Learning Soft Constrained MPC Value Functions: Efficient MPC Design and Implementation providing Stability and Safety Guarantees
CoRR(2024)
摘要
Model Predictive Control (MPC) can be applied to safety-critical control
problems, providing closed-loop safety and performance guarantees.
Implementation of MPC controllers requires solving an optimization problem at
every sampling instant, which is challenging to execute on embedded hardware.
To address this challenge, we propose a framework that combines a tightened
soft constrained MPC formulation with supervised learning to approximate the
MPC value function. This combination enables us to obtain a corresponding
optimal control law, which can be implemented efficiently on embedded
platforms. The framework ensures stability and constraint satisfaction for
various nonlinear systems. While the design effort is similar to that of
nominal MPC, the proposed formulation provides input-to-state stability (ISS)
with respect to the approximation error of the value function. Furthermore, we
prove that the value function corresponding to the soft constrained MPC problem
is Lipschitz continuous for Lipschitz continuous systems, even if the optimal
control law may be discontinuous. This serves two purposes: First, it allows to
relate approximation errors to a sufficiently large constraint tightening to
obtain constraint satisfaction guarantees. Second, it paves the way for an
efficient supervised learning procedure to obtain a continuous value function
approximation. We demonstrate the effectiveness of the method using a nonlinear
numerical example.
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