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In order to certify performance and safety, feedback control requires precise characterization of sensor errors. In this paper, we provide guarantees on such feedback systems when sensors are characterized by solving a supervised learning…
In this paper, we describe a constrained Lagrangian and Hamiltonian formalism for the optimal control of nonholonomic mechanical systems. In particular, we aim to minimize a cost functional, given initial and final conditions where the…
We are interested in the feedback stabilization of general linear multi-dimensional first order hyperbolic systems in $\mathbb{R}^d$. Using a Lyapunov function with a suited weight function depending on the system under consideration we…
Necessary conditions for existence of normal extremals in optimal control of systems subject to nonholonomic constraints are derived as solutions of a constrained second order variational problems. In this work, a geometric interpretation…
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…
This paper generalizes recent results by the authors on noninvasive model-reference adaptive control designs for control-based continuation of periodic orbits in periodically excited linear systems with matched uncertainties to a larger…
Optical surfaces represented by second-degree polynomials (quadratic or conics) are ubiquitous in optics. We revisit the equations of the conic shapes in the context of grazing incidence optics, gathering together the curves commonly used…
We consider the problem of finite-horizon optimal control design under uncertainty for imperfectly observed discrete-time systems with convex costs and constraints. It is known that this problem can be cast as an infinite-dimensional convex…
An analysis of stick-slip behavior and convergence of trajectories in the feedback-controlled motion systems with discontinuous Coulomb friction is provided. A closed-form parameter-dependent stiction region, around an invariant equilibrium…
For systems in canonical form with nonvanishing uncertainties/disturbances, this work presents an approach to full state regulation within prescribed time irrespective of initial conditions. By introducing the smooth hyperbolic-tangent-like…
We present a topological proof of the existence of invariant manifolds for maps with normally hyperbolic-like properties. The proof is conducted in the phase space of the system. In our approach we do not require that the map is a…
Boundary feedback control design is studied for 1D hyperbolic systems with an in-domain disturbance and a boundary feedback controller under the effect of actuator saturation. Nonlinear semigroup theory is used to prove well-posedness of…
We investigate necessary and sufficient conditions under which a general nonlinear affine control system with outputs can be written as a gradient control system corresponding to some pseudo-Riemannian metric defined on the state space. The…
This paper is devoted to a study of linear, differential and topological classifications for linear controlled systems governed by ordinary differential equations. The necessary and sufficient conditions for the linear and topological…
We derive an optimal control formulation for a nonholonomic mechanical system using the nonholonomic constraint itself as the control. We focus on Suslov's problem, which is defined as the motion of a rigid body with a vanishing projection…
Infinite-dimensional linear conic formulations are described for nonlinear optimal control problems. The primal linear problem consists of finding occupation measures supported on optimal relaxed controlled trajectories, whereas the dual…
We study a one-parameter family of time-reversible Hamiltonian vector fields in $\mathbb{R}^4$, which has received great attention in the literature. On the one hand, it is due to the role it plays in the context of certain applications in…
This paper addresses the problem of robust and optimal control for the class of nonlinear quadratic systems subject to norm-bounded parametric uncertainties and disturbances, and in presence of some amplitude constraints on the control…
Tangent points, especial dynamics existing only in piecewise-smooth systems, usually have dynamical properties like equilibria of smooth systems. Loops connecting tangent points own partly properties of limit cycles and homoclinic loops of…
In this paper, motivated by the study of optimal control problems for infinite dimensional systems with endpoint state constraints, we introduce the notion of finite codimensional (exact/approximate) controllability. Some equivalent…