The Dynamic Systems and Control group at UC San Diego integrates, at a fundamental level, system design, modeling, and control disciplines to obtain improved performance of the dynamic response of engineering systems using feedback. As such, the areas of research of the Dynamic Systems and Control group is a joint activity in the topics of systems integration, dynamic system modeling, feedback control design, and the fundamentals of systems theory as applied to linear and nonlinear dynamic systems, mechatronics, structural control, aerospace, and fluid-mechanical systems.
Spatial perception —the robot’s ability to sense and understand the surrounding environment— is a key enabler for robot navigation, manipulation, and human-robot interaction. Recent advances in perception algorithms and systems have enabled robots to create large-scale geometric maps of unknown environments and detect objects of interest.
Computing the Lyapunov function of a system plays a crucial role in optimal feedback control, for example when the policy iteration is used. This talk will focus on the Lyapunov function of a nonlinear autonomous finite-dimensional dynamical system which will be rewritten as an infinite-dimensional linear system using the Koopman operator. Since this infinite-dimensional system has the structure of a weak-* continuous semigroup in a specially weighted Lp-space one can establish a connection between the solution of an operator Lyapunov equation and the desired Lyapunov function.
The widespread availability of low-cost, low-power embedded computation has made it possible to apply online optimization to solve nonlinear control problems with hard state and input constraints, leading to the increasing popularity of Model Predictive Control (MPC) in numerous industrial applications. Online optimization has also become popular in solving estimation problems by taking advantage of known constraints on the state, measurement noise, and disturbances.
The past decade has witnessed success of learning-based control in a broad spectrum of applications, such as game play, robotics, and autonomous driving. As a result, the application of learning-based control in power systems has attracted surging attention recently. Despite the promise, one of the biggest challenges for its deployment in power system control is the lack of stability and performance guarantees. Since power systems are critical infrastructure, failure to maintain stability can lead to catastrophic consequences.
The rapidly increasing demand for computer simulations of complex physical, chemical, and other processes places a significant burden on the shoulders of computational scientists and engineers. Despite the remarkable rise of available computer resources and computing technologies, the need for model order reduction to cope with these problems is an ever-present reality. Reduced-order models are imperative in making computationally tractable outer-loop applications that require simulating systems for many scenarios with different parameters and under varying inputs.
We present some recent results on the interplay between control and Machine Learning.
We adopt the perspective of the simultaneous or ensemble control of systems of Residual Neural Networks (ResNets) and present a genuinely nonlinear and constructive method, allowing to show that such an ambitious goal can be achieved, estimating the complexity of the control strategies.
This property is rarely fulfilled by the classical dynamical systems in Mechanics and the very nonlinear nature of the activation function governing the ResNet dynamics plays a determinant role.
The question of what velocity fields effectively enhance or prevent transport and mixing, or steer a scalar field to the desired distribution, is of great interest and fundamental importance to the fluid mechanics community. In this talk, we mainly discuss the problem of optimal mixing of an inhomogeneous distribution of a scalar field via active control of the flow velocity, governed by the Stokes or the Navier-Stokes equations.
The emerging use of purely data-driven mechanisms to control and optimize in real time complex dynamical systems has led to the awareness of the pitfalls of model-free decision making without stability and robustness guarantees. This limitation can be further exacerbated by the interactions that emerge between continuous-time and discrete-time dynamics in many engineering and cyber-physical systems, which difficult the development of rigorous stability, convergence, and robustness certificates via control theoretic tools.
Most of the animals that move with legs in the world do so with six or more legs, yet humans have focused primarily on bipeds and quadrupeds in designing legged robots.
Automated reasoning develops combinatorial search and optimization algorithms that are crucial for the reliable engineering of digital systems, from hardware to software. Despite the clear NP-hardness of these problems, significant progress has been made in the past decades for solving large instances of practical relevance. There is a seemingly-wide gap between the discrete/combinatorial setting of automated reasoning and the continuous/analytic one for dynamics and control.
