System Level Synthesis

This article surveys the System Level Synthesis framework, which presents a novel perspective on constrained robust and optimal controller synthesis for linear systems. We show how SLS shifts the controller synthesis task from the design of a controller to the design of the entire closed loop system, and highlight the benefits of this approach in terms of scalability and transparency. We emphasize two particular applications of SLS, namely large-scale distributed optimal control and robust control. In the case of distributed control, we show how SLS allows for localized controllers to be computed, extending robust and optimal control methods to large-scale systems under practical and realistic assumptions. In the case of robust control, we show how SLS allows for novel design methodologies that, for the first time, quantify the degradation in performance of a robust controller due to model uncertainty -- such transparency is key in allowing robust control methods to interact, in a principled way, with modern techniques from machine learning and statistical inference. Throughout, we emphasize practical and efficient computational solutions, and demonstrate our methods on easy to understand case studies.Comment: To appear in Annual Reviews in Contro

System level synthesis

This article surveys the System Level Synthesis framework, which presents a novel perspective on constrained robust and optimal controller synthesis for linear systems. We show how SLS shifts the controller synthesis task from the design of a controller to the design of the entire closed loop system, and highlight the benefits of this approach in terms of scalability and transparency. We emphasize two particular applications of SLS, namely large-scale distributed optimal control and robust control. In the case of distributed control, we show how SLS allows for localized controllers to be computed, extending robust and optimal control methods to large-scale systems under practical and realistic assumptions. In the case of robust control, we show how SLS allows for novel design methodologies that, for the first time, quantify the degradation in performance of a robust controller due to model uncertainty – such transparency is key in allowing robust control methods to interact, in a principled way, with modern techniques from machine learning and statistical inference. Throughout, we emphasize practical and efficient computational solutions, and demonstrate our methods on easy to understand case studies

Distributed and Large-Scale Optimization

This dissertation is motivated by the pressing need for solving real-world large-scale optimization problems with the main objective of developing scalable algorithms that are capable of solving such problems efficiently. Large-scale optimization problems naturally appear in complex systems such as power networks and distributed control systems, which are the main systems of interest in this work. This dissertation aims to address four problems with regards to the theory and application of large-scale optimization problems, which are explained below: Chapter 2: In this chapter, a fast and parallelizable algorithm is developed for an arbitrary decomposable semidefinite program (SDP). Based on the alternating direction method of multipliers, we design a numerical algorithm that has a guaranteed convergence under very mild assumptions. We show that each iteration of this algorithm has a simple closed-form solution, consisting of matrix multiplications and eigenvalue decompositions performed by individual agents as well as information exchanges between neighboring agents. The cheap iterations of the proposed algorithm enable solving a wide spectrum of real-world large-scale conic optimization problems that could be reformulated as SDP. Chapter 3: Motivated by the application of sparse SDPs to power networks, the objective of this chapter is to design a fast and parallelizable algorithm for solving the SDP relaxation of a large-scale optimal power flow (OPF) problem. OPF is fundamental problem used for the operation and planning of power networks, which is non-convex and NP-hard in the worst case. The proposed algorithm would enable a real-time power network management and improve the system's reliability. In particular, this algorithm helps with the realization of Smart Grid by allowing to make optimal decisions very fast in response to the stochastic nature of renewable energy. The proposed algorithm is evaluated on IEEE benchmark systems. Chapter 4: The design of an optimal distributed controller using an efficient computational method is one of the most fundamental problems in the area of control systems, which remains as an open problem due to its NP-hardness in the worst case. In this chapter, we first study the infinite-horizon optimal distributed control (ODC) problem (for deterministic systems) and then generalize the results to a stochastic ODC problem (for stochastic systems). Our approach rests on formulating each of these problems as a rank-constrained optimization from which an SDP relaxation can be derived. We show that both problems admit sparse SDP relaxations with solutions of rank at most~3. Since a rank-1 SDP matrix can be mapped back into a globally-optimal controller, the rank-3 solution may be deployed to retrieve a near-global controller. We also propose computationally cheap SDP relaxation for each problem and then develop effective heuristic methods to recover a near-optimal controller from the low-rank SDP solution. The design of several near-optimal structured controllers with global optimality degrees above 99\% will be demonstrated. Chapter 5: The frequency control problem in power networks aims to control the global frequency of the system within a tight range by adjusting the output of generators in response to the uncertain and stochastic demand. The intermittent nature of distributed power generation in smart grid makes the traditional decentralized frequency controllers less efficient and demands distributed controllers that are able to deal with the uncertainty in the system introduced by non-dispatchable supplies (such as renewable energy), fluctuating loads, and measurement noise. Motivated by this need, we study the frequency control problem using the results developed in Chapter 4. In particular, we formulate the problem and then conduct a case study on the IEEE 39-Bus New England system. The objective is to design a near-global optimal distributed frequency controller for the New England test system by optimally adjusting the mechanical power input to each generator based on the real-time measurement received from neighboring generators through a user-defined communication topology

