Parallel Model Predictive Control for Deterministic Systems

TL;DR

The paper tackles infinite-horizon deterministic discrete-time optimal control, where exact DP is intractable. It introduces Parallel Model Predictive Control (Parallel MPC), which runs multiple MPC lookahead minimizations in parallel with horizons ell_i and terminal costs/constraints J_i, applying the first control from the unit yielding the lowest predicted cost. The authors prove an equivalence to a single-lookahead problem (T^ell bar J)(x) with ell = min_i ell_i and bar J derived from the J_i, establishing Lyapunov-type guarantees that J_tilde_mu(x) <= (T^ell bar J)(x) <= min_i (T^{ell_i} J_i)(x), and they present a simplified variant using bar T to ease computation. Computational experiments on linear-quadratic and switching examples demonstrate meaningful runtime savings and improved performance bounds, highlighting the method's potential for real-time deterministic control on scalable problems.

Abstract

In this note, we consider infinite horizon optimal control problems with deterministic systems. Since exact solutions to these problems are often intractable, we propose a parallel model predictive control (MPC) method that provides an approximate solution. Our method computes multiple lookahead minimization problems at each time, where each minimization may involve a different number of lookahead steps, and terminal cost and constraint. The policy computed via parallel MPC applies the first control of the lookahead minimization with the lowest cost. We show that the proposed method can harnesses the power of multiple computing units. Moreover, we prove that the policy computed via parallel MPC has better performance guarantee than that computed via the single lookahead minimization involved in parallel MPC.

Figures (1)

• Figure 1: The computational time of parallel MPC (labeled as Parallel in the figure) is compared to that of the alternative approach with binary variables. The horizontal axis represents the index of the state along the state trajectories $\{x_k\}$, which are generated under the parallel MPC policy $\tilde{\mu}$. The computational time is averaged over $100$ trials.

Theorems & Definitions (24)

• Example 1.1
• Proposition 2.1
• Example 3.1
• Proposition 3.1
• proof
• Remark 3.1
• Proposition 3.2
• proof
• Proposition 3.3
• proof