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Direct data-driven control of linear systems: SOS, please
Sum-of-Squares (SOS) relaxation is a beautiful technique to solve nonconvex optimization problems. As computational capabilities continue to increase, so is the scope of engineering challenges that can be tackled with this method. The goal of this project is to exploit the flexibility of SOS relaxations to design new data-driven control methods for linear dynamics, that can more efficiently incorporate prior knowledge on the system and cope with noisy input-output data.
Keywords: Data-driven control, linear systems, Sum-of-Squares optimization, polynomial programming
The need to ensure the efficient operation of dynamical systems of increasing complexity (e.g., smart buildings and interconnected power grids) has recently sparked renewed interest in “direct data-driven control” methods.
This term refers to designing controllers using exclusively measured data, without the identification of a model ― the most expensive and time-consuming process.
Since the true plant is assumed to be unknown, the goal consists in finding a controller that can work for all the plausible systems ― i.e., all those compatible with the available measurements. One way to recast and solve this challenging robust-control problem is by using SOS optimization; this solution has been explored in the recent literature, but with the drawback of heavily relying on state measurement (or reconstruction).
The need to ensure the efficient operation of dynamical systems of increasing complexity (e.g., smart buildings and interconnected power grids) has recently sparked renewed interest in “direct data-driven control” methods. This term refers to designing controllers using exclusively measured data, without the identification of a model ― the most expensive and time-consuming process.
Since the true plant is assumed to be unknown, the goal consists in finding a controller that can work for all the plausible systems ― i.e., all those compatible with the available measurements. One way to recast and solve this challenging robust-control problem is by using SOS optimization; this solution has been explored in the recent literature, but with the drawback of heavily relying on state measurement (or reconstruction).
The goal of this project is to develop analysis and control techniques for an unknown linear system, only based on a few noisy measurements. To this end, we use tools from polynomial optimization and SOS programming: this approach allows us to deal with the challenging case of output (rather than state) measurement, and to incorporate any prior knowledge on the system (e.g., sparsity) in the controller design. The student will have the opportunity to learn about SOS polynomials and data-driven control, before analytically investigating solution techniques and evaluating their performance numerically.
The goal of this project is to develop analysis and control techniques for an unknown linear system, only based on a few noisy measurements. To this end, we use tools from polynomial optimization and SOS programming: this approach allows us to deal with the challenging case of output (rather than state) measurement, and to incorporate any prior knowledge on the system (e.g., sparsity) in the controller design. The student will have the opportunity to learn about SOS polynomials and data-driven control, before analytically investigating solution techniques and evaluating their performance numerically.