Related papers: Control Contraction Metrics on Finsler Manifolds
Optimal control for safety-critical systems is often dependent on the conservativeness of constraints. Control Barrier Functions (CBFs) serve as a medium to represent such constraints, but constructing a minimally conservative CBF is a…
Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…
Very high dimensional nonlinear systems arise in many engineering problems due to semi-discretization of the governing partial differential equations, e.g. through finite element methods. The complexity of these systems present…
In this paper we address the problem of tracking control of nonlinear systems via contraction analysis. The necessary conditions of the systems which can achieve universal asymptotic tracking are studied under several different cases. We…
We consider a class of structured fractional minimization problems, in which the numerator part of the objective is the sum of a differentiable convex function and a convex non-smooth function, while the denominator part is a convex or…
Tendon-Driven Continuum Robots (TDCRs) have the potential to be used in minimally invasive surgery and industrial inspection, where the robot must enter narrow and confined spaces. We propose a Model Predictive Control (MPC) approach to…
In this paper, we present a geometric framework for the reachability analysis of attitude control systems. We model the attitude dynamics on the product manifold $\mathrm{SO}(3) \times \mathbb{R}^3$ and introduce a novel parametrized family…
Lyapunov stability theory is the bedrock of direct adaptive control. Fundamentally, Lyapunov stability requires constructing a distance-like function which must decrease with time to ensure stability. Feedback linearization, backstepping,…
Inertial motion capture is a promising approach for capturing motion outside the laboratory. However, as one major drawback, most of the current methods require different quantities to be calibrated or computed offline as part of the setup…
The nonlinear equations describing all the nonsingular pencils of metrics of constant Riemannian curvature are derived and the integrability of these nonlinear equations by the method of inverse scattering problem is proved. It is proved…
This paper explores the role of symmetries and reduction in nonlinear control and optimal control systems. The focus of the paper is to give a geometric framework of symmetry reduction of optimal control systems as well as to show how to…
In this paper we study the sub-Finsler geometry as a time-optimal control problem. In particular, we consider non-smooth and non-strictly convex sub-Finsler structures associated with the Heisenberg, Grushin, and Martinet distributions.…
We propose a convex controller synthesis framework for a large class of constrained linear systems, including those described by (deterministic and stochastic) partial differential equations and integral equations, commonly used in fluid…
This paper proposes a novel real-time affordable solution to the trajectory tracking control problem for self-driving cars subject to longitudinal and steering angular velocity constraints. To this end, we develop a dual-mode Model…
We investigate the Coherence--Curvature Model (CCM), a dynamical ensemble of connected graphs governed by a Hamiltonian that couples algebraic connectivity, Ollivier-Ricci curvature, and an edge-density penalty. Using connected simulated…
This paper presents a general framework for the design of linear controllers for linear systems subject to time-domain constraints. The design framework exploits sums-of-squares techniques to incorporate the time-domain constraints on…
In dissipative ordinary differential equation systems different time scales cause anisotropic phase volume contraction along solution trajectories. Model reduction methods exploit this for simplifying chemical kinetics via a time scale…
Computing geodesics for Riemannian manifolds is a difficult task that often relies on numerical approximations. However, these approximations tend to be either numerically unstable, have slow convergence, or scale poorly with manifold…
Model Predictive Control (MPC) is a widely known control method that has proved to be particularly effective in multivariable and constrained control. Closed-loop stability and recursive feasibility can be guaranteed by employing accurate…
This paper presents a novel Nonlinear Model Predictive Control (NMPC) scheme for underwater robotic vehicles operating in a constrained workspace including static obstacles. The purpose of the controller is to guide the vehicle towards…