A convex optimization approach to synthesizing state feedback data-driven controllers for switched linear systems

This paper seeks to develop a computationally tractable framework for data-driven control of switched linear systems . Specifically, given a model structure and experimental data collected at different operating points, we seek to directly design a state-feedback controller that stabilizes a system that arbitrarily switches amongst all sub-systems that could have generated the observed data, without an explicit plant identification step. The main result of the paper shows that this robust optimization problem can be recast, through the use of duality, into a polynomial optimization form and efficiently solved, leading to a robust controller with guaranteed ℓ ∞ worst-case performance. The effectiveness of the proposed technique is illustrated with several examples, including control of the horizontal motion of a quadcopter