Supervisory, Time-distributed, and Optimization-based Strategies for Model Predictive Control

Abstract

This dissertation explores several methods for reducing the computational cost of implementing Model Predictive Control (MPC) in real-time systems. MPC is a feedback control strategy that has seen wide adoption, both in academia and industry, due to its ability to systematically account for constraints. However, MPC can be difficult to implement in practice since MPC inputs are generated by solving a constrained Optimal Control Problem (OCP) at each time step. Thus, onboard processors must be capable of solving these OCPs faster than the required sampling period of the controller. This is particularly challenging in applications with fast dynamics and limited onboard computing power (e.g., aerospace and automotive applications). Furthermore, the algorithms used to solve these OCPs must reliable to be useful in real-world applications. The contributions of this dissertation are as follows.

First, I present two supervisory strategies for reducing the computational cost of linear-quadratic MPC with state and control constraints. These strategies augment the reference command supplied to an MPC policy in manner that ensures asymptotic stability can be maintained with shorter prediction horizons. Hence, the prediction horizon (and consequentially the computational cost) of the MPC policy can be reduced without sacrificing asymptotic stability of the resulting closed-loop system. The first strategy is a stability governor that improves the closed-loop properties of MPC without terminal stability constraints. The second strategy is feasibility governor that reduces the prediction horizon length necessary for recursive feasibility of an MPC policy with previewed disturbance information.

Second, I present three strategies for suboptimal and time-distributed MPC. These approaches compute MPC inputs by performing a limited number of iterations of an optimization algorithm at each time step. To begin, I derive a closed-form bound on number of iterations per time step required to asymptotically stabilize a linear system controlled by suboptimal MPC with control constraints. Thereafter, these results are extended to a shrinking horizon MPC formulation where the control objective is to navigate the system to a terminal set over a finite time interval. Finally, I present a supervisory strategy that reduces the online number of iterations required to implement a suboptimal MPC strategy.

Third, I present an optimizer-specific supervisory strategy for linear-quadratic MPC with state and control constraints. The proposed approach consists of three key components: First, a log-domain interior-point method used to solve the receding horizon OCPs; second, a method of warm-starting this optimizer by using the MPC solution from the previous time step; and third, a computational governor that expands the closed-loop region of attraction and bounds the suboptimality of the warm-start by altering the reference command provided to the OCP. The proposed scheme reduces the computational cost of implementing MPC by simultaneously allowing for the use of shorter prediction horizons and by ensuring that the optimization problems are well-initialized.

Finally, I present a framework for implementing log-domain interior-point quadratic programming methods (LDIPMs) using inexact Newton steps. A generalized inexact iteration scheme is established that is globally convergent and locally quadratically convergent towards centered points if the residual of the inexact Newton step satisfies a set of termination criteria. Three inexact LDIPM implementations based on the conjugate gradient (CG) method are developed using this framework.