Dual-mode Model Predictive Control Research Articles

Disturbance Rejection Event-Triggered Robust Model Predictive Control for Tracking of Constrained Uncertain Robotic Manipulators.

A novel hierarchical control framework combining computed-torque-like control (CTLC) with disturbance-observer-based event-triggered robust model predictive control (DO-ET-RMPC) is proposed for the trajectory tracking control of robotic manipulators with bounded disturbances and state and control input constraints. The CTLC approach is first used to cancel the exact nonlinear dynamics of the original tracking error system to obtain a set of decoupling linear tracking error subsystems, thus reducing the optimization complexity of model predictive control (MPC). The composite DO-ET-RMPC scheme is then developed based on the so-called dual-mode MPC approach to robustly stabilize the tracking error subsystems, which could improve the robustness of MPC and save its computational resources simultaneously. The continuous-time theoretical properties of the DO-ET-RMPC scheme, considering disturbances and state and control input constraints simultaneously, are provided for the first time, including the avoidance of Zeno behavior, robust constraint satisfaction, recursive feasibility, and stability. In the end, the superiorities of the proposed control scheme are verified by the comparative simulations.

Optimization of the model predictive control meta-parameters through reinforcement learning

Model predictive control (MPC) is increasingly being considered for control of fast systems and embedded applications. However, MPC has some significant challenges for such systems, such as its high computational complexity. Further, the MPC parameters must be tuned, which is largely a trial-and-error process that affects the control performance, the robustness, and the computational complexity of the controller to a high degree. This paper presents a multivariate optimization method based on reinforcement learning (RL) that automatically tunes the control algorithm’s parameters from data to achieve optimal closed-loop performance. The main contribution of our method is the inclusion of state-dependent optimization of the meta-parameters of MPC, i.e. parameters that are non-differentiable wrt. the MPC solution. Our control algorithm is based on an event-triggered MPC, where we learn when the MPC should be re-computed, and a dual-mode MPC and linear state feedback control law applied in between MPC computations. We formulate a novel mixture-distribution RL policy determining the meta-parameters of our control algorithm and show that with joint optimization we achieve improvements that do not present themselves with univariate optimization of the same parameters. We demonstrate our framework on the inverted pendulum control task, reducing the total computation time of the control system by 36% while also improving the control performance by 18.4%.

MPC-Based Cooperative Enclosing for Nonholonomic Mobile Agents Under Input Constraint and Unknown Disturbance.

In this article, a model predictive control (MPC)-based cooperative target enclosing control approach is investigated for multiple nonholonomic mobile agents with input constraints and unknown disturbances. The agents are required to move along a desired circular orbit centered at a stationary target and maintain an even distribution on the orbit. Based on a dual-mode MPC strategy, a cooperative target enclosing control law is designed by only using the local sensing information. When the agents are inside a terminal region, a locally cooperative stabilizing control law is designed with a signal function defined componentwise part compensating for the unknown disturbances. A robust MPC algorithm is designed for the agents to enter the terminal region in finite time. Global asymptotic stability is guaranteed for multiple nonholonomic mobile agents with input constraints and unknown disturbances. Simulation results illustrate the effectiveness of the proposed approach.

Model Predictive Control-Based Attitude Control of Under-Actuated Spacecraft Using Solar Radiation Pressure

An attitude control strategy for an under-actuated spacecraft with two reaction wheels is proposed, using the active assistance of solar radiation pressure torque. By changing the rotation angles of the solar panels, the magnitude and direction of the solar radiation pressure torque is assumed to be adjustable in this paper. The attitude dynamic model of a rigid spacecraft with two reaction wheels and two solar panels is established and transformed into the form of a non-linear system. An integrated control scheme based on dual-mode model predictive control is proposed, which obtains the rotation speeds of the solar panels and the rotation accelerations of the reaction wheels directly as control quantities. Using this control method, not only are the constraints of rotation speeds and rotation angles of the panels satisfied, but also the robustness of the closed-loop system is ensured. The simulation results prove the validity of the proposed control method.

