Dynamic Systems & Controls

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.

The ability of machine learning techniques to leverage data and process rich sensory inputs (e.g., vision) makes them highly appealing for use in robotic systems. However, the inclusion of learning-based components in the control loop poses an important challenge: how can we guarantee the safety of such systems? For safety, we present a controller synthesis technique based on the computation of reachable sets, using optimal control and game theory.

Automatic control systems are increasingly deployed in unstructured environments featuring novel and dynamically changing conditions. Ensuring successful operation in such scenarios requires revisiting the core problems of stabilization and tracking to impose strict safety constraints.

This talk will cover some of our recent work that enables provable safe control  of robots when there are dynamic uncertainties and constraints. The safe control is designed under the framework of energy-function-based methods, where a scalar energy function (also known as barrier function, safety index, etc) needs to be synthesized first such that safe states are with low energy, then the safety controller will be synthesized to dissipate the system energy.

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 ex

Koopman operator linearization approximates a nonlinear system of differential equations as a higher-dimensional linear system. This is attractive since many types of analysis, including formal verification using reachability analysis, are significantly more tractable for linear systems.

We present an extension of the linear-quadratic regulator problem to polynomial systems.  The resulting feedback control can be written as a solution to the Hamilton-Jacobi-Bellman equations.  The Kronecker product structure of the problem found in polynomial systems leads to an elegant formulation of Al'Brekht's approximation algorithm.  The sequence of large linear systems that arise are solved using an nWay version of the Bartels-Stewart algorithm for modest system dimension with low single digit polynomial degrees for the control law.  We demonstrate this algorithm on a few test problem

Wildfires can pose threats to life, property and critical infrastructure, but wildland fire is an unavoidable part of many ecosystems.  Improving our ability to cope with wildfires and avoiding catastrophic fire scenarios requires better understand how they interact with their surrounding environment.