Fed-Batch Dynamic Optimization using Generalized Dual Heuristic Programming

Traditionally fed-batch biochemical process optimization and control uses complicated theoretical off-line optimizers, with no online model adaptation or re-optimization. This study demonstrates the applicability, effectiveness, and economic potential of a simple phenomenological model for modeling, and an adaptive critic design, generalized dual heuristic programming, for online re-optimization and control of an aerobic fed-batch fermentor. The results are compared with those obtained using a heuristic random optimize

Dynamic Re-Optimization of a Fed-Batch Fermentor using Adaptive Critic Designs

Traditionally, fed-batch biochemical process optimization and control uses complicated off-line optimizers, with no online model adaptation or re-optimization. This study demonstrates the applicability of a class of adaptive critic designs for online re-optimization and control of an aerobic fed-batch fermentor. Specifically, the performance of an entire class of adaptive critic designs, viz., heuristic dynamic programming, dual heuristic programming and generalized dual heuristic programming, was demonstrated to be superior to that of a heuristic random optimizer, on optimization of a fed-batch fermentor operation producing monoclonal antibodie

Optimisation of Mobile Communication Networks - OMCO NET

The mini conference “Optimisation of Mobile Communication Networks” focuses on advanced methods for search and optimisation applied to wireless communication networks. It is sponsored by Research & Enterprise Fund Southampton Solent University. The conference strives to widen knowledge on advanced search methods capable of optimisation of wireless communications networks. The aim is to provide a forum for exchange of recent knowledge, new ideas and trends in this progressive and challenging area. The conference will popularise new successful approaches on resolving hard tasks such as minimisation of transmit power, cooperative and optimal routing

