Time-distributed optimization for real-time model predictive control: Stability, robustness, and constraint satisfaction

Liao‐McPherson, Dominic; Nicotra, Marco M.; Kolmanovsky, Ilya

doi:10.1016/j.automatica.2020.108973

Cited by 59 publications

(35 citation statements)

References 51 publications

(86 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One of the largest drawbacks of MPC is the computational footprint. Our controller uses the real‐time iteration scheme, 56 a kind of time‐distributed sequential quadratic programming, 58 a new QP solver, 21 and symbolic code generation tools 22 to reduce the worst case total execution time to around 715

μ

s on a 2.6 GHz rapid prototyping unit. Assuming a 256 MHz ECU and estimating the computation time using a clock speed scaling analysis we arrive at an estimate of

0.715 milliseconds \cdot \frac{2.6 GHz}{256 MHz} = 7.26

milliseconds which is slightly below the current 8 milliseconds sampling period.…”

Section: Discussionmentioning

confidence: 99%

“…56 This is a type of time-distributed sequential quadratic programming and, under appropriate conditions, convergence to a solution of the nonlinear OCP can be guaranteed over time. 57,58 The SMPC control update is then computed as…”

Section: Supervisory Controllermentioning

confidence: 99%

“…56 Despite only solving one QP per timestep, under appropriate conditions, the real-time iteration scheme converges to the solution of the nonlinear OCP. 57,58 By using exterior penalties we are only able to solve (23) and (22) in an approximate sense. In exchange we solve a single-linear system per timestep for each NMPC problem which significantly reduces the computational cost of the controller.…”

Section: Airpath Controllermentioning

confidence: 99%

“…We solve one instance of (27) per timestep as in the real‐time iteration scheme 56 . This is a type of time‐distributed sequential quadratic programming and, under appropriate conditions, convergence to a solution of the nonlinear OCP can be guaranteed over time 57,58 . The SMPC control update is then computed as

\begin{matrix} u_{k} = {[z_{k, 1} z_{k, 2}]}^{T}, & z_{k} = z_{k - 1} + Δ z_{k,} \end{matrix}

where z k = [ z k,1 z k,2 … z k,3N ] T .…”

Section: Controller Implementationmentioning

confidence: 99%

“…As with the SMPC problem this procedure is a variant of the real‐time iteration scheme 56 . Despite only solving one QP per timestep, under appropriate conditions, the real‐time iteration scheme converges to the solution of the nonlinear OCP 57,58 . By using exterior penalties we are only able to solve (23) and (22) in an approximate sense.…”

Section: Controller Implementationmentioning

confidence: 99%

See 4 more Smart Citations

Model predictive emissions control of a diesel engine airpath: Design and experimental evaluation

Liao‐McPherson

Huang

Kim

et al. 2020

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

This article presents the development and experimental validation of an emissions oriented model predictive controller for a diesel engine. The control objective is to minimize cumulative NOx and hydrocarbon emissions while limiting visible smoke production and without compromising fuel economy or torque response. This is accomplished by using a supervisory model predictive controller (SMPC) and nonlinear model predictive controller (NMPC) in tandem. The SMPC controller coordinates the exhaust gas recirculation (EGR) rate target and fuel supplied to the engine in real time to satisfy combustion quality constraints, while the NMPC controller tracks the EGR rate target by manipulating the EGR throttle, EGR valve, and variable geometry turbine. The NMPC controller uses MPC for feedforward and feedback in a novel configuration to simultaneously achieve fast tracking performance, disturbance rejection, and robustness. We demonstrate that the proposed diesel engine MPC controller is able to reduce cumulative emissions by 10% to 15% relative to a state of the art benchmark strategy when placed in closed loop with an engine on a transient dynamometer.

show abstract

μ

s on a 2.6 GHz rapid prototyping unit. Assuming a 256 MHz ECU and estimating the computation time using a clock speed scaling analysis we arrive at an estimate of

