Contract-based hierarchical control using predictive feasibility value functions

TL;DR

The paper tackles the challenge of safely integrating modular, independently designed controllers in a hierarchical setup by introducing a contract-based framework. A slack-value function, derived from the lower-level soft-constrained MPC, serves as the feasibility measure, which is approximated explicitly (e.g., by a neural network) to enable real-time feasibility assessment without exposing lower-level models or costs. The approach provides a feasibility-aware higher-level planning objective, extends to receding-horizon operation, and is demonstrated on an autonomous-driving planner-motion-control example, where feasible references yield safe obstacle avoidance. This mechanism promotes modularity and confidentiality while maintaining safety guarantees in complex, multi-rate control systems.

Abstract

Today's control systems are often characterized by modularity and safety requirements to handle complexity, resulting in hierarchical control structures. Although hierarchical model predictive control offers favorable properties, achieving a provably safe, yet modular design remains a challenge. This paper introduces a contract-based hierarchical control strategy to improve the performance of control systems facing challenges related to model inconsistency and independent controller design across hierarchies. We consider a setup where a higher-level controller generates references that affect the constraints of a lower-level controller, which is based on a soft-constrained MPC formulation. The optimal slack variables serve as the basis for a contract that allows the higher-level controller to assess the feasibility of the reference trajectory without exact knowledge of the model, constraints, and cost of the lower-level controller. To ensure computational efficiency while maintaining model confidentiality, we propose using an explicit function approximation, such as a neural network, to represent the cost of optimal slack values. The approach is tested for a hierarchical control setup consisting of a planner and a motion controller as commonly found in autonomous driving.

Figures (3)

• Figure 1: Considered controller architecture: The higher-level controller generates references $r^{\mathrm{H,*}}_{\cdot|k_{\mathrm{H}}}$ which are tracked by the lower-level controller that applies inputs $u(k)$ to the system. The gray part represents a contract designed offline (before operation), allowing the higher-level controller to assess feasibility of a given trajectory for the lower-level controller during operation. $x(k)$ and $x^{\mathrm{H}}(k)$ are the states of the lower- and higher-level controller, respectively.
• Figure 2: The left figure shows the considered scenario with obstacle as gray box, black dot as initial, and red dot as target position. For the proposed reference by the higher-level controller $h^*(x(k),r^{\mathrm{H}}_{\cdot|k_{\mathrm{H}}}) > 0$. The simulation of the closed-loop shows that this plan leads to violation of the constraints \ref{['eq:relative_position_constraints']}. The right figure shows the deviation of the state to the reference.
• Figure 3: The left figure shows the considered scenario with obstacle as gray box, black dot as initial, and red dot as target position. For the proposed reference by the higher-level controller $h^*(x(k),r^{\mathrm{H}}_{\cdot|k_{\mathrm{H}}}) = 0$. The simulation of the closed-loop shows that this plan does not lead to violation of the constraints \ref{['eq:relative_position_constraints']}. The right figure shows the deviation of the state to the reference.

Theorems & Definitions (4)

• Theorem 1
• proof
• Theorem 2
• proof