Guaranteed Collision-Free Reference Tracking in Constrained Multi Unmanned Vehicle Systems

In this article, we face the reference tracking control problem for a system of heterogeneous multiple unmanned vehicles (MUVs) moving in a 2-D planar environment. We consider a scenario, where each vehicle follows a trajectory imposed by a local planner and where each unmanned vehicle can have different linear dynamics as well as different constraints and disturbances. In this contest, we design a novel control architecture, where a centralized traffic manager, in conjunction with ad-hoc designed local vehicle controllers, is capable of ensuring the absence of collisions. The proposed solution is obtained by exploiting, for the local vehicles’ controllers, a dual-mode model-predictive controller and, for the traffic manager, set-theoretic and controllability properties. Moreover, after modeling the potential vehicle collisions with a graph, connectivity arguments are used to obtain an optimal collision resolution, which minimizes the number of vehicles that need to be stopped. The resulting control scheme ensures collision-free signal tracking. Results of the simulation conducted on an MUV system are shown to provide tangible evidence of the features of the proposed framework.

Event‐triggered MPC for linear systems with bounded disturbances: An accumulated error based approach

A novel accumulated error based event-triggered model predictive control (MPC) algorithm is put forward on the basis of the dual-mode control strategy and state-feedback control for constrained continuous-time linear time-invariant (LTI) systems with constraints and bounded disturbances. First, a new event-triggered mechanism (ETM) is constructed based on the accumulated error (AE) between the optimal state trajectory and the real state trajectory. Next, in order to stabilize the system, the dual-mode event-triggered MPC strategy is established. Then, sufficient conditions are established to guarantee the algorithm feasibility, system stability, and to avoid the Zeno behavior. Finally, the numerical simulation shows the validity of the algorithm.

Model predictive longitudinal control for autonomous electric vehicles with tracking differentiator

ABSTRACT In this paper, the longitudinal control is investigated for an autonomous electric vehicle with a tracking differentiator. The autonomous electric vehicle is modelled as a longitudinal system for model predictive control. The tracking differentiator is proposed to obtain the transition profile and acceleration information. A dual-mode model predictive controller is designed for the longitudinal system to find the optimal control input, which is restricted with some constraints on the desired acceleration and its increment. Both iterative feasibility and its stability issues are analysed for the longitudinal system under the dual-mode model predictive controller. Experimental results are given to show the effectiveness of the proposed strategy.

A Nonlinear Model Predictive Control with Enlarged Region of Attraction via the Union of Invariant Sets

In the dual-mode model predictive control (MPC) framework, the size of the stabilizable set, which is also the region of attraction, depends on the terminal constraint set. This paper aims to formulate a larger terminal set for enlarging the region of attraction in a nonlinear MPC. Given several control laws and their corresponding terminal invariant sets, a convex combination of the given sets is used to construct a time-varying terminal set. The resulting region of attraction is the union of the regions of attraction from each invariant set. Simulation results show that the proposed MPC has a larger stabilizable initial set than the one obtained when a fixed terminal set is used.

Robust model predictive control based on recurrent multi‐dimensional Taylor network for discrete‐time non‐linear time‐delay systems

This study is concerned with the robust model predictive control (MPC) based on recurrent multi-dimensional Taylor network (RMTN) for the discrete-time non-linear time-delay systems. Regarding the MPC algorithm for the discrete-time time-delay systems, the existing literature only considers the linear case. In this study, by designing the suitable terminal cost and terminal region, the MPC scheme is firstly investigated for the non-linear case. Meanwhile, to reduce the computational burden of MPC using the existing model types (e.g. recurrent neural network) as the identified model, an RMTN possessing the concise structure and high computational efficiency is constructed to approximate the state-space model of the system. After trained by the backpropagation through time algorithm, the RMTN obtaining the high accuracy of prediction over a long-range horizon is capable of serving as the prediction model in the MPC scheme. Furthermore, aiming at alleviating the adverse effect of the inevitable identification error, the tube-based MPC is proposed via leveraging dual-mode MPC to guarantee that actual trajectory is contained within a robust tube. The stability of the considered system is proved theoretically, and numerical simulation is employed to validate the effectiveness of the proposed method.

Dual-mode dynamic window approach to robot navigation with convergence guarantees

In this paper, a novel, dual-mode model predictive control framework is introduced that combines the dynamic window approach to navigation with generic path planning techniques through a dual-mode model predictive control framework. The planned path adds information on the connectivity of the free space to the obstacle avoidance capabilities of the dynamic window approach. This allows for guaranteed convergence to a goal location while navigating through an unknown environment at relatively high speeds. The framework is applied in a combined simulation/hardware implementation to demonstrate the computational feasibility and the ability to cope with the constraints of a dynamic system.

