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The area of polynomial optimization has been actively studied in computer science, operations research, applied mathematics and engineering, where the goal is to find a high-quality solution using an efficient computational method. This area has attracted much attention in the control community since several long-standing control problems could be converted to polynomial optimization problems. The current researches on this area have been mostly focused on various important questions: i) how does the underlying structure of an optimization problem affect its complexity? Ii) how does sparsity help? iii) how to find a near globally optimal solution whenever it is hard to find a global minimum? iv) how to design an efficient numerical algorithm for large-scale non-convex optimization problems? v) how to deal with problems with a mix of continuous and discrete variables? In this talk, we will develop a unified mathematical framework to study the above problems. Our framework rests on recent advances in graph theory and optimization, including the notions of OS-vertex sequence and treewidth, matrix completion, semidefinite programming, and low-rank optimization. We will also apply our results to two areas of power systems and distributed control. In particular, we will discuss how our results could be used to address several hard problems for power systems such as optimal power flow (OPF), security-constrained OPF, state estimation, and unit commitment.
Network systems have received a lot of attention in the past decade. They are used to analyze and design communication network, smart grid technology, social media, social dynamics, formation and consensus problems, etc. Several analysis and control methods have been developed for network systems. However, often, their large scale nature makes it difficult to analyze and to design a controller. We develop methods to reduce the order of the network while preserving the network structure, as well as some structure of the (linear) node dynamics. In particular, second order network dynamics structure is preserved. We use node clustering methods, as well as a state space singular value decomposition based method. For the first we provide error bounds. We illustrate the results with help of some relevant high order examples.
Model predictive control has become a pervasive advanced control technology in which optimal control of a multivariable system with input and state constraints is combined with a moving horizon to produce a feedback controller. In applications, model predictive control is often used to solve constrained tracking problems. The tracking problem arises in some settings as the basic goal of the control system, and the constraint handling capabilities of MPC are what make it attractive. In other applications, however, there may be a higher-level goal, such as economic optimization of a process, and this goal is first translated into a steady-state tracking problem. Since MPC enables the designer to choose the objective function that is optimized online, it offers the potential to treat the higher-level control goal directly within the MPC controller bypassing this translation into a steady-state setpoint and tracking problem. In this talk we explore the possibilities enabled by MPC to address these types of high-level goals. We also outline some of the open research challenges presented by this approach; these include modeling, optimization, and controller design challenges. The talk concludes with a brief presentation of a recently deployed economic optimization technology developed by Johnson Controls to control the campus energy system at Stanford University.
The field of control provides the principles and methods used to design physical, biological and information systems that maintain desirable performance by sensing and automatically adapting to changes in the environment. The opportunities to apply control principles and methods are exploding. In this talk I will briefly review some of the past predictions for future directions in control (including some of my own) and provide some thoughts on how well the field is doing in terms of living up to its past promises of future success. The ultimate goal of the talk is to help inspire the next generation of controls researchers, balance theory with application, provide a view into the possible futures of control, give credit where it is due, and let the guard down and talk about personal stuff a bit.
Distributed and large-scale optimization problems have gained a significant attention in the context of cyber-physical, peer-to-peer, and ad-hoc networked systems. The large-scale property is reflected in the number of decision variables, the number of constraints, or both, while the distributed nature of the problems is inherent due to partial (local) knowledge of the problem data (e.g., a portion of the cost function or a subset of the constraints is known to different entities in the system). The talk will focus on some recent developments on optimization models and algorithmic approaches for solving such problems with applications in domains ranging from control to machine learning.
Smart Cities are an example of Cyber-Physical Systems whose goals include improvements in transportation, energy distribution, emergency response, and infrastructure maintenance, to name a few. One of the key elements of a Smart City is the ability to monitor and dynamically allocate its resources. The availability of large amounts of data, ubiquitous wireless connectivity, and the critical need for scalability open the door for new control and optimization methods which are both data-driven and event-driven. The talk will present such an optimization framework and its properties. It will then describe several applications that arise in Smart Cities, some of which have been tested in the City of Boston: a “Smart Parking” system which dynamically assigns and reserves an optimal parking space for a user (driver); the “Street Bump” system which uses standard smartphone capabilities to collect roadway obstacle data and identify and classify them for efficient maintenance and repair; adaptive traffic light control; optimal control of connected autonomous vehicles. Lastly, to address the “social’’ dimension, the talk will describe how a large traffic data set from the Massachusetts road network was analyzed to estimate the Price of Anarchy in comparing “selfish” user-centric behavior to “social” system-centric optimal traffic routing solutions.
