Related papers: Learning deep Koopman operators with convex stabil…
Trajectory optimization is a widely used tool in the design and control of dynamical systems. Typically, not only nonlinear dynamics, but also couplings of the initial and final condition through implicit boundary constraints render the…
Finding an embedding space for a linear approximation of a nonlinear dynamical system enables efficient system identification and control synthesis. The Koopman operator theory lays the foundation for identifying the nonlinear-to-linear…
Over the past decades, the Koopman operator has been widely applied in data-driven control, yet its theoretical foundations remain underexplored. This paper establishes a unified framework to address the robust stabilization problem in…
This work addresses the finite-horizon robust covariance control problem for discrete-time, partially observable, linear system affected by random zero mean noise and deterministic but unknown disturbances restricted to lie in what is…
In this work, we consider the controllability of a discrete-time linear dynamical system with sparse control inputs. Sparsity constraints on the input arises naturally in networked systems, where activating each input variable adds to the…
This paper presents a novel stochastic gradient descent algorithm for constrained optimization. The proposed algorithm randomly samples constraints and components of the finite sum objective function and relies on a relaxed logarithmic…
Nonlinearity in dynamics has long been a major challenge in robotics, often causing significant performance degradation in existing control algorithms. For example, the navigation of bipedal robots can exhibit nonlinear behaviors even under…
High order momentum-based parameter update algorithms have seen widespread applications in training machine learning models. Recently, connections with variational approaches have led to the derivation of new learning algorithms with…
Dynamical systems are ubiquitous and are often modeled using a non-linear system of governing equations. Numerical solution procedures for many dynamical systems have existed for several decades, but can be slow due to high-dimensional…
The Koopman operator framework provides a perspective that non-linear dynamics can be described through the lens of linear operators acting on function spaces. As the framework naturally yields linear embedding models, there have been…
Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…
This paper develops a parametric Koopman operator framework for Stochastic Model Predictive Control (SMPC), where the Koopman operator is parametrized by Polynomial Chaos Expansions (PCEs). The model is learned from data using the Extended…
This paper presents a unified and scalable framework for predictive and safe autonomous navigation in dynamic transportation environments by integrating model predictive control (MPC) with distributed Koopman operator learning.…
We prove that stochastic gradient descent efficiently converges to the global optimizer of the maximum likelihood objective of an unknown linear time-invariant dynamical system from a sequence of noisy observations generated by the system.…
Koopman operator theory has served as the basis to extract dynamics for nonlinear system modeling and control across settings, including non-holonomic mobile robot control. There is a growing interest in research to derive robustness…
We present novel sufficient conditions for the global stability of equilibria in the case of nonlinear dynamics with analytic vector fields. These conditions provide stability criteria that are directly expressed in terms of the Taylor…
In this paper we propose a novel approach to compute the Koopman operator from sparse time series data. In recent years there has been considerable interests in operator theoretic methods for data-driven analysis of dynamical systems.…
Developing agents that can perform complex control tasks from high-dimensional observations is a core ability of autonomous agents that requires underlying robust task control policies and adapting the underlying visual representations to…
Achieving rapid and time-deterministic stabilization for complex systems characterized by strong nonlinearities and parametric uncertainties presents a significant challenge. Traditional model-based control relies on precise system models,…
We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising…