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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.
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.
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.
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.
Systems with dynamics evolving in distinct slow and fast timescales include aircraft (Khalil & Chen, 1990), robotic manipulators, (Tavasoli, Eghtesad, & Jafarian, 2009), electrical power systems (Sauer, 2011), chemical reactions (Mélykúti, Hespanha, & Khammash, 2014), production planning in manufacturing (Soner, 1993), and so on. The Geometric Singular Perturbation theory (Fenichel, 1979) is a powerful control law development tool for multiple-timescale systems because it provides physical insight into the evolution of the states in more than one timescale. The behaviour of the full-order system can be approximated by the slow subsystem, provided that the fast states can be stabilised on an equilibrium manifold. The fast subsystem describes how the fast states evolve from their initial conditions to their equilibrium trajectory or the manifold. This presentation develops two nonlinear, multiple-time-scale, output feedback tracking controllers for a class of nonlinear, nonstandard systems with slow and fast states, slow and fast actuators, and model uncertainties. The class of systems is motivated by aircraft with uncertain inertias, control derivatives, engine time-constant, and without direct measurement of angle-of-attack and sideslip angle. One controller achieves the control objective of slow state tracking, while the other does simultaneous slow and fast state tracking. Each controller is synthesized using time-scale separation, lower-order reduced subsystems, and estimates of unknown parameters and unmeasured states. The estimates are updated dynamically, using an online parameter estimator and a nonlinear observer. The update laws are so chosen that errors remain ultimately bounded for the full-order system. The controllers are simulated on a six-degree-of-freedom, high-performance aircraft model commanded to perform a demanding, combined longitudinal and lateral/directional maneuver. Even though two important aerodynamic angles are not measured, tracking is adequate and as good as a previously developed full-state feedback controller handling similar parametric uncertainties. Additionally, even though the two controllers in theory achieve two different control objectives, it is possible to choose either one of them for the same maneuver. Of the two new output feedback controllers, the slow state tracker accomplishes the maneuver with less control effort, while the simultaneous slow and fast state tracker does so with a smaller number of gains to tune.