This talk examines the transient modeling of power flow for transient thermal systems. The focus is on dynamic phenomena starting with a basic thermodynamic cycle and building up to more complex systems. The overall goal of the modeling process is to develop systems-level models that are sufficiently flexible to be used on a variety of different applications. These models balance complexity with accuracy to obtain models that are sufficient for dynamic optimization and design as well as control algorithms In addition to the modeling approach we present control strategies aimed at managing the flow of thermal power. We present a particular hierarchical approach to power flow that accommodates multiple power modes. The hierarchy allows for systems operating on different time scales to be coordinated. It also allows for different control tools to be used at different levels of the hierarchy based on the needs of the physical systems under control. Stability results exploit the system structure to provide guarantees. Recent results will be presented representing both interconnected complex systems with specific examples from industrial partners.
At the quantum level, feedback loops have to take into account measurement back-action. The goal of this talk is to explain, in a tutorial way and on the first experimental realization of a quantum-state feedback, how such purely quantum effect can be exploited in models and stabilization control schemes. This closed-loop experiment was conducted in 2011 by the group of Serge Haroche (Physics Nobel Prize 2012). The control goal was to stabilize a small number of micro-wave photons trapped between two super-conducting mirrors and subject to quantum non-demolition measurement via probe off-resonant Rydberg atoms. The implemented control scheme was decomposed into two parts. The first part estimates in real-time the quantum state of the trapped photons via a discrete-time Belavkin quantum filter. The second part is a nonlinear quantum-state feedback based on control Lyapunov functions. It stabilizes via suitable coherent displacements the number of photon(s) towards its set-point, namely an integer less than 5 in the experiment. This control scheme relies on a hidden control Markov model whose structure combines three quantum rules: unitary deterministic Schrödinger evolution; stochastic collapse of the wave packet induced by the measurement; tensor product for the composite systems. These basic quantum rules characterize the structure of all Markovian models describing open-quantum systems. These rules explain also the existence to two kinds of feedback schemes currently developed for quantum error correction: measurement-based feedback where an open quantum system is stabilized by a classical controller; coherent or autonomous feedback (reservoir engineering) where an open quantum system is passively stabilized through its coupling with another highly dissipative quantum system, namely the quantum controller.
Thirty years ago, computer-aided control system design involved an exclusive community of engineers, typically in top research labs or large companies, running esoteric codes on timeshared minicomputers to design and analyze control algorithms, often for expensive systems produced in low volumes. Today, computer-aided control system design has grown into Model-Based Design, encompassing not only system analysis and algorithm design, but also implementation through code generation, plus verification and validation on both models and embedded code. It is used in every industry that creates today’s smart systems – aerospace, automotive, industrial automation, medical devices, robotics, energy, and many more – not only for the controls but integrating computer vision, communication, and machine learning. In this talk, Jack Little reviews the evolution of control design tools, and the corresponding changes in controls education and research. Jack then looks forward to the future of Model-Based Design and how it is addressing the next generation of control engineers: researchers and developers working on challenges such as cyber-physical systems and distributed systems, but also students and makers taking advantage of easy-to-use software with low-cost hardware – everyone building the smarter controlled systems of the future.
Many current products and systems employ sophisticated mathematical algorithms to automatically make complex decisions, or take action, in real-time. Examples include recommendation engines, search engines, spam filters, on-line advertising systems, fraud detection systems, automated trading engines, revenue management systems, supply chain systems, electricity generator scheduling, flight management systems, and advanced engine controls.
I'll cover the basic ideas behind these and other applications, emphasizing the central role of mathematical optimization and the associated areas of machine learning and automatic control. The talk will be nontechnical, but the focus will be on understanding the central issues that come up across many applications, such as the development or learning of mathematical models, the role of uncertainty, the idea of feedback or recourse, and computational complexity.
