated against a high-fidelity model in the simulation environment Bladed™ for an industrial 3 MW wind turbine. Under favorable shutdown scenarios, i.e. when the wind turbine is operating properly and the actuators and sensors are not faulty, large reductions of the first compressive peak and subsequent compressive/tensile peaks of the tower load pattern are obtained at various above-rated wind speeds compared with normal pitch control shutdown. Extension to more challenging shutdown scenarios are also discussed. Copyright © 2013 John Wiley & Sons, Ltd. Copyright © 2013 John Wiley & Sons, Ltd.

For good performance in practice, real-time optimization schemes need to be able to deal with the inevitable model-mismatch problem. Unlike the two-step schemes combining parameter estimation and optimization, the modifier-adaptation approach uses experimental gradient information and does not require the model parameters to be estimated on-line. The dual modifier-adaptation approach presented in this paper drives the process towards optimality, while paying attention to the accuracy of the estimated gradients. The gradients are estimated from the successive operating points generated by the optimization algorithm. The novelty lies in the development of an upper bound on the gradient estimation error, which is used as a constraint for locating the next operating point. The proposed approach is demonstrated in simulation by the real-time optimization of a continuous reactor.

The adoption of stricter effluent requirements by the European Union rises large problems for small communities having few economical and technical resources. These problems motivate the synthesis of advanced optimisation-based controllers in order to enhance the performances of small-size wastewater treatment plants. The aim of this study is to develop a methodology of dynamic optimisation and optimal control of small-size alternating aerobic-anoxic activated sludge plants. The first part deals with the improvements which can be potentially obtained through the application of dynamic optimisation techniques. Two problems are considered: the minimisation of nitrogen discharge and the reduction of the operating costs. These are constrained, non-convex and high-dimensional problems that exhibit hybrid discrete/continuous and combinatorial behaviour. In both cases, the application of the resulting optimal aeration strategies leads to large improvements of the process performances, while satisfying the discharge requirements and the operating constraints; it is also verified that the long-term implementation of the optimal control profiles guarantees durable process improvement. The embedding of the optimal aeration strategies within closed-loop controllers is dealt with in the second part of the thesis. Optimal control consists in (i) the on-line joint observation/estimation of both state variables a nd parameters and, (ii) the use of a non-linear model predictive control scheme to update the aeration profiles. Beforehand, a reduced model is derived by simplifying the general ASM~1 model and sensitivity analyses are performed to quantify the influence of unmeasured disturbances and model mismatch on the optimisation results. Numerical implementations show that the resulting closed-loop controller brings large improvements with respect to usual operating modes either in terms of nitrogen discharge or in terms of energy consumption.