MPC-Based Offset-Free Tracking Control for Intermittent Transonic Wind Tunnel

This paper addresses the offset-free model predictive control (MPC) for the intermittent transonic wind tunnel (ITWT). The offset-free property holds by introducing the controller state equation which introduces an integral action, while the controller state can keep as the decision variable. The infinite-horizon control moves are parameterized as a sequence of degrees of freedom followed by a control law. The terminal constraint set and terminal control law are designed based on the asymptotic invariance ellipsoid in which physical constraints are satisfied. The previous dual-mode MPC is appropriately modified withholding the closed-loop stability. Simulation results verify the effectiveness of the proposed methods.

Dual-Mode Model Predictive Control of an Omnidirectional Wheeled Inverted Pendulum

This article describes the position and heading control of a novel form of omnidirectional wheeled inverted pendulum platform known as a collinear Mecanum drive. This concept uses four collinear Mecanum wheels to balance in a similar manner to a typical two-wheeled inverted pendulum while also being able to simultaneously translate directly along its balance axis. Control is performed using a constrained time-optimal infinite horizon model predictive controller, with feasibility maintained across the full reference input set. Explored in this article is the derivation of the system dynamics model and controller, a systematic approach to selection of controller parameters and analysis of their effect on control performance and complexity, and an evaluation of the controller's efficacy in both simulation and on a real-world experimental prototype for simple and complex trajectories.

A First Course in Predictive Control, Second Edition [Bookshelf

As the demand for individualized products increases, there is a need for advanced control at the supervisory level, where model predictive control (MPC) becomes an established solution in industry. This is an excellent text that provides numerous MPC algorithms supported by highly relevant, illustrative industry examples. The book opens with a comprehensive chapter about industry’s need for predictive control, reminding readers that MPC originated in business and expanded into academia, where it captured the attention of several seminal researchers. Addresses some of the following topics: major concepts of PID; properties of model-based control and requirements of MPCs; predictive function control (PFC); basic predictive control algorithms; principle components of dual-mode MPC; and constraint handling mechanisms. The book has a set of Matlab code (from MathWorks) and sources to help readers reproduce the illustrations in each chapter. A First Course in Predictive Control can be considered as a textbook, since it includes introductory subchapters to guide lecturers and help filter the sections for teaching from areas outside the course. In summary, this book provides an excellent course in MPC, presented in the form of a textbook, and great support for lecturers. It also offers a substantial starting point for MPC-related research for industrial applications.

Generic framework for valve stiction detection and compensation with ANFIS-activated dual-mode MPC

Due to its continuous motion, control valve performance tends to deteriorate over time due to the presence of static-friction or also known as stiction. This, in turn, leads to high variability in product quality and an increased frequency of valve maintenance. Model Predictive Control (MPC) based stiction compensation methods can remove oscillations caused by stiction but it assumes that stiction is known a –priori to exist in the related loops. To overcome this limitation, an integrated framework is proposed to automate the detection of stiction using only process variable and controller output while compensating for stiction with MPC. The detection algorithm, which was validated using industrial data, uses an adaptive neuro-fuzzy inference system (ANFIS). Out of the 78 benchmark industrial loops tested, the proposed Intuitive ANFIS-based Method (IAM) has a detection accuracy of 65%, placing it on par with the best of the currently available methods reported in the literature for loops with stiction. Within the proposed framework, the detection component only activates the MPC-based compensation when needed. In a simulation of a multivariable process, it is demonstrated that the dual-mode MPC manages to eliminate oscillation caused by stiction with no chattering. This results in better overall performance when controlling a loop throughout the service life of the valve.

Energy Efficiency and Tracking Performance Evaluation for Dual-Mode Model Predictive Control of HVAC Systems

This paper presents evaluation of the energy consumption and tracking performance associated with the use of a recently introduced dual-mode model predictive controller (DMMPC) for control of a heating, ventilation, and air conditioning (HVAC) system. The study was conducted using detailed simulations of an HVAC system, which included a multizone air loop, a water loop, and a chiller. Energy consumption and tracking performance are computed from the simulations and evaluated in the presence of different types and magnitudes of noise and disturbances. Performance of the DMMPC is compared with a baseline proportional-integral-derivative (PID) control structure commonly used for HVAC system control, and this comparison showed clear and consistent superiority of the DMMPC.