모델기반강화학습을이용한공정제어및최적화

학위논문(박사)--서울대학교 대학원 :공과대학 화학생물공학부,2020. 2. 이종민.순차적 의사결정 문제는 공정 최적화의 핵심 분야 중 하나이다. 이 문제의 수치적 해법 중 가장 많이 사용되는 것은 순방향으로 작동하는 직접법 (direct optimization) 방법이지만, 몇가지 한계점을 지니고 있다. 최적해는 open-loop의 형태를 지니고 있으며, 불확정성이 존재할때 방법론의 수치적 복잡도가 증가한다는 것이다. 동적 계획법 (dynamic programming) 은 이러한 한계점을 근원적으로 해결할 수 있지만, 그동안 공정 최적화에 적극적으로 고려되지 않았던 이유는 동적 계획법의 결과로 얻어진 편미분 방정식 문제가 유한차원 벡터공간이 아닌 무한차원의 함수공간에서 다루어지기 때문이다. 소위 차원의 저주라고 불리는 이 문제를 해결하기 위한 한가지 방법으로서, 샘플을 이용한 근사적 해법에 초점을 둔 강화학습 방법론이 연구되어 왔다. 본 학위논문에서는 강화학습 방법론 중, 공정 최적화에 적합한 모델 기반 강화학습에 대해 연구하고, 이를 공정 최적화의 대표적인 세가지 순차적 의사결정 문제인 스케줄링, 상위단계 최적화, 하위단계 제어에 적용하는 것을 목표로 한다. 이 문제들은 각각 부분관측 마르코프 결정 과정 (partially observable Markov decision process), 제어-아핀 상태공간 모델 (control-affine state space model), 일반적 상태공간 모델 (general state space model)로 모델링된다. 또한 각 수치적 모델들을 해결하기 위해 point based value iteration (PBVI), globalized dual heuristic programming (GDHP), and differential dynamic programming (DDP)로 불리는 방법들을 도입하였다. 이 세가지 문제와 방법론에서 제시된 특징들을 다음과 같이 요약할 수 있다: 첫번째로, 스케줄링 문제에서 closed-loop 피드백 형태의 해를 제시할 수 있었다. 이는 기존 직접법에서 얻을 수 없었던 형태로서, 강화학습의 강점을 부각할 수 있는 측면이라 생각할 수 있다. 두번째로 고려한 하위단계 제어 문제에서, 동적 계획법의 무한차원 함수공간 최적화 문제를 함수 근사 방법을 통해 유한차원 벡터공간 최적화 문제로 완화할 수 있는 방법을 도입하였다. 특히, 심층 신경망을 이용하여 함수 근사를 하였고, 이때 발생하는 여러가지 장점과 수렴 해석 결과를 본 학위논문에 실었다. 마지막 문제는 상위 단계 동적 최적화 문제이다. 동적 최적화 문제에서 발생하는 제약 조건하에서 강화학습을 수행하기 위해, 원-쌍대 미분동적 계획법 (primal-dual DDP) 방법론을 새로 제안하였다. 앞서 설명한 세가지 문제에 적용된 방법론을 검증하고, 동적 계획법이 직접법에 비견될 수 있는 방법론이라는 주장을 실증하기 위해 여러가지 공정 예제를 실었다.Sequential decision making problem is a crucial technology for plant-wide process optimization. While the dominant numerical method is the forward-in-time direct optimization, it is limited to the open-loop solution and has difficulty in considering the uncertainty. Dynamic programming method complements the limitations, nonetheless associated functional optimization suffers from the curse-of-dimensionality. The sample-based approach for approximating the dynamic programming, referred to as reinforcement learning (RL) can resolve the issue and investigated throughout this thesis. The method that accounts for the system model explicitly is in particular interest. The model-based RL is exploited to solve the three representative sequential decision making problems; scheduling, supervisory optimization, and regulatory control. The problems are formulated with partially observable Markov decision process, control-affine state space model, and general state space model, and associated model-based RL algorithms are point based value iteration (PBVI), globalized dual heuristic programming (GDHP), and differential dynamic programming (DDP), respectively. The contribution for each problem can be written as follows: First, for the scheduling problem, we developed the closed-loop feedback scheme which highlights the strength compared to the direct optimization method. In the second case, the regulatory control problem is tackled by the function approximation method which relaxes the functional optimization to the finite dimensional vector space optimization. Deep neural networks (DNNs) is utilized as the approximator, and the advantages as well as the convergence analysis is performed in the thesis. Finally, for the supervisory optimization problem, we developed the novel constraint RL framework that uses the primal-dual DDP method. Various illustrative examples are demonstrated to validate the developed model-based RL algorithms and to support the thesis statement on which the dynamic programming method can be considered as a complementary method for direct optimization method.1. Introduction 1 1.1 Motivation and previous work 1 1.2 Statement of contributions 9 1.3 Outline of the thesis 11 2. Background and preliminaries 13 2.1 Optimization problem formulation and the principle of optimality 13 2.1.1 Markov decision process 15 2.1.2 State space model 19 2.2 Overview of the developed RL algorithms 28 2.2.1 Point based value iteration 28 2.2.2 Globalized dual heuristic programming 29 2.2.3 Differential dynamic programming 32 3. A POMDP framework for integrated scheduling of infrastructure maintenance and inspection 35 3.1 Introduction 35 3.2 POMDP solution algorithm 38 3.2.1 General point based value iteration 38 3.2.2 GapMin algorithm 46 3.2.3 Receding horizon POMDP 49 3.3 Problem formulation for infrastructure scheduling 54 3.3.1 State 56 3.3.2 Maintenance and inspection actions 57 3.3.3 State transition function 61 3.3.4 Cost function 67 3.3.5 Observation set and observation function 68 3.3.6 State augmentation 69 3.4 Illustrative example and simulation result 69 3.4.1 Structural point for the analysis of a high dimensional belief space 72 3.4.2 Infinite horizon policy under the natural deterioration process 72 3.4.3 Receding horizon POMDP 79 3.4.4 Validation of POMDP policy via Monte Carlo simulation 83 4. A model-based deep reinforcement learning method applied to finite-horizon optimal control of nonlinear control-affine system 88 4.1 Introduction 88 4.2 Function approximation and learning with deep neural networks 91 4.2.1 GDHP with a function approximator 91 4.2.2 Stable learning of DNNs 96 4.2.3 Overall algorithm 103 4.3 Results and discussions 107 4.3.1 Example 1: Semi-batch reactor 107 4.3.2 Example 2: Diffusion-Convection-Reaction (DCR) process 120 5. Convergence analysis of the model-based deep reinforcement learning for optimal control of nonlinear control-affine system 126 5.1 Introduction 126 5.2 Convergence proof of globalized dual heuristic programming (GDHP) 128 5.3 Function approximation with deep neural networks 137 5.3.1 Function approximation and gradient descent learning 137 5.3.2 Forward and backward propagations of DNNs 139 5.4 Convergence analysis in the deep neural networks space 141 5.4.1 Lyapunov analysis of the neural network parameter errors 141 5.4.2 Lyapunov analysis of the closed-loop stability 150 5.4.3 Overall Lyapunov function 152 5.5 Simulation results and discussions 157 5.5.1 System description 158 5.5.2 Algorithmic settings 160 5.5.3 Control result 161 6. Primal-dual differential dynamic programming for constrained dynamic optimization of continuous system 170 6.1 Introduction 170 6.2 Primal-dual differential dynamic programming for constrained dynamic optimization 172 6.2.1 Augmented Lagrangian method 172 6.2.2 Primal-dual differential dynamic programming algorithm 175 6.2.3 Overall algorithm 179 6.3 Results and discussions 179 7. Concluding remarks 186 7.1 Summary of the contributions 187 7.2 Future works 189 Bibliography 192Docto

Hybrid simulation-optimization based approach for the optimal design of single-product biotechnological processes

