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Control theory is hardly alone among scientific communities experiencing some obsolescence anxiety in the face of machine learning, where decades - or centuries - of building first-principles models and designs are supplanted by data. While ML real-time feedback is unlikely to attain the adaptive control's closed-loop guarantees for unstable plants that lack persistency of excitation, our community, adept at harnessing new ideas, has generated in a few years many other adroit ways to incorporate ML-from lightening methodological complexities to circumventing difficult constructions.
Rather than walking away from certificate-bearing control tools built by generations of control researchers, in this lecture I seek game-changing supporting roles for ML, in control implementation. I present the emerging subject of employing the latest breakthrough in deep learning approximations of not functions but function-to-function mappings (nonlinear operators) in the complex field of PDE control. With neural operators, entire PDE control methodologies are encoded into what amounts to a function evaluation, leading to a thousandfold speedup and enabling PDE control implementations. Deep neural operators, such as DeepONet, mathematically guaranteed to provide an arbitrarily close accuracy in rapidly computing control inputs, preserve the stabilization guarantees of the existing PDE backstepping controllers. Applications range from traffic and epidemiology to manufacturing, energy generation, and supply chains.
The term dual control was introduced in the 1960s to describe the tradeoff between short term control objectives and actions to promote learning. A closely related term is the exploration-exploitation tradeoff. This lecture will review some settings where dual controllers can be optimized efficiently, both for practical purposes and for a more fundamental understanding of the interplay between learning and control.
The starting point will be the standard setting of linear systems optmized with respect to quadratic cost. However much of modern learning theory is developed in a discrete setting. By investigating similarities and differences between the two frameworks, we will shed light on the dual control problem and discover new promising results and directions for research.
A multi-agent system should be capable of fast and flexible decision-making if it is to successfully manage the uncertainty, variability, and dynamic change encountered when operating in the real world. Decision-making is fast if it breaks indecision as quickly as indecision becomes costly. This requires fast divergence away from indecision in addition to fast convergence to a decision. Decision-making is flexible if it adapts to signals important to successful operations, even if they are weak or rare. This requires tunable sensitivity to input for modulating regimes in which the system is ultra-sensitive and in which the system is robust. Nonlinearity and feedback in the multi-agent decision-making dynamics are necessary to meet these requirements.
I will present theoretical principles, analytical results, and applications of a general model of decentralized, multi-agent, and multi-option, nonlinear opinion dynamics that enables fast and flexible decision-making. I will explain how the critical features of fast and flexible multi-agent decision-making depend on nonlinearity, feedback, and the structure of the inter-agent communication network and a belief system network. And I will show how the theory and results provide a principled and systematic means for designing and analyzing multi-agent decision-making in systems ranging from multi-robot teams to social networks.
A typical multi-agent system is composed of a follower system consisting of multiple subsystems called followers and a leader system whose output is to be tracked by the followers. What makes the control of a multi-agent system challenging is that the control law needs to be distributed in the sense that it must satisfy time-varying communication constraints. A special case of distributed control is where all the followers can access the information of the leader. For this special case, one can design, for each follower, a conventional control law based on the information of the leader. The collection of these conventional control laws constitutes the so-called purely decentralized control law for the multi-agent system. Nevertheless, the purely decentralized control law is not feasible due to the communication constraints. In this talk, we will introduce a framework for designing a distributed control law by cascading a purely decentralized control law and a so-called distributed observer for the leader system, which is a dynamic compensator that estimates and transmits the leader’s information to each follower over a communication network. Such a control law is called the distributed observer-based control law and has found its applications to such problems as consensus, synchronization, flocking, formation, and distributed Nash equilibrium seeking. The core of this design framework is the distributed observer for a linear leader system, which was initiated in 2010 for dealing with the cooperative output regulation problem, and has experienced three phases of developments. In the first phase, the distributed observer is only capable of estimating and transmitting the leader’s state to every follower assuming every follower knows the dynamics of the leader. In the second phase which started in 2015, the distributed observer is rendered the capability of estimating and transmitting not only the leader’s state but also the dynamics of the leader to every follower provided that the leader’s children know the information of the leader. Such a dynamic compensator is called an adaptive distributed observer for a known leader system. The distributed observer was further developed in 2017 for linear leader systems containing unknown parameters, thus entering its third phase of the development. Such a dynamic compensator is called an adaptive distributed observer for an unknown leader as it not only estimates the state but also the unknown parameters of the leader. We will start with an overview on the development of the distributed observer and then highlight the recent results on establishing an output-based adaptive distributed observer for an unknown leader system over jointly connected communication networks. Extensions, variants and applications of the distributed observer will also be touched.
