Convex Model Predictive Control for Safe Output Consensus of Nonlinear Multi-Agent Systems

TL;DR

This work tackles safe output consensus for nonlinear multi-agent systems under safety constraints by reframing the MPC problem as a sequence of convex quadratic programs. It introduces Convex Model Predictive Control (CMPC) that employs a Sequential Quadratic Programming (SQP) scheme with linearized dynamics and a tangent-line projection to convexify discrete-time high-order control barrier function (DHCBF) constraints. The authors prove local SQP convergence, recursive feasibility, and stability, ensuring safe, asymptotic consensus of outputs. Simulation on a unicycle MAS demonstrates substantial real-time computational gains (roughly 35–52x faster than baselines) while preserving safety and convergence, indicating strong practical applicability for real-time safe coordination.

Abstract

Nonlinear dynamics and safety constraints typically result in a nonlinear programming problem when applying model predictive control to achieve safe output consensus. To avoid the heavy computational burden of solving a nonlinear programming problem directly, this paper proposes a novel Convex Model Predictive Control (CMPC) approach based on a Sequential Quadratic Programming (SQP) scheme. The core of our method lies in transforming the nonlinear constraints into linear forms: we linearize the system dynamics and convexify the discrete-time high-order control barrier functions using a proposed tangent-line projection method. Consequently, the original problem is reduced to a quadratic program that can be iteratively solved within the SQP scheme at each time step of CMPC. Furthermore, we provide the formal guarantee of the convergence of the SQP scheme, and subsequently guarantee the recursive feasibility and stability of CMPC. Simulations on multi-agent systems with unicycle dynamics demonstrate a 35-52 times reduction in computation time compared with baseline methods, confirming the suitability of the proposed approach for real-time safe output consensus control.

Figures (7)

• Figure 1: Structure of the iterative process at time step $t$.
• Figure 2: Convex formulation of safety constraints.
• Figure 3: State trajectories of system \ref{['simdyn']} under the CMPC.
• Figure 4: Control inputs generated by the CMPC.
• Figure 5: Time evolution of the DHCBF under the CMPC.