skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Optimal Sensor Gain Control for Minimum-Information Estimation of Continuous-Time Gauss-Markov Processes
We consider the scenario in which a continuous-time Gauss-Markov process is estimated by the Kalman-Bucy filter over a Gaussian channel (sensor) with a variable sensor gain. The problem of scheduling the sensor gain over a finite time interval to minimize the weighted sum of the data rate (the mutual information between the sensor output and the underlying Gauss-Markov process) and the distortion (the mean-square estimation error) is formulated as an optimal control problem. A necessary optimality condition for a scheduled sensor gain is derived based on Pontryagin’s minimum principle. For a scalar problem, we show that an optimal sensor gain control is of bang-bang type, except the possibility of taking an intermediate value when there exists a stationary point on the switching surface in the phase space of canonical dynamics. Furthermore, we show that the number of switches is at most two and the time instants at which the optimal gain must be switched can be computed from the analytical solutions to the canonical equations.  more » « less
Award ID(s):
1944318
PAR ID:
10488430
Author(s) / Creator(s):
; ;
Publisher / Repository:
IEEE
Date Published:
Journal Name:
American Control Conference
Page Range / eLocation ID:
60-66
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; (, IEEE)
    A modified form of Legendre-Gauss orthogonal direct collocation is developed for solving optimal control problems whose solutions are nonsmooth due to control discon- tinuities. This new method adds switch time variables, control variables, and collocation conditions at both endpoints of a mesh interval, whereas these new variables and collocation con- ditions are not included in standard Legendre-Gauss orthogonal collocation. The modified Legendre-Gauss collocation method alters the search space of the resulting nonlinear programming problem and optimizes the switch point of the control solution. The transformed adjoint system of the modified Legendre- Gauss collocation method is then derived and shown to satisfy the necessary conditions for optimality. Finally, an example is provided where the optimal control is bang-bang and contains multiple switches. This method is shown to be capable of solving complex optimal control problems with nonsmooth solutions. 
    more » « less
  2. ; (, ACM)
    In this paper, we study a sampling and transmission scheduling problem for multi-source remote estimation, where a scheduler determines when to take samples from multiple continuous-time Gauss-Markov processes and send the samples over multiple channels to remote estimators. The sample transmission times are i.i.d. across samples and channels. The objective of the scheduler is to minimize the weighted sum of the time-average expected estimation errors of these Gauss-Markov sources. This problem is a continuous-time Restless Multi-armed Bandit (RMAB) problem with a continuous state space. We prove that the bandits are indexable and derive an exact expression of the Whittle index. To the extent of our knowledge, this is the first Whittle index policy for multi-source signal-aware remote estimation of Gauss-Markov processes. We further investigate signal-agnostic remote estimation and develop a Whittle index policy for multi-source Age of Information (AoI) minimization over parallel channels with i.i.d. random transmission times. Our results unite two theoretical frameworks for remote estimation and AoI minimization: threshold-based sampling and Whittle index-based scheduling. In the single-source, single-channel scenario, we demonstrate that the optimal solution to the sampling and scheduling problem can be equivalently expressed as both a threshold-based sampling strategy and a Whittle index-based scheduling policy. Notably, the Whittle index is equal to zero if and only if two conditions are satisfied: (i) the channel is idle, and (ii) the estimation error is precisely equal to the threshold in the threshold-based sampling strategy. Moreover, the methodology employed to derive threshold-based sampling strategies in the single-source, single-channel scenario plays a crucial role in establishing indexability and evaluating the Whittle index in the more intricate multi-source, multi-channel scenario. Our numerical results show that the proposed policy achieves high performance gain over the existing policies when some of the Gauss-Markov processes are highly unstable. 
    more » « less
  3. (, American Control Conference)
    We consider a dynamic sensor fusion problem where a large number of remote sensors observe a common Gauss-Markov process and the observations are transmitted to a fusion center over a resource constrained communication network. The design objective is to allocate an appropriate data rate to each sensor in such a way that the total data traffic to the fusion center is minimized, subject to a constraint on the fusion center's state estimation error covariance. We show that the problem can be formulated as a difference-of-convex program, to which we apply the convex-concave procedure (CCP) and the alternating direction method of multiplier (ADMM). Through a numerical study on a truss bridge sensing system, we observe that our algorithm tends to allocate zero data rate to unneeded sensors, implying that the proposed method is an effective heuristic for sensor selection. 
    more » « less
  4. ; (, ESAIM: Control, Optimisation and Calculus of Variations)
    We investigate how to control optimally a traffic flow through a junction on the line by acting only on speed reduction or traffic light at the junction. We show the existence of an optimal control and, under structure assumptions, provide optimality conditions. We use this analysis to investigate thoroughly the maximization of the flux on a space-time subset and show the existence of an optimal control which is bang-bang. 
    more » « less
  5. ; (, Mathematical Finance)
    Abstract We develop a continuous‐time control approach to optimal trading in a Proof‐of‐Stake (PoS) blockchain, formulated as a consumption‐investment problem that aims to strike the optimal balance between a participant's (or agent's) utility from holding/trading stakes and utility from consumption. We present solutions via dynamic programming and the Hamilton–Jacobi–Bellman (HJB) equations. When the utility functions are linear or convex, we derive close‐form solutions and show that the bang‐bang strategy is optimal (i.e., always buy or sell at full capacity). Furthermore, we bring out the explicit connection between the rate of return in trading/holding stakes and the participant's risk‐adjusted valuation of the stakes. In particular, we show when a participant is risk‐neutral or risk‐seeking, corresponding to the risk‐adjusted valuation being a martingale or a sub‐martingale, the optimal strategy must be to either buy all the time, sell all the time, or first buy then sell, and with both buying and selling executed at full capacity. We also propose a risk‐control version of the consumption‐investment problem; and for a special case, the “stake‐parity” problem, we show a mean‐reverting strategy is optimal. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email