Diffusion processes refer to a class of stochastic processes driven by Brownian motion. They have been widely used in various applications, ranging from engineering to science to finance. In this talk, I will discuss my experiences with diffusion and how this powerful tool has shaped our research programs. I will go over several research projects in the area of control, inference, and machine learning, where we have extensively utilized tools from diffusion processes. In particular, I will present our research on four topics: i) covariance control in which we aim to regulate the uncertainties of a dynamic system; ii) distribution control where we seek to herd population dynamics; iii) Monte Carlo Markov chain sampling for general inference tasks; iv) and diffusion models for generative modeling in machine learning.
Wind farms comprise a network of dynamical systems that operate within a continuous space, i.e., the turbulent atmospheric boundary layer (ABL). Viewing the turbines as actuators that adjust the flow field to collectively produce a desired overall power output, wind farms are an excellent prototype for flow control in which the actuators are well-defined and located in the region of interest. In this talk we introduce models and control strategies that adopt this viewpoint. We first demonstrate that taking into account both the challenges and opportunities arising through interactions with the ABL can enable wind farms to participate in markets that support the grid with improved efficiency. We then focus on the dynamic interconnections within the farm, which we formulate in terms of a graph with time-varying edge connectivity that accounts for changes in the incoming wind direction and turbine yaw angles. An example implementation of this simplified graph model within a combined pitch and yaw controller demonstrates the potential and limitations of yaw for augmenting pitch control in power tracking applications. In the final part of the talk, we discuss new approaches for developing similar types of control oriented models that focus on the critical flow features in other types of wall-bounded shear flows.
Bob Behnken’s journey from science and engineering student to Ph.D. candidate, to test pilot school student, and NASA astronaut culminated with the opportunity to be a part of the team that recreated a capability to transport humans to and from low earth orbit. He’ll share his experience, insight, and perspective on being a part of the NASA / SpaceX team’s endeavor to accomplish that mission in 2020 and take questions on his experience flying into space and living and working aboard the International Space Station.
In everyday driving, many traffic maneuvers such as merges, lane changes, passing through an intersection, require negotiation between independent actors/agents. The same is true for mobile robots autonomously operating in a space open to other agents (humans, robots, etc.). Negotiation is an inherently difficult concept to code into a software algorithm. It has been observed in computer simulations that some “decentralized” algorithms produce gridlocks while others never do. It has turned out that gridlocking algorithms create locally stable equilibria in the joint inter-agent space, while, for those that don’t gridlock, equilibria are unstable – hence the title of the talk.
We use Control Barrier Function (CBF) based methods to provide collision avoidance guarantees. The main advantage of CBFs is that they provide easier to solve convex programs even for nonlinear systems and inherently non-convex obstacle avoidance problems. Six different CBF-based control policies were compared for collision avoidance and liveness (fluidity of motion, absence of gridlocks) on a 5-agent, holonomic-robot system. The outcome was then correlated with stability analysis on a simpler, yet representative problem. The results are illustrated by extensive simulations including an intersection example where the (in)stability insights are used to explain otherwise difficult to understand vehicle behaviors.
Control theory and control technology have received renewed interests from applications involving service robots during the last two decades. In many scenarios, service robots are employed as networked mobile sensing platforms to collect data, sometimes in extreme environments in unprecedented ways. These applications post higher goals for autonomy that have never been achieved before, triggering new developments towards convergence of sensing, control, and communication.
