1,477 research outputs found
Consensus-based control for a network of diffusion PDEs with boundary local interaction
In this paper the problem of driving the state of a network of identical
agents, modeled by boundary-controlled heat equations, towards a common
steady-state profile is addressed. Decentralized consensus protocols are
proposed to address two distinct problems. The first problem is that of
steering the states of all agents towards the same constant steady-state
profile which corresponds to the spatial average of the agents initial
condition. A linear local interaction rule addressing this requirement is
given. The second problem deals with the case where the controlled boundaries
of the agents dynamics are corrupted by additive persistent disturbances. To
achieve synchronization between agents, while completely rejecting the effect
of the boundary disturbances, a nonlinear sliding-mode based consensus protocol
is proposed. Performance of the proposed local interaction rules are analyzed
by applying a Lyapunov-based approach. Simulation results are presented to
support the effectiveness of the proposed algorithms
Adaptive Control By Regulation-Triggered Batch Least-Squares Estimation of Non-Observable Parameters
The paper extends a recently proposed indirect, certainty-equivalence,
event-triggered adaptive control scheme to the case of non-observable
parameters. The extension is achieved by using a novel Batch Least-Squares
Identifier (BaLSI), which is activated at the times of the events. The BaLSI
guarantees the finite-time asymptotic constancy of the parameter estimates and
the fact that the trajectories of the closed-loop system follow the
trajectories of the nominal closed-loop system ("nominal" in the sense of the
asymptotic parameter estimate, not in the sense of the true unknown parameter).
Thus, if the nominal feedback guarantees global asymptotic stability and local
exponential stability, then unlike conventional adaptive control, the newly
proposed event-triggered adaptive scheme guarantees global asymptotic
regulation with a uniform exponential convergence rate. The developed adaptive
scheme is tested to a well-known control problem: the state regulation of the
wing-rock model. Comparisons with other adaptive schemes are provided for this
particular problem.Comment: 29 pages, 12 figure
Data Transmission Over Networks for Estimation and Control
We consider the problem of controlling a linear time invariant process when the controller is located at a location remote from where the sensor measurements are being generated. The communication from the sensor to the controller is supported by a communication network with arbitrary topology composed of analog erasure channels. Using a separation principle, we prove that the optimal linear-quadratic-Gaussian (LQG) controller consists of an LQ optimal regulator along with an estimator that estimates the state of the process across the communication network. We then determine the optimal information processing strategy that should be followed by each node in the network so that the estimator is able to compute the best possible estimate in the minimum mean squared error sense. The algorithm is optimal for any packet-dropping process and at every time step, even though it is recursive and hence requires a constant amount of memory, processing and transmission at every node in the network per time step. For the case when the packet drop processes are memoryless and independent across links, we analyze the stability properties and the performance of the closed loop system. The algorithm is an attempt to escape the viewpoint of treating a network of communication links as a single end-to-end link with the probability of successful transmission determined by some measure of the reliability of the network
An integrative perspective to LQ and ℓ∞ control for delayed and quantized systems
Deterministic and stochastic approaches to handle uncertainties may incur very different complexities in computation time and memory usage, in addition to different uncertainty models. For linear systems with delay and rate constrained communications between the observer and the controller, previous work shows that a deterministic approach, the ℓ ∞ control has low complexity but can only handle bounded disturbances. In this article, we take a stochastic approach and propose a linear-quadratic (LQ) controller that can handle arbitrarily large disturbance but has large complexity in time and space. The differences in robustness and complexity of the ℓ ∞ and LQ controllers motivate the design of a hybrid controller that interpolates between the two: The ℓ ∞ controller is applied when the disturbance is not too large (normal mode) and the LQ controller is resorted to otherwise (acute mode). We characterize the switching behavior between the normal and acute modes. Using our theoretical bounds which are supplemented by numerical experiments, we show that the hybrid controller can achieve a sweet spot in the robustness-complexity tradeoff, i.e., reject occasional large disturbance while operating with low complexity most of the time
LQG Control and Sensing Co-Design
We investigate a Linear-Quadratic-Gaussian (LQG) control and sensing
co-design problem, where one jointly designs sensing and control policies. We
focus on the realistic case where the sensing design is selected among a finite
set of available sensors, where each sensor is associated with a different cost
(e.g., power consumption). We consider two dual problem instances:
sensing-constrained LQG control, where one maximizes control performance
subject to a sensor cost budget, and minimum-sensing LQG control, where one
minimizes sensor cost subject to performance constraints. We prove no
polynomial time algorithm guarantees across all problem instances a constant
approximation factor from the optimal. Nonetheless, we present the first
polynomial time algorithms with per-instance suboptimality guarantees. To this
end, we leverage a separation principle, that partially decouples the design of
sensing and control. Then, we frame LQG co-design as the optimization of
approximately supermodular set functions; we develop novel algorithms to solve
the problems; and we prove original results on the performance of the
algorithms, and establish connections between their suboptimality and
control-theoretic quantities. We conclude the paper by discussing two
applications, namely, sensing-constrained formation control and
resource-constrained robot navigation.Comment: Accepted to IEEE TAC. Includes contributions to submodular function
optimization literature, and extends conference paper arXiv:1709.0882
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