One Layer Nonlinear Economic Closed-Loop Generalized Predictive Control for a Wastewater Treatment Plant

The main scope of this paper is the proposal of a new single layer Nonlinear Economic Closed-Loop Generalized Predictive Control (NECLGPC) as an efficient advanced control technique for improving economics in the operation of nonlinear plants. Instead of the classic dual-mode MPC (model predictive controller) schemes, where the terminal control law defined in the terminal region is obtained offline solving a linear quadratic regulator problem, here the terminal control law in the NECLGPC is determined online by an unconstrained Nonlinear Generalized Predictive Control (NGPC). In order to make the optimization problem more tractable two considerations have been made in the present work. Firstly, the prediction model consisting of a nonlinear phenomenological model of the plant is expressed with linear structure and state dependent matrices. Secondly, instead of including the nonlinear economic cost in the objective function, an approximation of the reduced gradient of the economic function is used. These assumptions allow us to design an economic unconstrained nonlinear GPC analytically and to state the NECLGPC allow for the design of an economic problem as a QP (Quadratic Programing) problem each sampling time. Four controllers based on GPC that differ in designs and structures are compared with the proposed control technique in terms of process performance and energy costs. Particularly, the methodology is implemented in the N-Removal process of a Wastewater Treatment Plant (WWTP) and the results prove the efficiency of the method and that it can be used profitably in practical cases.

Addressing infinite-horizon optimization in MPC via Q-learning

Model predictive control (MPC) is the standard approach to infinite-horizon optimal control which usually optimizes a finite initial fragment of the cost function so as to make the problem computationally tractable. Globally optimal controllers are usually found by Dynamic Programming (DP). The computations involved in DP are notoriously hard to perform, especially in online control. Therefore, different approximation schemes of DP, the so-called “critics”, were suggested for infinite-horizon cost functions. This work proposes to incorporate such a critic into dual-mode MPC as a particular means of addressing infinite-horizon optimal control. The proposed critic is based on Q-learning and is used for online approximation of the infinite-horizon cost. Stability of the new approach is analyzed and certain sufficient stabilizing constraints on the critic are derived. A case study demonstrates the applicability.

Aperiodic Robust Model Predictive Control for Constrained Continuous-Time Nonlinear Systems: An Event-Triggered Approach.

The event-triggered control is a promising solution to cyber-physical systems, such as networked control systems, multiagent systems, and large-scale intelligent systems. In this paper, we propose an event-triggered model predictive control (MPC) scheme for constrained continuous-time nonlinear systems with bounded disturbances. First, a time-varying tightened state constraint is computed to achieve robust constraint satisfaction, and an event-triggered scheduling strategy is designed in the framework of dual-mode MPC. Second, the sufficient conditions for ensuring feasibility and closed-loop robust stability are developed, respectively. We show that robust stability can be ensured and communication load can be reduced with the proposed MPC algorithm. Finally, numerical simulations and comparison studies are performed to verify the theoretical results.

A Dual-Mode Model Predictive Control Algorithm Trajectory Tracking in Discrete-Time Nonlinear Dynamic Systems

In this paper, a dual-mode model predictive/linear control method is presented, which extends the concept of dual-mode model predictive control (MPC) to trajectory tracking control of nonlinear dynamic systems described by discrete-time state-space models. The dual-mode controller comprises of a time-varying linear control law, implemented when the states lie within a sufficiently small neighborhood of the reference trajectory, and a model predictive control strategy driving the system toward that neighborhood. The boundary of this neighborhood is characterized so as to ensure stability of the closed-loop system and terminate the optimization procedure in a finite number of iterations, without jeopardizing the stability of the closed-loop system. The developed controller is applied to the central air handling unit (AHU) of a two-zone variable air volume (VAV) heating, ventilation, and air conditioning (HVAC) system.

Robust model predictive control for constrained continuous-time nonlinear systems

ABSTRACTIn this paper, a robust model predictive control (MPC) is designed for a class of constrained continuous-time nonlinear systems with bounded additive disturbances. The robust MPC consists of a nonlinear feedback control and a continuous-time model-based dual-mode MPC. The nonlinear feedback control guarantees the actual trajectory being contained in a tube centred at the nominal trajectory. The dual-mode MPC is designed to ensure asymptotic convergence of the nominal trajectory to zero. This paper extends current results on discrete-time model-based tube MPC and linear system model-based tube MPC to continuous-time nonlinear model-based tube MPC. The feasibility and robustness of the proposed robust MPC have been demonstrated by theoretical analysis and applications to a cart-damper springer system and a one-link robot manipulator.