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The use of mobile actuators for the control of spatially distributed systems governed by PDEs results in both implementational and computational challenges. First it requires the backward-in-time solution to the actuator guidance and the backward-in-time solution to the control operator Riccati equation. A way to address this computational challenge is to consider a continuous-discrete alternative whereby the mobile actuator is repositioned at discrete instances and resides in a specific spatial location for a certain time interval. In order to find optimal paths for a given time interval, a set of feasible locations is derived using the reachability set. These reachability sets are further constrained to take into account the time it takes to travel to any spatial position with a prescribed maximum velocity. The proposed hybrid continuous-discrete control and actuator guidance is demonstrated for a 2D diffusion PDE that uses no constraints and angular constraints on the actuator motion.
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Using local reachability sets in guiding mobile actuator and its orbiting sensors to approximate state feedback kernels in output control of PDEs
This paper considers a class of distributed parameter systems that can be controlled by an actuator onboard a mobile platform. In order to avoid computational costs and control architecture complexity associated with a joint optimization of actuator guidance and control law, a suboptimal policy is proposed that significantly reduces the computational costs. By utilizing a continuous-discrete optimal control design, a mobile actuator moves to a new position at the beginning of a new time interval and resides for a prescribed time. Using the cost to go with variable lower limit, the optimization simplifies to solving algebraic Riccati equations instead of differential Riccati equations. Adding a hardware feature whereby the mobile sensors are constrained to stay within the proximity of the mobile actuator, a feedback kernel decomposition scheme is proposed to approximate a full state feedback controller by the weighted sum of sensor measurements.
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- Award ID(s):
- 1825546
- PAR ID:
- 10480274
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- 2022 IEEE 61st Conference on Decision and Control (CDC)
- ISSN:
- 2576-2370
- ISBN:
- 978-1-6654-6761-2
- Page Range / eLocation ID:
- 6082 to 6088
- Format(s):
- Medium: X
- Location:
- Cancun, Mexico
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/CDC51059.2022.9993034