In this talk, I will describe some of our work on nanomechanics of biological systems and design of medical devices for hospitals in resource poor countries. These may sound like very disparate areas. However, you may be surprised to see how well the skills students learn in one translate well to the other. Atomic Force Microscopy and high precision instrumentation are common tools for the basic sciences. We can use these systems to measure small-scale intermolecular forces and characterize the nano-structures of individual cellular components. These types of measurements help to build more accurate models of tissues and organs to predict behavior during disease and injury. Beyond the basic sciences, the same types of concepts and skills needed for nanoscience work can be applied to solve real-world engineering problems in resource poor hospitals today. Working with engineers and clinicians in Tanzania, our students have designed several novel solutions to problems they have seen in clinics. These range from infant warmers to ink-jet printed diabetes test supplies to basket woven neck braces. In addition, while in the hospitals, our students put their debugging skills to the test by helping to repair and maintain clinical devices and equipment. Experiences in the lab and in the field give students a rounded perspective on engineering and a clearer outlook on their future career paths.
Humans have the ability to walk with deceptive ease, navigating everything from daily environments to uneven and uncertain terrain with efficiency and robustness. With the goal of achieving human-like abilities on robotic systems, this talk presents the process of formally achieving bipedal robotic walking through controller synthesis inspired by human locomotion, and it demonstrates these methods through experimental realization on numerous bipedal robots and robotic assistive devices. Motivated by the hierarchical control present in humans, human-inspired virtual constraints are utilized to synthesize a novel type of control Lyapunov function (CLF); when coupled with hybrid system models of locomotion, this class of CLFs yields provably stable robotic walking. Going beyond explicit feedback control strategies, these CLFs can be used to formulate an optimization-based control methodology that dynamically accounts for torque and contact constraints while being implementable in real-time. This sets the stage for the unification of control objectives with safety-critical constraints through the use of a new class of control barrier functions provably enforcing these constraints. The end result is the generation of bipedal robotic walking that is remarkably human-like and is experimentally realizable, together with a novel control framework for highly dynamic behaviors on bipedal robots. Furthermore, these methods form the basis for achieving a variety of advanced walking behaviors—including multi-domain locomotion, e.g., human-like heel-toe behaviors—and therefore have application to the control of robotic assistive devices, as evidenced by the demonstration of the resulting controllers on multiple robotic walking platforms, humanoid robots and prostheses.
Robotic technology can: (i) deliver therapy to aid recovery after neurological disease; (ii) replace limb function following amputation; and (iii) provide assistance to restore function. This exciting new frontier of robotic applications requires sensitive but forceful physical interaction with a human, yet physical contact can severely de-stabilize robots. Despite these challenges, clinical evidence shows that robot therapy is both effective and cost-effective. Motorized amputation prostheses present even greater challenges. They must manage physical interaction with objects in the world as well as with the amputee. This presentation will review how machine mimicry of natural control provides the gentleness required for robotic therapy and enables seamless coordination of natural and prosthetic limbs. A pre-requisite for success in these applications is a quantitative knowledge of the human motor control system.
Electricity production in the US has changed dramatically since 2000, with the percent of electricity produced from gas growing from 16% to 30%, while coal dropped from 52% to 37%. These changes are primarily driven by two technologies used in shale rock formations, directional drilling to create horizontal wells, and hydraulic fracturing to release the gas within the relatively impermeable rock. This presentation will first give a brief operational overview of hydraulic fracturing. Next, challenges that relate to the control of this technology are described. Lastly, two examples are presented, one a theoretical study investigating the potential of model-based feedback control of the hydraulic fracturing process and the other an implementation that highlights the importance of measurements and data uncertainty when designing effective and robust controllers.
In the past, robotic manipulators, machine tools, measurement devices, and other systems were designed with rigid structures and operated at relatively low speeds. With a growing demand for fuel efficiency, smaller actuators, and speed, lighter weight materials are increasingly used in many systems, making them more flexible. Achieving high-performance control of flexible structures is a difficult task, but one that is now critical to the success of many important applications, such as atomic force microscopes, disk drives, tape drives, robotic manipulators, gantry cranes, wind turbines, satellites, and the space station remote manipulator system. The unwanted vibration that results from maneuvering or controlling a flexible structure often dictates limiting factors in the performance of the system. Over the last few decades, many feedback, feedforward, and combined feedforward/feedback control methods have been developed for flexible structures. We will discuss and compare several of these control methods in conjunction with overviewing some of the issues in the modeling of flexible structures, and we will highlight a few recurring themes across the diverse application areas mentioned above.
