Learning-Based SMPC for Reference Tracking Under State-Dependent Uncertainty: An Application to Atmospheric Pressure Plasma Jets for Plasma Medicine
Angelo D. Bonzanini, David B. Graves, Ali Mesbah
Abstract
The increasing complexity of modern technical systems can exacerbate model uncertainty in model-based control, posing a great challenge to safe and effective system operation under closed loop. Online learning of model uncertainty can enhance control performance by reducing plant–model mismatch. This article presents a learning-based stochastic model predictive control (LB-SMPC) strategy for reference tracking of stochastic linear systems with additive state-dependent uncertainty. The LB-SMPC strategy adapts the state-dependent uncertainty model online to reduce plant–model mismatch for control performance optimization. Standard reachability and statistical tools are leveraged along with the state-dependent uncertainty model to develop a chance constraint-tightening approach, which ensures state constraint satisfaction in probability. The stability and recursive feasibility of the LB-SMPC strategy are established for tracking time-varying targets, without the need to redesign the controller every time the target is changed. The performance of the LB-SMPC strategy is experimentally demonstrated on an atmospheric pressure plasma jet (APPJ) testbed with prototypical applications in plasma medicine and materials processing. Real-time control comparisons with learning-based MPC with no uncertainty handling and offset-free MPC showcase the usefulness of LB-SMPC for predictive control of safety-critical systems with hard-to-model and/or time-varying dynamics.