1,219 research outputs found
Localized LQR Optimal Control
This paper introduces a receding horizon like control scheme for localizable
distributed systems, in which the effect of each local disturbance is limited
spatially and temporally. We characterize such systems by a set of linear
equality constraints, and show that the resulting feasibility test can be
solved in a localized and distributed way. We also show that the solution of
the local feasibility tests can be used to synthesize a receding horizon like
controller that achieves the desired closed loop response in a localized manner
as well. Finally, we formulate the Localized LQR (LLQR) optimal control problem
and derive an analytic solution for the optimal controller. Through a numerical
example, we show that the LLQR optimal controller, with its constraints on
locality, settling time, and communication delay, can achieve similar
performance as an unconstrained H2 optimal controller, but can be designed and
implemented in a localized and distributed way.Comment: Extended version for 2014 CDC submissio
System Level Synthesis
This article surveys the System Level Synthesis framework, which presents a
novel perspective on constrained robust and optimal controller synthesis for
linear systems. We show how SLS shifts the controller synthesis task from the
design of a controller to the design of the entire closed loop system, and
highlight the benefits of this approach in terms of scalability and
transparency. We emphasize two particular applications of SLS, namely
large-scale distributed optimal control and robust control. In the case of
distributed control, we show how SLS allows for localized controllers to be
computed, extending robust and optimal control methods to large-scale systems
under practical and realistic assumptions. In the case of robust control, we
show how SLS allows for novel design methodologies that, for the first time,
quantify the degradation in performance of a robust controller due to model
uncertainty -- such transparency is key in allowing robust control methods to
interact, in a principled way, with modern techniques from machine learning and
statistical inference. Throughout, we emphasize practical and efficient
computational solutions, and demonstrate our methods on easy to understand case
studies.Comment: To appear in Annual Reviews in Contro
A Sub-optimal Algorithm to Synthesize Control Laws for a Network of Dynamic Agents
We study the synthesis problem of an LQR controller when the matrix describing the control law is constrained to lie in a particular vector space. Our motivation is the use of such control laws to stabilize networks of autonomous agents in a decentralized fashion; with the information flow being dictated by the constraints of a pre-specified topology. In this paper, we consider the finite-horizon version of the problem and provide both a computationally intensive optimal solution and a sub-optimal solution that is computationally more tractable. Then we apply the technique to the decentralized vehicle formation control problem and show that the loss in performance due to the use of the sub-optimal solution is not huge; however the topology can have a large effect on performance
Optimal LQG Control Across a Packet-Dropping Link
We examine optimal Linear Quadratic Gaussian control for a system in which communication between the sensor (output of the plant) and the controller occurs across a packet-dropping link. We extend the familiar LQG separation principle to this problem that allows us to solve this problem using a standard LQR state-feedback design, along with an optimal algorithm for propagating and using the information across the unreliable link. We present one such optimal algorithm, which consists of a Kalman Filter at the sensor side of the link, and a switched linear filter at the controller side. Our design does not assume any statistical model of the packet drop events, and is thus optimal for an arbitrary packet drop pattern. Further, the solution is appealing from a practical point of view because it can be implemented as a small modification of an existing LQG control design
Random Finite Set Theory and Optimal Control of Large Collaborative Swarms
Controlling large swarms of robotic agents has many challenges including, but
not limited to, computational complexity due to the number of agents,
uncertainty in the functionality of each agent in the swarm, and uncertainty in
the swarm's configuration. This work generalizes the swarm state using Random
Finite Set (RFS) theory and solves the control problem using Model Predictive
Control (MPC) to overcome the aforementioned challenges. Computationally
efficient solutions are obtained via the Iterative Linear Quadratic Regulator
(ILQR). Information divergence is used to define the distance between the swarm
RFS and the desired swarm configuration. Then, a stochastic optimal control
problem is formulated using a modified L2^2 distance. Simulation results using
MPC and ILQR show that swarm intensities converge to a target destination, and
the RFS control formulation can vary in the number of target destinations. ILQR
also provides a more computationally efficient solution to the RFS swarm
problem when compared to the MPC solution. Lastly, the RFS control solution is
applied to a spacecraft relative motion problem showing the viability for this
real-world scenario.Comment: arXiv admin note: text overlap with arXiv:1801.0731
Resource-aware IoT Control: Saving Communication through Predictive Triggering
The Internet of Things (IoT) interconnects multiple physical devices in
large-scale networks. When the 'things' coordinate decisions and act
collectively on shared information, feedback is introduced between them.
Multiple feedback loops are thus closed over a shared, general-purpose network.
Traditional feedback control is unsuitable for design of IoT control because it
relies on high-rate periodic communication and is ignorant of the shared
network resource. Therefore, recent event-based estimation methods are applied
herein for resource-aware IoT control allowing agents to decide online whether
communication with other agents is needed, or not. While this can reduce
network traffic significantly, a severe limitation of typical event-based
approaches is the need for instantaneous triggering decisions that leave no
time to reallocate freed resources (e.g., communication slots), which hence
remain unused. To address this problem, novel predictive and self triggering
protocols are proposed herein. From a unified Bayesian decision framework, two
schemes are developed: self triggers that predict, at the current triggering
instant, the next one; and predictive triggers that check at every time step,
whether communication will be needed at a given prediction horizon. The
suitability of these triggers for feedback control is demonstrated in hardware
experiments on a cart-pole, and scalability is discussed with a multi-vehicle
simulation.Comment: 16 pages, 15 figures, accepted article to appear in IEEE Internet of
Things Journal. arXiv admin note: text overlap with arXiv:1609.0753
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