Research Interests

My current research effort is mainly focused on the Analysis, Stability, and Control of:

Macroscopic traffic flow models Macroscopic traffic flow models describe the traffic flow as a liquid that is characterized by macroscopic quantities such as flow, density, and  means speed of vehicles. Since connected and automated vehicles use sensors and can communicate their presence and state to other vehicles, thy can "nudge" following vehicles and increase their speed. In [C5], [J5], we focused on proving the existence and uniqueness of classical solutions for a non-local conservation law on a ring-road with possible nudging (or ‘look behind’) terms. More specifically, we considered traffic models described by partial differential equations of the form

The first-order traffic model discussed above presents many limitations such as unrealistic vehicle accelerations or decelerations and predicts that the exit flow from a congested area is equal to the capacity flow. This does not apply to real traffic networks (capacity drop). These limitations motivate us to study the effects of non-local terms and in particular the effects of nudging for second-order models. Thus, in the papers [J7] and [J9] the following systems of partial differential equations were proposed that describe the macroscopic flow of vehicle traffic  

and

Finally, in paper [J7] we proved that for model (2) without viscosity terms, if the density is sufficiently small, then the macroscopic model has a solution that exponentially approximates the equilibrium velocity (in the sup norm) while the density converges exponentially to a traveling wave.

Microscopic models: Contrary to the macroscopic models, the microscopic models describe the behavior of each single vehicle in the traffic stream. In [S1], [C7] we designed an Adaptive Cruise Control (ACC) system for platoons of vehicles that allows each vehicle to maintain a constant speed and a constant space from the preceding vehicle. A nonlinear controller was designed by leveraging Lyapunov functions and Barrier functions and guarantees that the vehicles will not collide with each other, the vehicles will respect the road speed limits, the accelerations will be bounded, and all the vehicle speeds and inter-vehicles distances will converge to a desired value. Next, in [S2, C8] we designed a novel model for the two-dimensional movement of autonomous vehicles on lane-free roads. The bicycle kinematic model was used to model the dynamics of the vehicles, and it was proved by using Lyapunov and potential functions that with the proposed controller the vehicles do not collide with each other or with the boundary of the road, their speeds remains within the road speed limits and converge to a desired longitudinal set-point. 

Event-triggered control and sampled-data feedback stabilization of nonlinear systems. The constant evolution of digital technologies is based on the increasing usage of digital control systems. In this context, a control system is characterized by the digital computation of a control law from sampled measurements. In this subject, I focused in the sampled-data feedback stabilization of nonlinear systems. For a given increasing sequence of times, the control law is updated at each of those time instants and is fed into the system as a constant input until the next time instant when it is updated again.  In  [1, C1], we studied the semi-global stabilization of nonlinear systems by sampled-data feedback using certain asymptotic controllability conditions. The main results was the derivation of Lie-algebraic conditions for the semi-global asymptotic stabilization with sampled-data feedback for affine in the control nonlinear systems. Those conditions generalize the well-known Artestein-Sontag condition for asymptotic stabilization with almost smooth feedback. In [4, C2, C3, C4], I focused in the stabilization by sampled-data feedback by using event-triggered and self-triggered mechanisms. Event-triggered techniques use a mechanism to monitor the real-time state of the system and generate the sampling times only when necessary resulting in non-periodic controller updates. This methodology was applied in cascade connected systems as well as in interconnected systems in [C2, C4] with immediate applications in multi-agent systems, networked control systems and vehicle platoons. Finally, in [4, C3] we studied the self-triggered stabilization with time-delays where the next controller update time is generated based on the last measurement of the system’s state and does not require continuous monitoring of the system's state. 


Observer design and state estimation for nonlinear systems. Observer design plays a central role in control applications, since in many cases, some of the system’s states may not be available for measurement. In this subject, I focused on the solvability of the observer design problem for a class of time-varying triangular control systems. For the case of triangular control systems studied in [2], it was shown that under certain weak observability assumptions, the observer design problem is solvable by means of a non-causal time-varying Luenberger-type observer. In [3], we studied triangular control systems that may be unobservable in unknown time-intervals of arbitrary length. It was shown that the observer design problem is solvable by means of a switching sequence of observers with time-delay. Finally, in [C6], we studied that state estimation problem for a class of linear systems with quadratic output measurements. For this particular class of systems, we employed an immersion type technique to extend the system's state by a finite number of components which allows the state estimation to be achieved by means of a linear Kalman-type observer. Finally, by using single range measurements, we studied the position and speed estimation of a vehicle moving in the n-dimensional Euclidean space. The considered class of systems has immediate applications in localization and navigation of autonomous vehicles by using range measurements from a single source. Currently, this methodology has been generalized for general linear and bilinear systems with applications in tracking of systems described by chain of integrators, [U1]. Future work will focus on the problems of navigation and localization of multi-robot system by using single range measurements as well as the distributed state estimation with range measurements from multiple sources.