35 research outputs found
Approximation of Continuous-Time Infinite-Horizon Optimal Control Problems Arising in Model Predictive Control - Supplementary Notes
These notes present preliminary results regarding two different
approximations of linear infinite-horizon optimal control problems arising in
model predictive control. Input and state trajectories are parametrized with
basis functions and a finite dimensional representation of the dynamics is
obtained via a Galerkin approach. It is shown that the two approximations
provide lower, respectively upper bounds on the optimal cost of the underlying
infinite dimensional optimal control problem. These bounds get tighter as the
number of basis functions is increased. In addition, conditions guaranteeing
convergence to the cost of the underlying problem are provided.Comment: Supplementary notes, 10 page
On the Approximation of Constrained Linear Quadratic Regulator Problems and their Application to Model Predictive Control - Supplementary Notes
By parametrizing input and state trajectories with basis functions different
approximations to the constrained linear quadratic regulator problem are
obtained. These notes present and discuss technical results that are intended
to supplement a corresponding journal article. The results can be applied in a
model predictive control context.Comment: 19 pages, 1 figur
Distributed Event-Based State Estimation for Networked Systems: An LMI-Approach
In this work, a dynamic system is controlled by multiple sensor-actuator
agents, each of them commanding and observing parts of the system's input and
output. The different agents sporadically exchange data with each other via a
common bus network according to local event-triggering protocols. From these
data, each agent estimates the complete dynamic state of the system and uses
its estimate for feedback control. We propose a synthesis procedure for
designing the agents' state estimators and the event triggering thresholds. The
resulting distributed and event-based control system is guaranteed to be stable
and to satisfy a predefined estimation performance criterion. The approach is
applied to the control of a vehicle platoon, where the method's trade-off
between performance and communication, and the scalability in the number of
agents is demonstrated.Comment: This is an extended version of an article to appear in the IEEE
Transactions on Automatic Control (additional parts in the Appendix
Online Learning under Adversarial Nonlinear Constraints
In many applications, learning systems are required to process continuous
non-stationary data streams. We study this problem in an online learning
framework and propose an algorithm that can deal with adversarial time-varying
and nonlinear constraints. As we show in our work, the algorithm called
Constraint Violation Velocity Projection (CVV-Pro) achieves regret
and converges to the feasible set at a rate of , despite the fact
that the feasible set is slowly time-varying and a priori unknown to the
learner. CVV-Pro only relies on local sparse linear approximations of the
feasible set and therefore avoids optimizing over the entire set at each
iteration, which is in sharp contrast to projected gradients or Frank-Wolfe
methods. We also empirically evaluate our algorithm on two-player games, where
the players are subjected to a shared constraint
Optimal transport with constraints: from mirror descent to classical mechanics
Finding optimal trajectories for multiple traffic demands in a congested
network is a challenging task. Optimal transport theory is a principled
approach that has been used successfully to study various transportation
problems. Its usage is limited by the lack of principled and flexible ways to
incorporate realistic constraints. We propose a principled physics-based
approach to impose constraints flexibly in such optimal transport problems.
Constraints are included in mirror descent dynamics using the principle of
D'Alembert-Lagrange from classical mechanics. This leads to a sparse, local and
linear approximation of the feasible set leading in many cases to closed-form
updates.Comment: 14 pages, 8 figure