Dynamic modeling, intelligent control and diagnostics of hot water heating systems

Heating, ventilating and air-conditioning (HVAC) systems have been extensively used to provide desired indoor environment in buildings. It is well acknowledged that 25-35% of the total energy use is consumed by buildings, and space heating systems account for 50-60% of the building energy consumption. Furthermore, roughly half of the energy consumed goes to operation of heating systems. In the past few years the energy use has shown rapid growth. Therefore, it is necessary to design and operate HVAC systems to reduce energy consumption and improve occupant comfort. To improve energy efficiency, HVAC systems should be optimally controlled and operated. This study focuses on developing advanced control strategies and fault tolerant control (FTC) using information from fault detection and diagnosis (FDD) for hot water heating (HWH) systems. To begin with, HWH system dynamic models are developed based on mass, momentum and energy balance principles. Then, embedded intelligent control strategies: fuzzy logic control and fuzzy logic adaptive control are designed for the overall system to achieve better performance and energy efficiency. Moreover, in designing the advanced control strategies, the parameter uncertainty and noise from measurement and process are taken into account. The extended Kalman filter (EKF) technique is utilized to handle system uncertainty and measurement noise, and to improve system control performance. After that, a supervisory control strategy for the HWH system is designed and simulated to achieve optimal operation. Finally, model-based FDD methods were developed by using fuzzy logic to detect and isolate measurement and process faults occurring in HWH systems. The FDD information was employed to design model-based FTC systems for various faults and to extend the operating range under failure situations. The contributions of this study include the development of a large scale dynamic model of a HWH system for a high-rise building; design of fuzzy logic adaptive control strategies to improve energy efficiency of heating systems and design of model-based FTC systems by using FDD information

Integration of design and control for large-scale applications: a back-off approach