0.715 milliseconds \cdot \frac{2.6 GHz}{256 MHz} = 7.26

milliseconds which is slightly below the current 8 milliseconds sampling period.…”

Section: Discussionmentioning

confidence: 99%

Section: Supervisory Controllermentioning

confidence: 99%

Section: Airpath Controllermentioning

confidence: 99%

\begin{matrix} u_{k} = {[z_{k, 1} z_{k, 2}]}^{T}, & z_{k} = z_{k - 1} + Δ z_{k,} \end{matrix}

where z k = [ z k,1 z k,2 … z k,3N ] T .…”

Section: Controller Implementationmentioning

confidence: 99%

Section: Controller Implementationmentioning

confidence: 99%

See 3 more Smart Citations

Model predictive emissions control of a diesel engine airpath: Design and experimental evaluation

Liao‐McPherson

Huang

Kim

et al. 2020

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

show abstract

Superiority of model predictive control with robust and stable approach for sliding wheeled mobile systems in the presence of obstacles

Korayem,

Namdarpour,

Lademakhi

2024

Optim Control Appl Methods

View full text Add to dashboard Cite

In this paper, we present two distinct linear Model Predictive Control (MPC) methods for controlling mobile robots in the presence of obstacles while considering the wheel slip. Predictability of the controller enables the robot to automatically choose an alternative path to avoid obstacles. However, environmental conditions and disturbances, including slip, may impact the system model. Therefore, to accurately represent the system, slip angle and slip ratio are factored into the modeling process. Then the kinematic model is linearized using the successive method to reduce computational cost. Next, both Stable MPC (SMPC) and Robust MPC have been designed and implemented on the linearized time‐variant model to control the robot. The superiority of the robust predictive control method over the stable method has been discussed in terms of safety and optimal performance considering wheel slip. Finally, based on experimental tests, it has been found that the robust predictive controller is more effective than stable control when the surface is slippery and there is an obstacle in front of the robot. However, in a case where the wheel slip is neglectable, SMPC can be a better choice in presence of obstacles due to the lower computational cost.

show abstract

High‐order control barrier functions‐based optimization control for time‐varying nonlinear systems with full‐state constraints: A dynamic sub‐safe set approach

Wang

Peng

et al. 2023

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

Summary This study focuses on the problems of safety control and stabilization for time‐varying nonlinear systems in the presence of time‐varying full‐state constraints. High‐order control barrier functions (HoCBFs) without the assumption of forward completeness are introduced to prevent high‐relative degree constraint violations. The activated HoCBFs, which determine the dynamic sub‐safe sets, are proposed to indicate that the state constraints are already or about to be violated. Subsequently, the HoCBFs‐based controller is designed to obtain the admissible control set by utilizing the quadratic programming (QP) with activated HoCBFs conditions to synthesize the nominal controller. An explicit analytical expression is provided for the HoCBFs‐based controller. The input‐to‐state stable (ISS) property of the closed‐loop system under the proposed controller is investigated to ensure that all closed‐loop states remain bounded and achieve asymptotic tracking without violation of the constraint. Moreover, a Lyapunov‐like constraint is added to the HoCBFs‐based QP problem such that the solvability of the QP problem is a sufficient condition for the system ISS. The effectiveness of the proposed HoCBFs‐based control method for time‐varying nonlinear systems is illustrated using a numerical example.

show abstract

Time-distributed optimization for real-time model predictive control: Stability, robustness, and constraint satisfaction

Cited by 59 publications

References 51 publications

Model predictive emissions control of a diesel engine airpath: Design and experimental evaluation

Model predictive emissions control of a diesel engine airpath: Design and experimental evaluation

Superiority of model predictive control with robust and stable approach for sliding wheeled mobile systems in the presence of obstacles

High‐order control barrier functions‐based optimization control for time‐varying nonlinear systems with full‐state constraints: A dynamic sub‐safe set approach

Contact Info

Product

Resources

About