Session: 16-01-01: Government Agency Student Poster Competition

Paper Number: 149623

149623 - Direct Data-Driven Control of Constrained Dynamical Systems 

Introduction:
We have developed direct data-driven control algorithms for safety-critical cyber-physical systems. Our controllers use data to ensure these systems operate within their safety constraints to prevent damage to the machine, its environment, and human operators. Constrained control of safety-critical systems is challenging since they are subject to hard constraints and their dynamics are often unknown or highly uncertain, complicated, and nonlinear. For instance, constraint enforcement is vital to ensure safety in autonomous vehicles, surgical systems, and industrial robots. In other applications, such as air conditioning, constraint enforcement can increase the lifespan of the equipment. Designing constraint enforcing controllers for these systems is challenging since accurate models are often unavailable. A widely adopted approach is to replace the existing controller with a constraint-enforcing controller, such as model predictive control (MPC).  However, this discards the careful design and tuning of the existing controller. Additionally, control design techniques like MPC typically require a model, which may not be available.

Contribution:
Our approach involves adding an outer-loop controller to the closed-loop system, allowing the well-tuned primary inner-loop controller to remain in operation. For instance, in an assisted-driving vehicle, the primary controller is designed for stability, while our outer-loop controller ensures lane-keeping. Similarly, in an air-conditioning system, the primary controller optimizes energy consumption, and our outer-loop controller prevents liquid-phase refrigerant from entering the compressor, which is designed for gas-phase refrigerant, thus avoiding equipment damage. Our novel model-free approach has successfully solved the lane keeping problem for assisted-driving and equipment safety for air-conditioning systems, using offline empirical data. This is achieved through our novel controlled invariant (CI) set computation algorithm.

Methodology:
Invariant sets are essential for constrained control since they define sets of states in which the system dynamics can evolve without violating constraints. While existing works in the literature focus on approximating CI sets from data, our approach, to the best of our knowledge, is the first to compute controlled invariant sets from data with guaranteed invariance. This is important because approximations of an invariant set may not be approximately invariant. Thus, constraint violation may occur when the controller uses an approximate invariant set. Our novel approach reformulates the problem of learning invariant sets as the problem of learning a Lyapunov-like function. This enables the leveraging machine learning tools to synthesize invariant sets which provide rigorous safety guarantees. Learning-based methods show promise in constructing Lyapunov-like certificates that characterize the invariant sets, along with barrier functions. Our method for synthesizing functions is versatile and can be applied to an arbitrary function space by defining a complete set of basis-functions. This flexibility allows us to leverage a variety of machine learning tools, facilitating the synthesis of highly nonlinear functions that guarantee invariance and therefore safety.

Preliminary results:
Our novel model-free approach has successfully solved the lane keeping problem for assisted-driving and equipment safety for air-conditioning systems, using offline data.

Conclusion:
We solve constrained control problems using direct data-driven controllers with safety guarantees through our novel controlled invariant set computation algorithms.

Presenting Author: Ali Kashani University of New Mexico

Presenting Author Biography: Ali Kashani holds a graduate degree from University of Tehran. He is currenty a PhD candidate at University of New Mexico. His research is supported by the National Science Fundation (NSF CMMI-2303157) .

Authors:

Ali Kashani University of New Mexico
Ganiyu Azeez University of New Mexico
Claus Danielson University of New Mexico