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We prove optimal regularity and a detailed analysis of the free boundary of the solutions to the thin obstacle problem for nonparametric minimal surfaces with flat obstacles.
Piecewise smooth dynamical systems make use of discontinuities to model switching between regions of smooth evolution. This introduces an ambiguity in prescribing dynamics at the discontinuity: should it be given by a limiting value on one…
Slow parameter drift is common in many systems (e.g., the amount of greenhouse gases in the terrestrial atmosphere is increasing). In such situations, the attractor on which the system trajectory lies can be destroyed, and the trajectory…
We present a novel technique to drive a nonlinear system to reach a target state under input constraints. The proposed controller consists only of piecewise constant inputs, generated from a simple linear driftless approximation to the…
Topological defects play an important role in physics of elastic media and liquid crystals. Their kinematics is determined by constraints of topological origin. An example is the glide motion of dislocations which has been extensively…
Approximate dynamic programming has been investigated and used as a method to approximately solve optimal regulation problems. However, the extension of this technique to optimal tracking problems for continuous time nonlinear systems has…
The problem of tracking an arbitrary curve in the state space is considered for underactuated driftless control-affine systems. This problem is formulated as the stabilization of a time-varying family of sets associated with a neighborhood…
The use of available disturbance predictions within a nominal model predictive control formulation is studied. The main challenge that arises is the loss of recursive feasibility and stability guarantees when a persistent disturbance is…
We consider bounded extremum seeking controls for time-varying linear systems with uncertain coefficient matrices and measurement uncertainty. Using a new change of variables, Lyapunov functions, and a comparison principle, we provide…
In this paper, we provide a novel characterization of the reachable set of discrete-time switched linear control systems and a Kalman-type criterion for controllability, assuming that the switching parameter can be used as a control…
We present a new proof of the turnpike property for nonlinear optimal control problems, when the running target is a steady control-state pair of the underlying system. Our strategy combines the construction of quasi-turnpike controls via…
This paper presents a closed-form notion of controllability and observability for systems with communication delays, actuation delays, and locality constraints. The formulation reduces to classical notions of controllability and…
A prioritized inverse kinematics (PIK) solution can be considered as a (regulation or output tracking) control law of a dynamical system with prioritized multiple outputs. We propose a method that guarantees that a joint trajectory…
In this thesis, it is presented a set of results in adiabatic dynamics (closed and open system) and transitionless quantum driving that promote some advances in our understanding on quantum control and Hamiltonian inverse engineering. In…
We consider output trajectory tracking for a class of uncertain nonlinear systems whose internal dynamics may be modelled by infinite-dimensional systems which are bounded-input, bounded-output stable. We describe under which conditions…
This paper explores the concept of topological transitivity in nonautonomous dynamical systems, which are defined as sequences of continuous maps from a compact metric space to itself. It investigates various conditions (including…
It is first shown that a smooth controllable system on a compact manifold is finite time controllable. The technique of proof is close to the one of Sussmann's orbit theorem, and no rank condition is required. This technique is also used to…
We consider continuous-state and continuous-time control problems where the admissible trajectories of the system are constrained to remain on a union of half-planes which share a common straight line. This set will be named a junction. We…
We study minimal conditions under which mild solutions of linear evolutionary control systems are continuous for arbitrary bounded input functions. This question naturally appears when working with boundary controlled, linear partial…
As a core part of autonomous driving systems, motion planning has received extensive attention from academia and industry. However, real-time trajectory planning capable of spatial-temporal joint optimization is challenged by nonholonomic…