The Partial Integral Equation (PIE) framework provides a unified algebraic representation for use in analysis, control, and estimation of infinite-dimensional systems. However, the presence of input delays results in a PIE representation with dependence on the derivative of the control input, u˙. This dependence complicates the problem of optimal state-feedback control for systems with input delay – resulting in a bilinear optimization problem. In this paper, we present two strategies for convexification of the H∞-optimal state-feedback control problem for systems with input delay. In the first strategy, we use a generalization of Young's inequality to formulate a convex optimization problem, albeit with some conservatism. In the second strategy, we filter the actuator signal – introducing additional dynamics, but resulting in a convex optimization problem without conservatism. We compare these two optimal control strategies on four example problems, solving the optimization problem using the latest release of the PIETOOLS software package for analysis, control and simulation of PIEs.
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This content will become publicly available on October 1, 2024
On the Optimal Delay Growth Rate of Multi-Hop Line Networks: Asymptotically Delay-Optimal Designs and the Corresponding Error Exponents
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We consider an energy harvesting sensor transmit- ting latency-sensitive data over a fading channel. We aim to find the optimal transmission scheduling policy that minimizes the packet queuing delay given the available harvested energy. We formulate the problem as a Markov decision process (MDP) over a state-space spanned by the transmitter's buffer, battery, and channel states, and analyze the structural properties of the resulting optimal value function, which quantifies the long-run performance of the optimal scheduling policy. We show that the optimal value function (i) is non- decreasing and has increasing differences in the queue backlog; (ii) is non-increasing and has increasing differences in the battery state; and (iii) is submodular in the buffer and battery states. Our numerical results confirm these properties and demonstrate that the optimal scheduling policy outperforms a so-called greedy policy in terms of sensor outages, buffer overflows, energy efficiency, and queuing delay.more » « less
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null (Ed.)The ubiquitous usage of communication networks in modern sensing and control applications has kindled new interests on the timing-based coordination between sensors and controllers, i.e., how to use the “waiting time” to improve the system performance. Contrary to the common belief that a zero-wait policy is always optimal, Sun et al. showed that a controller can strictly improve the data freshness, the so-called Age-of-Information (AoI), by postponing transmission in order to lengthen the duration of staying in a good state. The optimal waiting policy for the sensor side was later characterized in the context of remote estimation. Instead of focusing on the sensor and controller sides separately, this work develops the optimal joint sensor/controller waiting policy in a Wiener-process system. The results can be viewed as strict generalization of the above two important results in the sense that not only do we consider joint sensor/controller designs (as opposed to sensor-only or controller only schemes), but we also assume random delay in both the forward and feedback directions (as opposed to random delay in only one direction). In addition to provable optimality, extensive simulation is used to verify the performance of the proposed scheme in various settings.more » « less
