Direct Data-Driven Control Synthesis for Linear Systems with Signal Temporal Logic Specifications

Core Concepts

This work develops a direct data-driven approach to automatically synthesize a controller for linear systems that satisfies a given signal temporal logic specification, without requiring an explicit model of the system.

Abstract

The key highlights and insights of this content are: Most control synthesis methods under temporal logic properties require a model of the system, which can be challenging to obtain in practice. This work develops a direct data-driven control synthesis method that does not require this explicit modeling step. After collecting a single sequence of input-output data from the system, a data-driven characterization of the system behavior is constructed. This characterization is then used to synthesize a controller that satisfies a (possibly unbounded) temporal logic specification. For bounded signal temporal logic (STL) specifications, an optimization problem is formulated and solved using mixed-integer linear programming (MILP) to synthesize the controller. For unbounded STL specifications, a novel loop constraint is introduced to handle the infinite-horizon case. The optimization problem is again solved using MILP. The proposed data-driven approach is shown to be sound, meaning that if the optimization problem returns a controller, the controlled system will satisfy the STL specification. Under certain conditions, the approach is also complete, meaning that if a satisfying controller exists, the optimization problem will have a feasible solution. The applicability of the results is demonstrated through simulation examples, including a car platoon problem and a temperature control problem in a building.

Stats

The following sentences contain key metrics or important figures used to support the author's key logics: The data sequence wdata has a length of 31 for the car platoon problem and 1050 for the temperature control problem. The computation time for the car platoon problem has an average of 7.25 seconds with a standard deviation of 0.73 seconds. The computation time for the temperature control problem has an average of 26.99 seconds with a standard deviation of 7.9 seconds. The memory usage for the car platoon problem is 19.78 MB and for the temperature control problem is 81.1 MB.

Quotes

"To achieve reliability of safety-critical systems, such as autonomous vehicles and power grids, it is crucial to obtain formal guarantees on their behavior." "Due to the increasing complexity of systems, obtaining an accurate model has become a challenging task in practice." "To the best of our knowledge, direct data-driven control has never been used to automatically construct a controller that guarantees the satisfaction of a temporal logic specification."

Key Insights Distilled From

Direct data-driven control with signal temporal logic specifications

by Birg... at arxiv.org 04-05-2024

https://arxiv.org/pdf/2304.02297.pdf

Deeper Inquiries

How can the proposed data-driven approach be extended to handle nonlinear systems and noisy data

To extend the proposed data-driven approach to handle nonlinear systems, one could leverage techniques such as system identification to approximate the nonlinear dynamics of the system. This could involve using nonlinear regression models, neural networks, or other machine learning algorithms to capture the system's behavior. By collecting input-output data from the nonlinear system and applying these identification methods, one can create a data-driven model that can be used for control synthesis. In the case of noisy data, one approach would be to incorporate robust control techniques into the data-driven control synthesis process. This could involve using methods such as H-infinity control or robust model predictive control to account for uncertainties and disturbances in the system. Additionally, filtering techniques like Kalman filters or particle filters could be employed to reduce the impact of noise on the data-driven control synthesis process.

What are the potential limitations or drawbacks of the loop constraint used to handle unbounded specifications, and are there alternative approaches that could be explored

The loop constraint used to handle unbounded specifications, while effective, may have limitations in terms of scalability and computational complexity. As the length of the loop increases, the number of constraints in the optimization problem grows, potentially leading to higher computational costs. Additionally, the loop constraint relies on the assumption that the system can be accurately represented by a finite trajectory followed by a loop, which may not always hold true for complex systems with long-term dependencies. An alternative approach to handling unbounded specifications could involve using receding horizon control techniques. By formulating the control synthesis problem as a receding horizon optimization problem, one can focus on optimizing the control inputs over a finite time horizon while still satisfying the unbounded specifications. This approach allows for flexibility in adapting to changing system dynamics and specifications over time.

Given the success of reinforcement learning in data-driven control, how could the techniques developed in this work be combined with reinforcement learning to further enhance the capabilities of data-driven control synthesis

The techniques developed in this work, particularly the direct data-driven control synthesis method, can be combined with reinforcement learning to enhance the capabilities of data-driven control synthesis further. Reinforcement learning algorithms can be used to learn optimal control policies based on the data-driven model of the system and the desired specifications encoded in temporal logic. One possible approach is to use reinforcement learning to fine-tune the control policies obtained from the data-driven synthesis method. By incorporating reinforcement learning algorithms such as deep Q-learning or policy gradient methods, the controller can adapt and improve its performance based on feedback from the system. This adaptive control approach can enhance the robustness and adaptability of the data-driven controller in real-world applications. Another way to combine these techniques is to use reinforcement learning for exploration and learning in uncertain or unknown regions of the state space, while relying on the data-driven control synthesis for stable and reliable control in known regions. This hybrid approach can leverage the strengths of both methods to achieve efficient and effective control synthesis in complex systems.