7,174 research outputs found
Some Applications of Polynomial Optimization in Operations Research and Real-Time Decision Making
We demonstrate applications of algebraic techniques that optimize and certify
polynomial inequalities to problems of interest in the operations research and
transportation engineering communities. Three problems are considered: (i)
wireless coverage of targeted geographical regions with guaranteed signal
quality and minimum transmission power, (ii) computing real-time certificates
of collision avoidance for a simple model of an unmanned vehicle (UV)
navigating through a cluttered environment, and (iii) designing a nonlinear
hovering controller for a quadrotor UV, which has recently been used for load
transportation. On our smaller-scale applications, we apply the sum of squares
(SOS) relaxation and solve the underlying problems with semidefinite
programming. On the larger-scale or real-time applications, we use our recently
introduced "SDSOS Optimization" techniques which result in second order cone
programs. To the best of our knowledge, this is the first study of real-time
applications of sum of squares techniques in optimization and control. No
knowledge in dynamics and control is assumed from the reader
Distributed Control of Positive Systems
A system is called positive if the set of non-negative states is left
invariant by the dynamics. Stability analysis and controller optimization are
greatly simplified for such systems. For example, linear Lyapunov functions and
storage functions can be used instead of quadratic ones. This paper shows how
such methods can be used for synthesis of distributed controllers. It also
shows that stability and performance of such control systems can be verified
with a complexity that scales linearly with the number of interconnections.
Several results regarding scalable synthesis and verfication are derived,
including a new stronger version of the Kalman-Yakubovich-Popov lemma for
positive systems. Some main results are stated for frequency domain models
using the notion of positively dominated system. The analysis is illustrated
with applications to transportation networks, vehicle formations and power
systems
Optimal Distributed Controller Synthesis for Chain Structures: Applications to Vehicle Formations
We consider optimal distributed controller synthesis for an interconnected
system subject to communication constraints, in linear quadratic settings.
Motivated by the problem of finite heavy duty vehicle platooning, we study
systems composed of interconnected subsystems over a chain graph. By
decomposing the system into orthogonal modes, the cost function can be
separated into individual components. Thereby, derivation of the optimal
controllers in state-space follows immediately. The optimal controllers are
evaluated under the practical setting of heavy duty vehicle platooning with
communication constraints. It is shown that the performance can be
significantly improved by adding a few communication links. The results show
that the proposed optimal distributed controller performs almost as well as the
centralized linear quadratic Gaussian controller and outperforms a suboptimal
controller in terms of control input. Furthermore, the control input energy can
be reduced significantly with the proposed controller compared to the
suboptimal controller, depending on the vehicle position in the platoon. Thus,
the importance of considering preceding vehicles as well as the following
vehicles in a platoon for fuel optimality is concluded
Optimal Distributed Controller Design with Communication Delays: Application to Vehicle Formations
This paper develops a controller synthesis algorithm for distributed LQG
control problems under output feedback. We consider a system consisting of
three interconnected linear subsystems with a delayed information sharing
structure. While the state-feedback case of this problem has previously been
solved, the extension to output-feedback is nontrivial, as the classical
separation principle fails. To find the optimal solution, the controller is
decomposed into two independent components. One is delayed centralized LQR, and
the other is the sum of correction terms based on additional local information.
Explicit discrete-time equations are derived whose solutions are the gains of
the optimal controller.Comment: Submitted to the 51nd IEEE Conference on Decision and Control, 201
- …