Using Radial Basis Functions to Approximate the LQG-Optimal Event-Based Sampling Policy

Andrén, Marcus Thelander

doi:10.23919/ecc.2019.8795838

Cited by 3 publications

(3 citation statements)

References 19 publications

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“…where γ 0 is continuous-time LQG optimal cost. The value of the second term in (20) is determined by the choice of sampling policy, which ideally should be as small as possible for a given average sampling rate. As detailed in [14], the event-based sampling policy that minimizes (20) is in the form of a threshold onη.…”

Section: Event-based Samplingmentioning

confidence: 99%

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LQG-Optimal versus Simple Event-Based PID Controllers

Cervin

Andrén

2020

2020 American Control Conference (ACC)

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In this paper, we study event-based PID control from an optimal stochastic control perspective. The purpose is to better understand what implementation features are critical for achieving good event-based PID performance. For this end, we formulate an LQG control design problem for a double integrator process with an integral disturbance, where the solution is an ideal PID controller. We then consider the tradeoff between LQG cost and average sampling rate and give an interpretation of the optimal sampled-data controller and eventbased sampling policy in terms of PID control. Based on insights from the optimal solution, we finally discuss how suboptimal but simple event-based PID controllers can be implemented. The proposed implementation is evaluated in a simulation study and compared to earlier work in event-based PID control. The results highlight the importance of considering both the triggering rule and the transmitted information in order to obtain an event-based PID controller with good performance.

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Section: Event-based Samplingmentioning

confidence: 99%

“…A line parallel to the LQ feedback gain vector [lx, ly, 1] (red) is plotted for reference. The threshold was obtained using the method described in [20]. signal generators infeasible.…”

Section: Simple Event-based Pid Implementationsmentioning

confidence: 99%

LQG-Optimal versus Simple Event-Based PID Controllers

Cervin

Andrén

2020

2020 American Control Conference (ACC)

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“…where the sum converges due to (3). Plugging in this expression in (4) yields the expression for the control cost as…”

Section: Model-based Networked Controlmentioning

confidence: 99%

Sample Complexity of Networked Control Systems Over Unknown Channels

Gatsis

Pappas

2018

2018 IEEE Conference on Decision and Control (CDC)

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Recent control trends are increasingly relying on communication networks and wireless channels to close the loop for Internetof-Things applications. Traditionally these approaches are model-based, i.e., assuming a network or channel model they are focused on stability analysis and appropriate controller designs. However the availability of such wireless channel modeling is fundamentally challenging in practice as channels are typically unknown a priori and only available through data samples. In this work we aim to develop algorithms that rely on channel sample data to determine the stability and performance of networked control tasks. In this regard our work is the first to characterize the amount of channel modeling that is required to answer such a question. Specifically we examine how many channel data samples are required in order to answer with high confidence whether a given networked control system is stable or not. This analysis is based on the notion of sample complexity from the learning literature and is facilitated by concentration inequalities. Moreover we establish a direct relation between the sample complexity and the networked system stability margin, i.e., the underlying packet success rate of the channel and the spectral radius of the dynamics of the control system. This illustrates that it becomes impractical to verify stability under a large range of plant and channel configurations. We validate our theoretical results in numerical simulations.

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Enhanced Exploration Least-Squares Methods for Optimal Stopping Problems

Forootani

Tipaldi

Iervolino

et al. 2022

IEEE Control Syst. Lett.

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This letter presents an Approximate Dynamic Programming (ADP) least-squares based approach for solving optimal stopping problems with a large state space. By extending some previous work in the area of optimal stopping problems, it provides a framework for their formulation and resolution. The proposed method uses a combined on/off policy exploration mechanism, where states are generated by means of state transition probability distributions different from the ones dictated by the underlying Markov decision processes. The contraction mapping property of the associated projected Bellman operator is analysed as well as the convergence of the resulting algorithm.

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Using Radial Basis Functions to Approximate the LQG-Optimal Event-Based Sampling Policy

Cited by 3 publications

References 19 publications

LQG-Optimal versus Simple Event-Based PID Controllers

LQG-Optimal versus Simple Event-Based PID Controllers

Sample Complexity of Networked Control Systems Over Unknown Channels

Enhanced Exploration Least-Squares Methods for Optimal Stopping Problems

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