Design and control are two distinct aspects of a process that are inherently related though these aspects are often treated independently. Performing a sequential design and control strategy may lead to poor control performance or overly conservative and thus expensive designs. Unsatisfactory designs stem from neglecting the connection of choices made at the process design stage that affects the process dynamics. Integration of design and control introduces the opportunity to establish a transparent link between steady-state economics and dynamic performance at the early stages of the process design that enables the identification of reliable and optimal designs while ensuring feasible operation of the process under internal and external disruptions. The dynamic nature of the current global market drives industries to push their manufacturing strategies to the limits to achieve a sustainable and optimal operation. Hence, the integration of design and control plays a crucial role in constructing a sustainable process since it increases the short and long-term profits of industrial processes. Simultaneous process design and control often results in challenging computationally intensive and complex problems, which can be formulated conceptually as dynamic optimization problems. The size and complexity of the conceptual integrated problem impose a limitation on the potential solution strategies that could be implemented on large-scale industrial systems. Thus far, the implementation of integration of design and methodologies on large-scale applications is still challenging and remains as an open question. The back-off approach is one of the proposed methodologies that relies on steady-state economics to initiate the search for optimal and dynamically feasible process design. The idea of the surrogate model is combined with the back-off approach in the current research as the key technique to propose a practical and systematic method for the integration of design and control for large-scale applications. The back-off approach featured with power series expansions (PSEs) is developed and extended to achieve multiple goals. The proposed back-off method focuses on searching for the optimal design and control parameters by solving a set of optimization problems using PSE functions. The idea is to search for the optimal direction in the optimization variables by solving a series of bounded PSE-based optimization problems. The approach is a sequential approximate optimization method in which the system is evaluated around the worst-case variability expected in process outputs. Hence, using PSE functions instead of the actual nonlinear dynamic process model at each iteration step reduces the computational effort. The method mostly traces the closest feasible and near-optimal solution to the initial steady-state condition considering the worst-case scenario. The term near-optimal refers to the potential deviations from the original locally optimum due to the approximation techniques considered in this work. A trust-region method has been developed in this research to tackle simultaneous design and control of large-scale processes under uncertainty. In the initial version of the back-off approach proposed in this research, the search space region in the PSE-based optimization problem was specified a priori. Selecting a constant search space for the PSE functions may undermine the convergence of the methodology since the predictions of the PSEs highly depend on the nominal conditions used to develop the corresponding PSE functions. Thus, an adaptive search space for individual PSE-optimization problems at every iteration step is proposed. The concept has been designed in a way that certifies the competence of the PSE functions at each iteration and adapts the search space of the optimization as the iteration proceeds in the algorithm. Metrics for estimating the residuals such as the mean of squared errors (MSE) are employed to quantify the accuracy of the PSE approximations. Search space regions identified by this method specify the boundaries of the decision variables for the PSE-based optimization problems. Finding a proper search region is a challenging task since the nonlinearity of the system at different nominal conditions may vary significantly. The procedure moves towards a descent direction and at the convergence point, it can be shown that it satisfies first-order KKT conditions. The proposed methodology has been tested on different case studies involving different features. Initially, an existent wastewater treatment plant is considered as a primary medium-scale case study in the early stages of the development of the methodology. The wastewater treatment plant is also used to investigate the potential benefits and capabilities of a stochastic version of the back-off methodology. Furthermore, the results of the proposed methodology are compared to the formal integration approach in a dynamic programming framework for the medium-scale case study. The Tennessee Eastman (TE) process is selected as a large-scale case study to explore the potentials of the proposed method. The results of the proposed trust-region methodology have been compared to previously reported results in the literature for this plant. The results indicate that the proposed methodology leads to more economically attractive and reliable designs while maintaining the dynamic operability of the system in the presence of disturbances and uncertainty. Therefore, the proposed methodology shows a significant accomplishment in locating dynamically feasible and near-optimal design and operating conditions thus making it attractive for the simultaneous design and control of large-scale and highly nonlinear plants under uncertainty

Diseño para operabilidad: Una revisión de enfoques y estrategias de solución

In the last decades the chemical engineering scientific research community has largely addressed the design-foroperability problem. Such an interest responds to the fact that the operability quality of a process is determined by design, becoming evident the convenience of considering operability issues in early design stages rather than later when the impact of modifications is less effective and more expensive. The necessity of integrating design and operability is dictated by the increasing complexity of the processes as result of progressively stringent economic, quality, safety and environmental constraints. Although the design-for-operability problem concerns to practically every technical discipline, it has achieved a particular identity within the chemical engineering field due to the economic magnitude of the involved processes. The work on design and analysis for operability in chemical engineering is really vast and a complete review in terms of papers is beyond the scope of this contribution. Instead, two major approaches will be addressed and those papers that in our belief had the most significance to the development of the field will be described in some detail.En las últimas décadas, la comunidad científica de ingeniería química ha abordado intensamente el problema de diseño-para-operabilidad. Tal interés responde al hecho de que la calidad operativa de un proceso esta determinada por diseño, resultando evidente la conveniencia de considerar aspectos operativos en las etapas tempranas del diseño y no luego, cuando el impacto de las modificaciones es menos efectivo y más costoso. La necesidad de integrar diseño y operabilidad esta dictada por la creciente complejidad de los procesos como resultado de las cada vez mayores restricciones económicas, de calidad de seguridad y medioambientales. Aunque el problema de diseño para operabilidad concierne a prácticamente toda disciplina, ha adquirido una identidad particular dentro de la ingeniería química debido a la magnitud económica de los procesos involucrados. El trabajo sobre diseño y análisis para operabilidad es realmente vasto y una revisión completa en términos de artículos supera los alcances de este trabajo. En su lugar, se discutirán los dos enfoques principales y aquellos artículos que en nuestra opinión han tenido mayor impacto para el desarrollo de la disciplina serán descriptos con cierto detalle.Fil: Blanco, Anibal Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; ArgentinaFil: Bandoni, Jose Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; Argentin