skip to main content


Title: A Computationally Governed Log-domain Interior-point Method for Model Predictive Control
This paper introduces a computationally efficient approach for solving Model Predictive Control (MPC) reference tracking problems with state and control constraints. The approach consists of three key components: First, a log-domain interior-point quadratic programming method that forms the basis of the overall approach; second, a method of warm-starting this optimizer by using the MPC solution from the previous timestep; and third, a computational governor that bounds the suboptimality of the warm-start by altering the reference command provided to the MPC problem. As a result, the closed-loop system is altered in a manner so that MPC solutions can be computed using fewer optimizer iterations per timestep. In a numerical experiment, the computational governor reduces the worst-case computation time of a standard MPC implementation by 90%, while maintaining good closed-loop performance.  more » « less
Award ID(s):
1904394
NSF-PAR ID:
10409013
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Proceedings of 2022 American Control Conference (ACC)
Page Range / eLocation ID:
900 to 905
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. This paper illustrates an approach to integrate learning into spacecraft automated rendezvous, proximity maneuvering, and docking (ARPOD) operations. Spacecraft rendezvous plays a significant role in many spacecraft missions including orbital transfers, ISS re-supply, on-orbit refueling and servicing, and debris removal. On one hand, precise modeling and prediction of spacecraft dynamics can be challenging due to the uncertainties and perturbation forces in the spacecraft operating environment and due to multi-layered structure of its nominal control system. On the other hand, spacecraft maneuvers need to satisfy required constraints (thrust limits, line of sight cone constraints, relative velocity of approach, etc.) to ensure safety and achieve ARPOD objectives. This paper considers an application of a learning-based reference governor (LRG) to enforce constraints without relying on a dynamic model of the spacecraft during the mission. Similar to the conventional Reference Governor (RG), the LRG is an add-on supervisor to a closed-loop control system, serving as a pre-filter on the command generated by the ARPOD planner. As the RG, LRG modifies, if it becomes necessary, the command to a constraint-admissible reference to enforce specified constraints. The LRG is distinguished, however, by the ability to rely on learning instead of an explicit model of the system, and guarantees constraints satisfaction during and after the learning. Simulations of spacecraft constrained relative motion maneuvers on a low Earth orbit are reported that demonstrate the effectiveness of the proposed approach. 
    more » « less
  2. This paper introduces the Feasibility Governor (FG): an add-on unit that enlarges the region of attraction of Model Predictive Control by manipulating the reference to ensure that the underlying optimal control problem remains feasible. The FG is developed for linear systems subject to polyhedral state and input constraints. Offline computations using polyhedral projection algorithms are used to construct the feasibility set. Online implementation relies on the solution of a convex quadratic program that guarantees recursive feasibility. The closed-loop system is shown to satisfy constraints, achieve asymptotic stability, and exhibit zero-offset tracking. 
    more » « less
  3. The trend toward soft wearable robotic systems creates a compelling need for new and reliable sensor systems that do not require a rigid mounting frame. Despite the growing use of inertial measurement units (IMUs) in motion tracking applications, sensor drift and IMU-to-segment misalignment still represent major problems in applications requiring high accuracy. This paper proposes a novel 2-step calibration method which takes advantage of the periodic nature of human locomotion to improve the accuracy of wearable inertial sensors in measuring lower-limb joint angles. Specifically, the method was applied to the determination of the hip joint angles during walking tasks. The accuracy and precision of the calibration method were accessed in a group of N = 8 subjects who walked with a custom-designed inertial motion capture system at 85% and 115% of their comfortable pace, using an optical motion capture system as reference. In light of its low computational complexity and good accuracy, the proposed approach shows promise for embedded applications, including closed-loop control of soft wearable robotic systems. 
    more » « less
  4. Abstract

    In recent years, cyber‐security of networked control systems has become crucial, as these systems are vulnerable to targeted cyberattacks that compromise the stability, integrity, and safety of these systems. In this work, secure and private communication links are established between sensor–controller and controller–actuator elements using semi‐homomorphic encryption to ensure cyber‐security in model predictive control (MPC) of nonlinear systems. Specifically, Paillier cryptosystem is implemented for encryption‐decryption operations in the communication links. Cryptosystems, in general, work on a subset of integers. As a direct consequence of this nature of encryption algorithms, quantization errors arise in the closed‐loop MPC of nonlinear systems. Thus, the closed‐loop encrypted MPC is designed with a certain degree of robustness to the quantization errors. Furthermore, the trade‐off between the accuracy of the encrypted MPC and the computational cost is discussed. Finally, two chemical process examples are employed to demonstrate the implementation of the proposed encrypted MPC design.

     
    more » « less
  5. null (Ed.)
    The performance of hierarchical Model Predictive Control (MPC) is highly dependent on the mechanisms used to coordinate the decisions made by controllers at different levels of the hierarchy. Conventionally, reference tracking serves as the primary coordination mechanism, where optimal state and input trajectories determined by upper-level controllers are communicated down the hierarchy to be tracked by lower-level controllers. As such, significant tuning is required for each controller in the hierarchy to achieve the desired closed-loop system performance. This paper presents a novel terminal cost coordination mechanism using constrained zonotopes, designed to improve system performance under hierarchical control. These terminal costs allow lower-level controllers to balance both short- and long-term control performance without the need for controller tuning. Unlike terminal costs widely used to guarantee MPC stability, the proposed terminal costs are time-varying and computed on-line based on the optimal state trajectory of the upper-level controllers. A numerical example demonstrates the provable performance benefits achieved using the proposed terminal cost coordination mechanism. 
    more » « less