Tube Model Predictive Control Research Articles

Convex distributed robust model predictive control for collision and obstacle avoidance

AbstractThe article proposes a convex distributed robust model predictive control algorithm for collision avoidance in multi‐agent systems with additive disturbances, which utilizes the concept of tube model predictive control to address the disturbances. To tackle the coupled collision avoidance constraints, each agent integrates assumed nominal position and input trajectories from its neighbors, rather than relying on actual ones. Compatibility constraints are then designed using the normal vector of the constructed separating hyperplanes for collision avoidance and the residual collision avoidance margin of the optimal solutions at the last time step to restrict deviations between assumed and actual trajectories and ensure consistency among the agents. The nonconvex collision and obstacle avoidance constraints are convexified using the concept of safe sets, transforming them into time‐varying closed polyhedral constraints while accounting for the impact of disturbances. Particularly, the residual collision avoidance margin is incorporated into the construction of safe sets for the satisfaction of coupled collision avoidance constraints. Consequently, the original collision avoidance optimal control problems can be efficiently and simultaneously solved for all agents using standard quadratic programming techniques. Under the design of local terminal constraint sets for each agent, the proposed algorithm ensures a rigorous analysis of robust constraint satisfaction for collision avoidance constraints, as well as an assessment of recursive feasibility and closed‐loop stability. The effectiveness of the algorithm is demonstrated through an illustrative example, and simulation results validate its ability to successfully achieve collision and obstacle avoidance even in the presence of disturbances.

Dynamic modeling and contraction metric-based tube model predictive control for mineral hydraulic collection

Efficient mineral hydraulic collection is a key issue in the mining of deep-sea minerals, where the collection efficiency is related to the lifted fluid velocity and the mineral particle velocity. In this paper, a robust control contraction metric (RCCM)-based tube model predictive control (Tube-MPC) for efficient mineral hydraulic collection is proposed. Firstly, a simplified control model is designed with empirical formula of hydrodynamic forces to avoid the computational burden in solution of the fluid equations. Secondly, a nonlinear programing problem (NLP) for efficiency optimization is formulated to calculate the nominal control law and the optimal state. To address external disturbance and model mismatch from the simplified model, a robust control contraction metric is utilized to calculate the feedback control law to track the optimal state. Finally, numerical simulations and experiments are conducted to verify the mineral hydraulic collection performance of the control strategy.

Disturbance rejection tube model predictive levitation control of maglev trains

Magnetic levitation control technology plays a significant role in maglev trains. Designing a controller for the levitation system is challenging due to the strong nonlinearity, open-loop instability, and the need for fast response and security. In this paper, we propose a Disturbance-Observe-based Tube Model Predictive Levitation Control (DO-TMPLC) scheme combined with a feedback linearization strategy for the levitation system. The proposed strategy incorporates state constraints and control input constraints, i.e., the air gap, the vertical velocity, and the current applied to the coil. A feedback linearization strategy is used to cancel the nonlinearity of the tracking error system. Then, a disturbance observer is implemented to actively compensate for disturbances while a TMPLC controller is employed to alleviate the remaining disturbances. Furthermore, we analyze the recursive feasibility and input-to-state stability of the closed-loop system. The simulation results indicate the efficacy of the proposed control strategy.

Robust Energy Management for Multi-Microgrids Based on Distributed Dynamic Tube Model Predictive Control

Robust Energy Management for Multi-Microgrids Based on Distributed Dynamic Tube Model Predictive Control

Tube-Based Event-Triggered Path Tracking for AUV against Disturbances and Parametric Uncertainties

In order to enhance the performance of disturbance rejection in AUV’s path tracking, this paper proposes a novel tube-based event-triggered path-tracking strategy. The proposed tracking strategy consists of a speed control law and an event-triggered tube model predictive control (tube MPC) scheme. Firstly, the speed control law using linear model predictive control (LMPC) technology is obtained to converge the nominal path-tracking deviation. Secondly, the event-triggered tube MPC scheme is used to calculate the optimal control input, which can enhance the performance of disturbance rejection. Considering the nonlinear hydrodynamic characteristics of AUV, a linear matrix inequality (LMI) is formulated to obtain tight constraints on the AUV and the feedback matrix. Moreover, to enhance real-time performance, tight constraints and the feedback matrix are all calculated offline. An event-triggering mechanism is used. When the surge speed change command does not exceed the upper bound, adaptive tight constraints are obtained. Finally, numerical simulation results show that the proposed tube-based event-triggered path-tracking strategy can enhance the performance of disturbance rejection and ensure good real-time performance.

The implicit rigid tube model predictive control

A computationally efficient reformulation of the rigid tube model predictive control is developed. A unique feature of the derived formulation is the utilization of the implicit set representations. This novel formulation does not require any set algebraic operations to be performed explicitly, and its implementation requires merely the use of the standard optimization solvers.

