Multistage Suboptimal Model Predictive Control With Improved Computational Efficiency

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Xiaotao Liu ◽  
Daniela Constantinescu ◽  
Yang Shi
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
The State ◽  
Admissible Set ◽  
Admissible Sets ◽  
Prediction Horizon ◽  
Terminal Set ◽  
Minimum Number ◽  
System States ◽  
The Stability

This paper proposes a multistage suboptimal model predictive control (MPC) strategy which can reduce the prediction horizon without compromising the stability property. The proposed multistage MPC requires a precomputed sequence of j-step admissible sets, where the j-step admissible set is the set of system states that can be steered to the maximum positively invariant set in j control steps. Given the precomputed admissible sets, multistage MPC first determines the minimum number of steps M required to drive the state to the terminal set. Then, it steers the state to the (M – N)-step admissible set if M > N, or to the terminal set otherwise. The paper presents the offline computation of the admissible sets, and shows the feasibility and stability of multistage MPC for systems with and without disturbances. A numerical example illustrates that multistage MPC with N = 5 can be used to stabilize a system which requires MPC with N ≥ 14 in the absence of disturbances, and requires MPC with N ≥ 22 when affected by disturbances.

scholarly journals Experimental Validation of a Guaranteed Nonlinear Model Predictive Control

Algorithms ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 248
Author(s):  
Mohamed Fnadi ◽  
Julien Alexandre dit Sandretto
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Nonlinear Model ◽  
Interval Analysis ◽  
Optimization Procedure ◽  
The State ◽  
Nonlinear Model Predictive Control ◽  
Control Input ◽  
Time Step ◽  
Prediction Horizon

This paper combines the interval analysis tools with the nonlinear model predictive control (NMPC). The NMPC strategy is formulated based on an uncertain dynamic model expressed as nonlinear ordinary differential equations (ODEs). All the dynamic parameters are identified in a guaranteed way considering the various uncertainties on the embedded sensors and the system’s design. The NMPC problem is solved at each time step using validated simulation and interval analysis methods to compute the optimal and safe control inputs over a finite prediction horizon. This approach considers several constraints which are crucial for the system’s safety and stability, namely the state and the control limits. The proposed controller consists of two steps: filtering and branching procedures enabling to find the input intervals that fulfill the state constraints and ensure the convergence to the reference set. Then, the optimization procedure allows for computing the optimal and punctual control input that must be sent to the system’s actuators for the pendulum stabilization. The validated NMPC capabilities are illustrated through several simulations under the DynIbex library and experiments using an inverted pendulum.

scholarly journals Position Control of a Flexible Joint via Explicit Model Predictive Control: An Experimental Implementation

2019 ◽  
Vol 3 (3) ◽  
pp. 146-156 ◽  
Author(s):  
Massoud Hemmasian Ettefagh ◽  
Mahyar Naraghi ◽  
Farzad Towhidkhah
Keyword(s):  
Model Predictive Control ◽  
State Space ◽  
Predictive Control ◽  
Position Control ◽  
The State ◽  
Experimental Plant ◽  
Explicit Model ◽  
Flexible Joint ◽  
Prediction Horizon ◽  
Explicit Model Predictive Control

This paper experimentally controls a flexible joint via explicit model predictive control (Explicit MPC) method. The scheme divides the state space into different partitions, then solves the associated multi parametric optimization in off-line computations. The result stores in a look-up table to be used in on-line algorithm. First, the state space equations of the flexible joint are derived and linearized around the working point. Then, in order to meet the plant’s specifications, desired performance and the limitation of processor/memory, the constraints, weights, sampling time and prediction horizon are determined for the system. Finally, the algorithm is applied on the experimental plant. Numerous simulations, the result of the experiment and comparison with other methods confirmed that the method was able to control the vibrations of the constrained flexible joint.

scholarly journals Reinforcement Learning of the Prediction Horizon in Model Predictive Control

2021 ◽  
Vol 54 (6) ◽  
pp. 314-320
Author(s):  
Eivind Bøhn ◽  
Sebastien Gros ◽  
Signe Moe ◽  
Tor Arne Johansen
Keyword(s):  
Reinforcement Learning ◽  
Model Predictive Control ◽  
Predictive Control ◽  
Prediction Horizon

scholarly journals Stable Model Predictive Control Design: Sequential Approach

2011 ◽  
Vol 62 (2) ◽  
pp. 99-103
Author(s):  
Vojtech Veselý
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Design Method ◽  
Control Design ◽  
Sequential Design ◽  
Stable Model ◽  
Sequential Approach ◽  
Prediction Horizon ◽  
Guaranteed Cost ◽  
One Step

Stable Model Predictive Control Design: Sequential Approach The paper addresses the problem of output feedback stable model predictive control design with guaranteed cost. The proposed design method pursues the idea of sequential design for N prediction horizon using one-step ahead model predictive control design approach. Numerical examples are given to illustrate the effectiveness of the proposed method.

