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This paper deals with the stabilization of a coupled system composed by an infinite-dimensional system and an ODE. Moreover, the control, which appears in the dynamics of the ODE, is subject to a general class of nonlinearities. Such a…
The robust tracking and model following problem of linear discrete-time systems is investigated in this paper. An approach to design robust tracking controllers is proposed. The system is controlled to track dynamic inputs generated from a…
We study the backstepping stabilization of higher order linear and nonlinear Schr\"odinger equations on a finite interval, where the boundary feedback acts from the left Dirichlet boundary condition. The plant is stabilized with a…
We propose a fully data-driven, Koopman-based framework for statistically robust control of discrete-time nonlinear systems with linear embeddings. Establishing a connection between the Koopman operator and contraction theory, it offers…
We present a novel methodology for designing output-feedback backstepping boundary controllers for an unstable 1-D diffusion-reaction partial differential equation with spatially-varying reaction. Using "folding" transforms the parabolic…
We treat the periodic trajectory tracking problem: given a periodic trajectory of a control-affine, left-invariant driftless system in a compact and connected Lie group $G$ and an initial condition in $G$, find another trajectory of the…
High performance tracking control can only be achieved if a good model of the dynamics is available. However, such a model is often difficult to obtain from first order physics only. In this paper, we develop a data-driven control law that…
We investigate the regulator problem (tracking and disturbance rejection) for a system (plant) described by a boundary controlled anti-stable linear one-dimensional Schrodinger equation, using the backstepping approach. The output to be…
Many of the existing works on quadrotor control address the trajectory tracking problem by employing a cascade design in which the translational and rotational dynamics are stabilized by two separate controllers. The stability of the…
Here classes of moving boundary problems of Stefan-type for both an established non-linear evolution equation of cuspon theory and novel reciprocally linked solitonic equations are shown to be solvable via Painleve' II symmetry reduction.
Most passivity based trajectory tracking algorithms for mechanical systems can only stabilise reference trajectories that have constant energy. This paper overcomes this limitation by deriving a single variable Hamiltonian model for the…
We propose a learning-based trajectory tracking controller for autonomous robotic platforms whose motion can be described kinematically on $\mathrm{SE}(3)$. The controller is formulated in the dual quaternion framework and operates at the…
We consider output-feedback stabilization problems for a class of two-component linear parabolic systems with boundary actuation and measurement. The state-feedback control laws are obtained using backstepping method and require measurement…
This thesis investigates optimal trajectory tracking of nonlinear dynamical systems with affine controls. The control task is to enforce the system state to follow a prescribed desired trajectory as closely as possible. The concept of…
Our Recent advancements in stochastic processes have illuminated a paradox associated with the Einstein model of Brownian motion. The model predicts an infinite propagation speed, conflicting with the second law of thermodynamics. The…
This manuscript reports the first step towards building a robust and efficient model reduction methodology to capture transient dynamics in a transmission level electric power system. Such dynamics is normally modeled on…
Real-world environments are inherently uncertain, and to operate safely in these environments robots must be able to plan around this uncertainty. In the context of motion planning, we desire systems that can maintain an acceptable level of…
We consider a decentralized bidirectional control of a platoon of N identical vehicles moving in a straight line. The control objective is for each vehicle to maintain a constant velocity and inter-vehicular separation using only the local…
We solve the optimal control problem of a one-dimensional reflected stochastic differential equation, whose coefficients can be path dependent. The value function of this problem is characterized by a backward stochastic partial…
This paper investigates a planar tracking problem between a leader and follower agent. We propose a novel feedback speed control law, paired with a constant bearing steering strategy, to maintain an abreast formation between the two agents.…