Homothetic Tube Model Predictive Control for Nonlinear Systems

Homothetic tube model predictive control is generalized to the setting of nonlinear discrete time systems. The developed generalization is natural in the sense that the utilized assumptions in the nonlinear setting are suitably generalized variants of the related assumptions deployed in the linear case. The main analysis is carried out for Lipschitz systems, and it is subsequently extended to set–valued systems and other classes of nonlinear systems as well as particularized for parameterically uncertain linear systems. All desirable computational and structural properties of homothetic tube MPC are preserved.

Sliding mode-based adaptive tube model predictive control for robotic manipulators with model uncertainty and state constraints

Sliding mode-based adaptive tube model predictive control for robotic manipulators with model uncertainty and state constraints

Robust adaptive MPC using control contraction metrics

We present a robust adaptive model predictive control (MPC) framework for nonlinear continuous-time systems with bounded parametric uncertainty and additive disturbance. We utilize general control contraction metrics (CCMs) to parameterize a homothetic tube around a nominal prediction that contains all uncertain trajectories. Furthermore, we incorporate model adaptation using set-membership estimation. As a result, the proposed MPC formulation is applicable to a large class of nonlinear systems, reduces conservatism during online operation, and guarantees robust constraint satisfaction and convergence to a neighborhood of the desired setpoint. One of the main technical contributions is the derivation of corresponding tube dynamics based on CCMs that account for the state and input dependent nature of the model mismatch. Furthermore, we online optimize over the nominal parameter, which enables general set-membership updates for the parametric uncertainty in the MPC. Benefits of the proposed homothetic tube MPC and online adaptation are demonstrated using a numerical example involving a planar quadrotor.

Adaptive Tube Model Predictive Control for Manipulating Micro- and Nanoparticles in Fluid Suspensions Under Global External Fields

Adaptive Tube Model Predictive Control for Manipulating Micro- and Nanoparticles in Fluid Suspensions Under Global External Fields

Distributed tube model predictive control for string stability of heterogeneous vehicle platoons

This article develops a distributed tube model predictive control method to guarantee the string stability of the heterogeneous vehicle platoon under external disturbance and controller saturation. The error model of each vehicle is proposed based on the desired distance and velocity, where the coupled factor between vehicles is treated as a random disturbance. The linear feedback controller is devised to reject disturbances by keeping the actual trajectory within a tube around the nominal trajectory, and a model predictive controller is proposed by treating the input saturation and string stability as state constraints in the optimization problem. Compared with previous results, the proposed control strategy achieves a better performance of disturbance rejection and greatly reduces the online computation burden, which would be more favorable in engineering applications. The method proposed in this article is illustrated to be effective by simulation.

Input-mapping based data-driven model predictive control for unknown linear systems with bounded disturbances

The data-driven model predictive control (MPC) approach has been an effective tool for unknown constrained systems. However, most of the existing designs rely on the prior collected data sequence through offline trials, which may be affected by time-varying disturbances, or the online estimated system model with the non-trivial computation cost. This limits the applications of these designs. To alleviate these restrictions, in this paper, an input-mapping data-driven scheme is developed. This scheme online directly maps the future control policy and the predicted state to the past online noisy input/state data which are updated once new data come. This overcomes the limitations of previous designs. To ensure the system constraints, this scheme is combined with a tube MPC method and the proposed input-mapping data-driven tube MPC can guarantee the recursive feasibility and the input-to state stability. Two examples illustrate the advantages of the proposed method.

Fast Tube Model Predictive Control for Driverless Cars Using Linear Data-Driven Models

Model predictive control (MPC) has been widely applied to different aspects of autonomous driving, typically using nonlinear physically derived models for prediction. However, feedback control systems inherently correct for model errors, and thus in many applications it is sufficient to use a linear time-invariant (LTI) model for control design, especially when using robust control methods. This philosophy of approach appears to have been neglected in current driverless car research and is the research gap that we aim to address here. Namely, instead of deriving meticulous nonlinear physical models of vehicle dynamics and solving a correspondingly complex optimal control problem (OCP), we identify a low-order data-driven LTI model and handle its uncertainty via robust linear MPC methods. We develop a two-step control scheme for driverless cars based on tube MPC (TMPC), which introduces structural robustness, ensuring constraint compliance despite modeling error in the data-driven prediction model. Furthermore, we use fast optimization methods designed to exploit the special structure of the linear MPC problem. We evaluate the proposed control scheme using a vehicle model identified from real-world data and simulations in IPGCarmaker, where the model of the vehicle under control is inherently nonlinear and uses detailed 3-D physics. Our results show that an LTI model can be effectively used for the task of lane-keeping, that TMPC can prevent lane departure and possible collisions due to model uncertainty, and that linear models allow for several algorithmic improvements that can decrease computation time by an order of magnitude compared with naive MPC implementations.

