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We compute probabilistic controlled invariant sets for nonlinear systems using Gaussian process state space models, which are data-driven models that account for unmodeled and unknown nonlinear dynamics. We propose a semidefinite…

Systems and Control · Electrical Eng. & Systems 2026-04-21 Paul Griffioen , Bingzhuo Zhong , Murat Arcak , Majid Zamani , Marco Caccamo

In this paper, we consider the problem of invariant set computation for black-box switched linear systems using merely a finite set of observations of system trajectories. In particular, this paper focuses on polyhedral invariant sets. We…

Systems and Control · Electrical Eng. & Systems 2020-12-18 Zheming Wang , Raphaël M. Jungers

Despite the celebrated success of stochastic control approaches for uncertain systems, such approaches are limited in the ability to handle non-Gaussian uncertainties. This work presents an adaptive robust control for linear uncertain…

Optimization and Control · Mathematics 2026-01-13 Xuehui Ma , Shiliang Zhang , Zhiyong Sun , Xiaohui Zhang , Sabita Maharjan

Discrete control systems, as considered here, refer to the control theory of discrete-time Lagrangian or Hamiltonian systems. These discrete-time models are based on a discrete variational principle, and are part of the broader field of…

Optimization and Control · Mathematics 2007-05-29 Taeyoung Lee , Melvin Leok , N. Harris McClamroch

In this paper, we consider a geometric formalism for optimal control of underactuated mechanical systems. Our techniques are an adaptation of the classical Skinner and Rusk approach for the case of Lagrangian dynamics with higher-order…

Mathematical Physics · Physics 2015-05-14 L. Colombo , D. Martin de Diego , M. Zuccalli

Recent results in control systems and numerical integration literature utilize invariant set theory to lift dynamical systems evolving on nonlinear manifolds to those evolving on vector spaces. We leverage this technique to propose an…

Optimization and Control · Mathematics 2022-08-09 Siddharth H. Nair

A geometric setup for control theory is presented. The argument is developed through the study of the extremals of action functionals defined on piecewise differentiable curves, in the presence of differentiable non-holonomic constraints.…

Optimization and Control · Mathematics 2015-05-18 Enrico Massa , Danilo Bruno , Enrico Pagani

The objective of this paper is to derive the essential invariance and contraction properties for the geometric periodic systems, which can be formulated as a category of differential inclusions, and primarily rendered in the phase…

Systems and Control · Electrical Eng. & Systems 2021-04-30 Chen Qian , Yongchun Fang

We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…

Differential Geometry · Mathematics 2018-05-09 María Barbero-Liñán , Marta Farré Puiggalí , Sebastián Ferraro , David Martín de Diego

This note proposes a general control approach, called vector-field guided constraint-following control, to solve the dynamics control problem of geometric path-following for a class of uncertain mechanical systems. More specifically, it…

Systems and Control · Electrical Eng. & Systems 2026-03-17 Hui Yin , Xiang Li , Yifan Liu , Weijia Yao

We develop aspects of geometric control theory on Lie groups G which may be infinite dimensional, and on smooth G-manifolds M modelled on locally convex spaces. As a tool, we discuss existence and uniqueness questions for differential…

Functional Analysis · Mathematics 2022-08-25 Helge Glockner , Joachim Hilgert

We consider the geometric numerical integration of Hamiltonian systems subject to both equality and "hard" inequality constraints. As in the standard geometric integration setting, we target long-term structure preservation. We…

Numerical Analysis · Mathematics 2011-06-02 Danny M. Kaufman , Dinesh K. Pai

We consider controllable linear discrete-time systems with bounded perturbations and present two methods to compute robust controlled invariant sets. The first method tolerates an arbitrarily small constraint violation to compute an…

Optimization and Control · Mathematics 2018-01-03 Matthias Rungger , Paulo Tabuada

Symmetries of nonlinear control systems in state representation are considered. To this end, a geometric approach to ordinary differential equations is advocated. Invariant feedback laws for systems with Lie symmetries, i.e. feedback laws…

Optimization and Control · Mathematics 2012-06-22 Carsten Collon , Joachim Rudolph

In this paper we present a direct adaptive control method for a class of uncertain nonlinear systems with a time-varying structure. We view the nonlinear systems as composed of a finite number of ``pieces,'' which are interpolated by…

Optimization and Control · Mathematics 2007-05-23 R. Ordonez , K. M. Passino

In recent years, advanced model-based and data-driven control methods are unlocking the potential of complex robotics systems, and we can expect this trend to continue at an exponential rate in the near future. However, ensuring safety with…

Robotics · Computer Science 2024-08-29 Gianni Lunardi , Asia La Rocca , Matteo Saveriano , Andrea Del Prete

In this article, we survey the primary research on polyhedral computing methods for constrained linear control systems. Our focus is on the modeling power of convex optimization, featured to design set-based robust and optimal controllers.…

Optimization and Control · Mathematics 2024-12-18 Boris Houska , Matthias A. Müller , Mario E. Villanueva

We consider the problem of computing the maximal invariant set of discrete-time linear systems subject to a class of non-convex constraints that admit quadratic relaxations. These non-convex constraints include semialgebraic sets and other…

Systems and Control · Electrical Eng. & Systems 2020-11-30 Zheming Wang , Raphaël M. Jungers , Chong-Jin Ong

We introduce the concept of a control contraction metric, extending contraction analysis to constructive nonlinear control design. We derive sufficient conditions for exponential stabilizability of all trajectories of a nonlinear control…

Systems and Control · Computer Science 2017-02-09 Ian R. Manchester , Jean-Jacques E. Slotine

We introduce a novel algorithm for controlling linear time invariant systems in a tracking problem. The controller is based on a Gaussian Process (GP) whose realizations satisfy a system of linear ordinary differential equations with…

Optimization and Control · Mathematics 2025-08-01 Jörn Tebbe , Andreas Besginow , Markus Lange-Hegermann