Data-driven design of safe control for polynomial systems

Abstract

We consider the problem of designing an invariant set using only a finite set of input-state data collected from an unknown polynomial system in continuous time. We consider noisy data, i.e., corrupted by an unknown-but-bounded disturbance. We derive a data-dependent sum-of-squares program that enforces invariance of a set and also optimizes the size of the invariant set while keeping it within a set of user-defined safety constraints; the solution of this program directly provides a polynomial invariant set and a state-feedback controller. We numerically test the design on a system of two platooning cars.

References in corpus (3)

• Data-driven control via Petersen's lemma
• Trade-offs in learning controllers from noisy data
• Chordal and factor-width decompositions for scalable semidefinite and polynomial optimization

Cited by in corpus (6)

• Data-based Transfer Stabilization in Linear Systems
• Data-driven stabilization of switched and constrained linear systems
• Data-driven control of nonlinear systems from input-output data
• Data-driven input-to-state stabilization with respect to measurement errors
• Data-driven input-to-state stabilization
• Setpoint control of bilinear systems from noisy data