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In networked control systems, the sensory signals are often quantized before being transmitted to the controller. Consequently, performance is affected by the coarseness of this quantization process. Modern communication technologies allow users to obtain resolution-varying quantized measurements based on the prices paid. In this paper, we consider the problem of joint optimal controller synthesis and quantizer scheduling for a partially observed quantized-feedback linear-quadratic-Gaussian system, where the measurements are quantized before being sent to the controller. The system is presented with several choices of quantizers, along with the cost of using each quantizer. The objective is to jointly select the quantizers and synthesize the controller to strike an optimal balance between control performance and quantization cost. When the innovation signal is quantized instead of the measurement, the problem is decoupled into two optimization problems: one for optimal controller synthesis, and the other for optimal quantizer selection. The optimal controller is found by solving a Riccati equation and the optimal quantizer-selection policy is found by solving a linear program---both of which can be solved offline.
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Quantizers with Parameterized Distortion Measures
In many quantization problems, the distortion function is given by the Euclidean metric to measure the distance of a source sample to any given reproduction point of the quantizer. We will in this work regard distortion functions, which are additively and multiplicatively weighted for each reproduction point resulting in a heterogeneous quantization problem, as used for example in deployment problems of sensor networks. Whereas, normally in such problems, the average distortion is minimized for given weights (parameters), we will optimize the quantization problem over all weights, i.e., we tune or control the distortion functions in our favor. For a uniform source distribution in one-dimension, we derive the unique minimizer, given as the uniform scalar quantizer with an optimal common weight. By numerical simulations, we demonstrate that this result extends to two-dimensions where asymptotically the parameter optimized quantizer is the hexagonal lattice with common weights. As an application, we will determine the optimal deployment of unmanned aerial vehicles (UAVs) to provide a wireless communication to ground terminals under a minimal communication power cost. Here, the optimal weights relate to the optimal flight heights of the UAVs.
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- Award ID(s):
- 1815339
- PAR ID:
- 10108985
- Date Published:
- Journal Name:
- Data Compression Conference (DCC-19)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