Model Predictive Control for DC–DC Boost Converters With Reduced-Prediction Horizon and Constant Switching Frequency

2018 ◽  
Vol 33 (10) ◽  
pp. 9064-9075 ◽  
Author(s):  
Long Cheng ◽  
Pablo Acuna ◽  
Ricardo P. Aguilera ◽  
Jiuchun Jiang ◽  
Shaoyuan Wei ◽  
...  
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Switching Frequency ◽  
Boost Converters ◽  
Prediction Horizon

scholarly journals MODEL PREDICTIVE CONTROL TOOLBOX DESIGN FOR NONSTATIONARY PROCESS

2021 ◽  
Author(s):  
Oleksandr V. Stepanets ◽  
Yurii I. Mariiash
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Model Predictive Control ◽  
Predictive Control ◽  
Complex Structure ◽  
Nonstationary Process ◽  
Actual State ◽  
Quadratic Functional ◽  
Linear Quadratic ◽  
Prediction Horizon

Background. Model predictive control (MPC) approach is the basic feedback scheme, combined with high adaptive properties, which determines its successful use in the practice of design and operation of control systems. These advantages allow managing multidimensional objects with a complex structure, including nonlinearity, optimizing processes in real time within the constraints on controlled and managed variables, taking into account uncertainties in the task of objects and perturbations. Objective. The purpose of the paper is to design and analyse control system of carbon monoxide oxidation in the convector cavity based on MPC with linear-quadratic cost functional with constraint. Methods. The design of MPC is based on mathematical model of an object (relatively simple). At the current step, the prediction of object dynamic response on some final period of time (prediction horizon) is carried out; control optimization is performed, the purpose of which is to approximate the control variables of the prediction model to the corresponding setpoint on the predict horizon. The found optimal control is applied and measurement of an actual state of object at the end of a step is carried out. The prediction horizon is shifted one step further, and this algorithm are repeated. Results. The results of modeling the automatic control system show that the MPC approach provides maintenance of carbon dioxide content when changing oxygen consumption and overshoot caused by introduction bulk does not exceed 0.6 % that meets the technological requirements of the process. Conclusions. A fuse of the MPC and the quadratic functional given the constraints on the input signals is proposed. The problems of control degree of carbon oxidation in the convector cavity include non-stationarity, so the use of classical control methods is difficult. The MPC approach minimizes the cost function that characterizes the quality of the process. The predicted behaviour of a dynamic system will usually differ from its actual motion. The obtained quadratic functional is optimized to find the optimal control of degree of CO oxidation to CO2.

A tube-based robust MPC for duty-cycled rotation needle steering systems with bounded disturbances

2021 ◽  
pp. 014233122110430
Author(s):  
Zhi Qi ◽  
Qianyue Luo ◽  
Hui Zhang
Keyword(s):  
Model Predictive Control ◽  
Linear Model ◽  
Predictive Control ◽  
Control Method ◽  
Controller Design ◽  
Control Approach ◽  
Bounded State ◽  
Non Linear ◽  
System States ◽  
Trajectory Tracking Controller

In this paper, we aim to design the trajectory tracking controller for variable curvature duty-cycled rotation flexible needles with a tube-based model predictive control approach. A non-linear model is adopted according to the kinematic characteristics of the flexible needle and a bicycle method. The modeling error is assumed to be an unknown but bounded disturbance. The non-linear model is transformed to a discrete time form for the benefit of predictive controller design. From the application perspective, the flexible needle system states and control inputs are bounded within a robust invariant set when subject to disturbance. Then, the tube-based model predictive control is designed for the system with bounded state vector and inputs. Finally, the simulation experiments are carried out with tube-based model predictive control and proportional integral derivative controller based on the particle swarm optimisation method. The simulation results show that the tube-based model predictive control method is more robust and it leads to much smaller tracking errors in different scenarios.

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