Safe Data-Driven Predictive Control

TL;DR

The paper tackles the computational and safety challenges of nonlinear model predictive control by proposing Safe Data-Driven Predictive Control, which learns both system dynamics and the control policy using spatial-temporal filters (STFs) and concurrent learning. Safety is guaranteed through an extended robust control barrier function (RCBF) integrated with a NMPC policy, while online policy correction compensates for model uncertainties and disturbances. The approach yields convergence guarantees for the learned model, robust safety under uncertainties, and a reduced online computation by approximating the NMPC policy with STF-based learning. Validation on a cart-inverted pendulum and a turbocharged engine demonstrates high identification and policy accuracy with significant computational savings, while maintaining safety under disturbances.

Abstract

In the realm of control systems, model predictive control (MPC) has exhibited remarkable potential; however, its reliance on accurate models and substantial computational resources has hindered its broader application, especially within real-time nonlinear systems. This study presents an innovative control framework to enhance the practical viability of the MPC. The developed safe data-driven predictive control aims to eliminate the requirement for precise models and alleviate computational burdens in the nonlinear MPC (NMPC). This is achieved by learning both the system dynamics and the control policy, enabling efficient data-driven predictive control while ensuring system safety. The methodology involves a spatial temporal filter (STF)-based concurrent learning for system identification, a robust control barrier function (RCBF) to ensure the system safety amid model uncertainties, and a RCBF-based NMPC policy approximation. An online policy correction mechanism is also introduced to counteract performance degradation caused by the existing model uncertainties. Demonstrated through simulations on two applications, the proposed approach offers comparable performance to existing benchmarks with significantly reduced computational costs.

Figures (11)

• Figure 1: Sequence of steps of online safe data-driven predictive control.
• Figure 2: Schematic of NMPC policy function approximation.
• Figure 3: Sequence of steps of discrete-time STF-based Concurrent Learning: i) First cluster-model is initialized for the first I/O data, ii) For next data, the dissimilarity metric is computed to either create a new cluster-model or update one of the existing ones, iii) For each iteration, all linear models are updated using the concurrent learning, and iv) The process is repeated until all training I/O data is used.
• Figure 4: Cart-inverted pendulum.
• Figure 5: Control input of cart-inverted pendulum.

Theorems & Definitions (17)

• Definition 1: Closed-Loop Performance
• Theorem 1: Discrete-Time STF-based Concurrent Learning
• proof
• Remark 1: System Identification
• Theorem 2: Robust Constraint Satisfaction
• proof
• Remark 2: Feasibility
• Corollary 1: Steady-State Optimization Problem krishnamoorthy2021adaptive
• Lemma 1: Modified Steady-State Optimization Problem
• proof