3 research outputs found
Optimal multiplexing of sparse controllers for linear systems
This article treats three problems of sparse and optimal multiplexing a
finite ensemble of linear control systems. Given an ensemble of linear control
systems, multiplexing of the controllers consists of an algorithm that selects,
at each time , only one from the ensemble of linear systems is actively
controlled whereas the other systems evolve in open-loop. The first problem
treated here is a ballistic reachability problem where the control signals are
required to be maximally sparse and multiplexed, the second concerns sparse and
optimally multiplexed linear quadratic control, and the third is a sparse and
optimally multiplexed Mayer problem. Numerical experiments are provided to
demonstrate the efficacy of the techniques developed here.Comment: 5 figure
On the Design of Structured Stabilizers for LTI Systems
Designing a static state-feedback controller subject to structural constraint
achieving asymptotic stability is a relevant problem with many applications,
including network decentralized control, coordinated control, and sparse
feedback design. Leveraging on the Projection Lemma, this work presents a new
solution to a class of state-feedback control problems, in which the controller
is constrained to belong to a given linear space. We show through extensive
discussion and numerical examples that our approach leads to several advantages
with respect to existing methods: first, it is computationally efficient;
second, it is less conservative than previous methods, since it relaxes the
requirement of restricting the Lyapunov matrix to a block-diagonal form.Comment: V1 fixes a few minor typos in the published version. V2 includes a
clarification and fixes some minor typos in the proof of Theorem
Feedback control of transitional shear flows: Sensor selection for performance recovery
The choice and placement of sensors and actuators is an essential factor
determining the performance that can be realized using feedback control. This
determination is especially important, but difficult, in the context of
controlling transitional flows. The highly non-normal nature of the linearized
Navier-Stokes equations makes the flow sensitive to small perturbations, with
potentially drastic performance consequences on closed-loop flow control
performance. Full-information controllers, such as the linear quadratic
regulator (LQR), have demonstrated some success in reducing transient energy
growth and suppressing transition; however, sensor-based output feedback
controllers with comparable performance have been difficult to realize. In this
study, we propose two methods for sensor selection that enable sensor-based
output feedback controllers to recover full-information control performance:
one based on a sparse controller synthesis approach, and one based on a
balanced truncation procedure for model reduction. Both approaches are
investigated within linear and nonlinear simulations of a sub-critical channel
flow with blowing and suction actuation at the walls. We find that sensor
configurations identified by both approaches allow sensor-based static output
feedback LQR controllers to recover full-information LQR control performance,
both in reducing transient energy growth and suppressing transition. Further,
our results indicate that both the sensor selection methods and the resulting
controllers exhibit robustness to Reynolds number variations