Identifying mathematical models of spatial-temporal processes from collected data along trajectories of mobile sensors is a baseline goal for active perception in complex environment. The controlled motion of mobile sensors induces information dynamics in the measurements taken for the underlying spatial-temporal processes, which are typically represented by models that have two major components: the trend model and the variation model. The trend model is often described by deterministic partial differential equations, and the variation model is often described by stochastic processes. Hence, information dynamics are constrained by these representations. Based on the information dynamics and the constraints, learning algorithms can be developed to identify parameters for spatial-temporal models.
Certain designs of active sensing algorithms are inspired by animal and human behaviors. Our research designed the speed-up and speeding strategy (SUSD) that is inspired by the extraordinary capabilities of phototaxis from swarming fish. SUSD is a distributed active sensing strategy that reduces the need for information sharing among agents. Furthermore, SUSD leads to a generic derivative free optimization algorithm that has been applied to solve optimization problems where gradients are not well-defined, including mixed integer programing problems.
A perceivable trend in the control community is the rapid transition of fundamental discoveries to swarm robot applications. This is enabled by a collection of software, platforms, and testbeds shared across research groups. Such transition will generate significant impact to address the growing needs of robot swarms in applications including scientific data collection, search and rescue, aquaculture, intelligent traffic management, as well as human-robot teaming.
This work describes how machine learning may be used to develop accurate and efficient nonlinear dynamical systems models for complex natural and engineered systems. We explore the sparse identification of nonlinear dynamics (SINDy) algorithm, which identifies a minimal dynamical system model that balances model complexity with accuracy, avoiding overfitting. This approach tends to promote models that are interpretable and generalizable, capturing the essential “physics” of the system. We also discuss the importance of learning effective coordinate systems in which the dynamics may be expected to be sparse. This sparse modeling approach will be demonstrated on a range of challenging modeling problems, for example in fluid dynamics, and we will discuss how to incorporate these models into existing model-based control efforts.
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In this seminar, Dr. L’Afflitto will present two recent advances in the state-of-the-art in model reference control systems design. The first of these results will concern the design of an adaptive control system that allows the user to impose both the rate of convergence on the closed-loop system during its transient stage and constraints on both the trajectory tracking error and the control input at all times, despite parametric and modeling uncertainties. Successively, our speaker will present the first extension of the model reference adaptive control architecture to switched dynamical systems within the Carathéodory and the Filippov framework. The applicability of these theoretical formulations will be shown by the results of numerical simulations and flight tests involving multi-rotor unmanned aerial systems such as tilt-rotor quadcopters and tailsitter UAVs.
In this talk, we will present some of our recent results and ongoing work on safety-critical control synthesis under state and time (spatiotemporal) constraints and input constraints, with some applications in multi-robot systems. The proposed framework aims to eventually develop and integrate estimation, learning and control methods towards provably-correct and computationally-efficient mission synthesis for multi-agent systems in the presence of spatiotemporal constraints and uncertainty.
Time-critical applications are often performed over a time interval [0, τ), where the utilized finite-time control algorithms are expected to assure a task completion at a user-defined convergence time τ. In this talk, we will explore how to address these applications using the time transformation approach, which allows us to transform a resulting algorithm over the prescribed time interval [0, τ) to an equivalent algorithm over the stretched infinite-time interval [0,∞) for stability analysis. In addition, a procedure for designing such finite-time control algorithms is presented. We further demonstrate the approach’s efficacy with numerical examples and experimental results involving networked multiagent systems.
There are two main approaches to control gain synthesis an internal model-based distributed dynamic state feedback control law for the linear cooperative output regulation problem: (i) agent-wise local design methods, (ii) global design methods. Agent-wise local design methods to synthesize distributed control gains focus on the individual dynamics of each agent to guarantee the overall stability of the system. They are powerful tools due to their scalability. However, the agent-wise local design methods are incapable of maximizing the overall system performance through, for example, decay rate assignment. On the other hand, design methods, which are predicated on a global condition, lead to nonconvex optimization problems. We present a convex formulation of this global design problem based on a structured Lyapunov inequality. Then, the existence of solutions to the structured Lyapunov inequality is investigated. Specifically, we analytically show that the solutions exist for the systems satisfying the agent-wise local sufficient condition. Finally, we compare the proposed method with the agent-wise local design method through numerical examples in terms of conservatism, performance maximization, graph dependency, and scalability.