High-gain observers play an important role in the design of feedback control for nonlinear systems. This lectures overviews the essentials of this technique. After a brief historical background, a motivating example is used to illustrate the main features of high-gain observers, with emphasis on the peaking phenomenon and the role of control saturation in dealing with it. The use of the observer in feedback control is discussed and a nonlinear separation principle is presented. The use of an extended high-gain observer as a disturbance estimator is covered. Challenges in implementing high-gain observers are discussed, with the effect of measurement noise as the most serious one. Techniques to cope with measurement noise are presented. The lecture ends by listing the speaker's experience with experimental testing of high-gain observers.
In the interim report on the fifth Science and Technology Basic Plan of Japan, the realization of Super Smart Society in our future is highlighted. The initiative for Smart Cities has been also promoted worldwide as societal-scale CPS (Cyber-Physical Systems) infrastructures. Along with efficient traffic/water/security management, distributed EMS (Energy Management Systems) should play a key role as we head toward low carbon environmental friendly society that is essential for sustainable development. To this goal, JST (Japan Science and Technology Agency) has launched a CREST research area for the distributed EMS building. The aim of this project is to create fundamental theory and advanced technology for optimal control of energy balancing between dynamic demand and supply. The topics covered include forecast and integration of renewable energy, management of electric vehicle/storage, demand response and human behavior, development of demand model, and platform building. A particular emphasis is on the promotion of international research collaboration with the US and European Funding Agencies, such as NSF (USA), DFG (Germany), RCN (Norway), CNR (Italy) and others. This would enable all the project researchers involved to catalyze networking and knowledge sharing with a broad array of disciplines. In this talk, the on-going exciting progress of the CREST EMS project will be presented.
Network systems are mathematical models for the study of cooperation, propagation, synchronization and other dynamical phenomena that arise among interconnected agents. Network systems are widespread in science as they are fundamental modeling tools, e.g., in sociology, ecology, and epidemiology. They also play a key growing role in technology, e.g., in the design of power grids, cooperative robotic behaviors and distributed computing algorithms. Their study pervades applied mathematics. This talk will review established and emerging frameworks for modeling, analysis and design of network systems. I will survey the available comprehensive theory for linear network systems and then highlight selected nonlinear concepts. Next, I will focus on recent developments by my group on (i) modeling of the evolution of opinions and social power in social networks, (ii) analysis of security and transmission capacity in power grids, and (iii) design of optimal strategies for robotic routing and coordination.
The emergence of large networked systems has brought about new challenges to researchers and practitioners alike. While such systems perform well under normal operations, they can exhibit fragility in response to certain disruptions that may lead to catastrophic cascades of failures. This phenomenon, referred to as systemic risk, emphasizes the role of the system interconnection in causing such, possibly rare, events. The flash crash of 2010, the financial crisis of 2008, the New England power outage of 2003, or simply extensive delays in air travel, are just a few of many examples of fragility and systemic risk present in complex interconnected systems. Robust interconnections have been the subject of study by the control community for several decades. Substantial progress has been made in the context of both stability and performance robustness for various types of interconnections. Typical problems addressed in the literature involve interconnections with simple topologies, but with more complex components (dynamic, sometimes with high dimensions). More recently, the attention of the research community has shifted towards networked systems where the topology of the network is fairly large and complicated, while the local dynamics are fairly simple. The term fragility is used in this context to highlight the system's closeness to failure. Notions of failure include large amplification of local disturbances (or shocks), instability, or a substantial increase in the probability of extreme events. Cascaded failures, or systemic risk, fit under this umbrella and focus on local failures synchronizing to cause a breakdown in the network. Many abstracted models from transportation, finance, or the power grid fit this framework well. The focus of research is to relate fragility to the size and characteristics of a network for certain types of local interactions. In this talk, I will address this emerging area. I will provide some constructive examples and highlight important research directions.
Modern air transportation systems are complex cyber-physical networks that are critical to global travel and commerce. As the demand for air transport has grown, so have congestion, flight delays, and the resultant environmental impacts. With further growth in demand expected, new control techniques are needed, perhaps even with redesign of some parts of the system, in order to prevent cascading delays and excessive pollution.
This talk presents examples of control and optimization algorithms for air transportation systems that are grounded in real-world data, including their implementation and testing in both simulations and in field trials. These algorithms help us address several challenges, including resource allocation with multiple stakeholders, robustness in the presence of operational uncertainties, and developing decision-support tools that account for human operators and their behavior.