In this work, we present a systematic method for the optimal development of bioprocesses that relies on the combined use of simulation packages and optimization tools. One of the main advantages of our method is that it allows for the simultaneous optimization of all the individual components of a bioprocess, including the main upstream and downstream units. The design task is mathematically formulated as a mixed-integer dynamic optimization (MIDO) problem, which is solved by a decomposition method that iterates between primal and master sub-problems. The primal dynamic optimization problem optimizes the operating conditions, bioreactor kinetics and equipment sizes, whereas the master levels entails the solution of a tailored mixed-integer linear programming (MILP) model that decides on the values of the integer variables (i.e., number of equipments in parallel and topological decisions). The dynamic optimization primal sub-problems are solved via a sequential approach that integrates the process simulator SuperPro Designer® with an external NLP solver implemented in Matlab®. The capabilities of the proposed methodology are illustrated through its application to a typical fermentation process and to the production of the amino acid L-lysine.Support from the Spanish Ministry of Education and Science (projects DPI2008-04099 and CTQ2009-14420-C02) and the Spanish Ministry of External Affairs (projects A/023551/09, A/031707/10 and HS2007-0006)

State Estimation, Covariance Estimation, and Economic Optimization of Semi-Batch Bioprocesses

One of the most critical aspects of any chemical process engineer is the ability to gather, analyze, and trust incoming process data as it is often required in control and process monitoring applications. In real processes, online data can be unreliable due to factors such as poor tuning, calibration drift, or mechanical drift. Outside of these sources of noise, it may not be economically viable to directly measure all process states of interest (e.g., component concentrations). While process models can help validate incoming process data, models are often subject to plant-model mismatches, unmodeled disturbances, or lack enough detail to track all process states (e.g., dissolved oxygen in a bioprocess). As a result, directly utilizing the process data or the process model exclusively in these applications is often not possible or simply results in suboptimal performance. To address these challenges and achieve a higher level of confidence in the process states, estimation theory is used to blend online measurements and process models together to derive a series of state estimates. By utilizing both sources, it is possible to filter out the noise and derive a state estimate close to the true process conditions. This work deviates from the traditional state estimation field that mostly addresses continuous processes and examines how techniques such as extended Kalman Filter (EKF) and moving horizon estimation (MHE) can be applied to semi-batch processes. Additionally, this work considers how plant-model mismatches can be overcome through parameter-based estimation algorithms such as Dual EKF and a novel parameter-MHE (P-MHE) algorithm. A galacto-oligosaccharide (GOS) process is selected as the motivating example as some process states are unable to be independently measured online and require state estimation to be implemented. Moreover, this process is representative of the broader bioprocess field as it is subject to high amounts of noise, less rigorous models, and is traditionally operated using batch/semi-batch reactors. In conjunction with employing estimation approaches, this work also explores how to effectively tune these algorithms. The estimation algorithms selected in this work require careful tuning of the model and measurement covariance matrices to balance the uncertainties between the process models and the incoming measurements. Traditionally, this is done via ad-hoc manual tuning from process control engineers. This work modifies and employs techniques such as direct optimization (DO) and autocovariance least-squares (ALS) to accurately estimate the covariance values. Poor approximation of the covariances often results in poor estimation of the states or drives the estimation algorithm to failure. Finally, this work develops a semi-batch specific dynamic real-time optimization (DRTO) algorithm and poses a novel costing methodology for this specific type of problem. As part of this costing methodology, an enzyme specific cost scaling correlation is proposed to provide a realistic approximation of these costs in industrial contexts. This semi-batch DRTO is combined with the GOS process to provide an economic analysis using Kluyveromyces lactis (K. lactis) β-galactosidase enzyme. An extensive literature review is carried out to support the conclusions of the economic analysis and motivate application to other bioprocesses

Handling Uncertainties in Process Optimization

Esta tesis doctoral presenta el estudio de técnicas que permiten manejar las incertidumbres en la optimización de procesos, desde el punto de vista del comportamiento aleatorio de las variables y de los errores en los modelos utilizados en la optimización. Para el tratamiento de las variables inciertas, se presenta la aplicación de la Programación de dos Etapas y Optimización Probabilística a un proceso de hidrodesulfuración. Los resultados permiten asegurar factibilidad en la operación, independiente del valor que tome la variable aleatoria dentro de su distribución de probabilidad. Acerca del manejo de la incertidumbre derivada del conocimiento parcial del proceso, se ha estudiado el método de Optimización en Tiempo Real con adaptación de modificadores, proponiendo mejoras que permiten: (1) evitar infactibilidades en su evolución, (2) obtener el óptimo real del proceso sin necesidad de estimar sus gradientes y (3) identificar las limitaciones para su aplicación en sistemas dinámicos de horizonteDepartamento de Ingeniería de Sistemas y Automátic