Inverse-Dynamics- and disturbance-Observer-Based tube model predictive tracking control of uncertain robotic manipulator

A novel robust hierarchical multi-loop composite control scheme is proposed for the trajectory tracking control of robotic manipulators subject to constraints and disturbances. The inner loop based on inverse dynamics control is used to reduce the nonlinear tracking error system to a set of decoupled linear subsystems to alleviate the computational effort during the sequel optimization. The feasible regions of the equivalent state and control input of each subsystem can be computed efficiently by choosing an appropriate inertia matrix estimate. The external loop, relying on a set of separate disturbance-observer-based tube model predictive composite controllers, is used to robustly stabilize the decoupled subsystems. In particular, the disturbance observers are designed to compensate for the disturbances actively, while the tube model predictive controllers are used to reject the residual disturbances. The robust tightened constraints are obtained by calculating the outer-bounding-tube-type residual disturbance invariant sets of the closed-loop subsystems. Furthermore, the recursive feasibility and input-to-state stability of the closed-loop system are investigated. The effectiveness of the proposed control scheme is verified by the simulation experiment on a PUMA 560 robotic manipulator.

A Tube Model Predictive Control Method for Autonomous Lateral Vehicle Control Based on Sliding Mode Control.

This paper aims to enhance the lateral path tracking control of autonomous vehicles (AV) in the presence of external disturbances. While AV technology has made significant strides, real-world driving scenarios often pose challenges such as slippery or uneven roads, which can adversely affect the lateral path tracking control and reduce driving safety and efficiency. Conventional control algorithms struggle to address this issue due to their inability to account for unmodeled uncertainties and external disturbances. To tackle this problem, this paper proposes a novel algorithm that combines robust sliding mode control (SMC) and tube model predictive control (MPC). The proposed algorithm leverages the strengths of both MPC and SMC. Specifically, MPC is used to derive the control law for the nominal system to track the desired trajectory. The error system is then employed to minimize the difference between the actual state and the nominal state. Finally, the sliding surface and reaching law of SMC are utilized to derive an auxiliary tube SMC control law, which helps the actual system keep up with the nominal system and achieve robustness. Experimental results demonstrate that the proposed method outperforms conventional tube MPC, linear quadratic regulator (LQR) algorithms, and MPC in terms of robustness and tracking accuracy, especially in the presence of unmodeled uncertainties and external disturbances.

Direct data driven safety control for aircraft flight system-Part 1: the theory case

Purpose This new paper aims to combine the recent new contributions about direct data driven control and other safety property to form an innovative direct data driven safety control for aircraft flight system. More specifically, within the framework of direct data driven strategy, the collected data are dealt with to get the identified plant and designed controller. After reviewing some priori information about aircraft flight system, a closed loop system with the unknown plant and controller simultaneously is considered. Data driven estimation is proposed to identify the plant and controller only through the ratios of two correlation functions, computed from the collected data. To achieve the dual missions about perfect tracking and safety property, a new notion about safety controller is introduced. To design this safety controller, direct data driven safety controller is proposed to solve one constrain optimization problem. Then the authors apply the Karush–Kuhn–Tucker (KKT) optimality conditions to derive the explicit safety controller. Design methodology approach First, consider one closed loop system corresponding to aircraft flight system with the unknown plant and feed forward controller, data driven estimation is used to identify the plant and feed forward controller. This identification process means nonparametric estimation. Second, to achieve the perfect tracking one given transfer function and guarantee the closed loop output response within one limited range simultaneously, safety property is introduced. Then direct data driven safety control is proposed to design the safety controller, while satisfying the dual goals. Third, as the data driven estimation and direct data driven safety control are all formulated as one constrain optimization problem, the KKT optimality conditions are applied to obtain the explicit safety controller. Findings Some aircraft system identification and aircraft flight controller design can be reformulated as their corresponding constrain optimization problems. Then through solving these constrain optimization problems, the optimal estimation and controller are yielded, while satisfying our own priori goals. First, data driven estimation is proposed to get the rough estimation about the plant and controller. Second, data driven safety control is proposed to get one safety controller before our mentioned safety concept. Originality/value To the best of the authors’ knowledge, some existing theories about nonparametric estimation and tube model predictive control are very mature, but few contributions are applied in practice, such as aircraft system identification and aircraft flight controller design. This new paper shows the new theories about data driven estimation and data driven safety control on aircraft, being corresponded to the classical nonparametric estimation and tube model predictive control. Specifically, data driven estimation gives the rough estimations for the aircraft and its feed forward controller. Furthermore, after introducing the safety concept, data driven safety control is introduced to achieve the desired dual missions with the combination of KKT optimality conditions.

Dynamic tube model predictive control for a class of soft manipulators with fluidic actuation

Dynamic tube model predictive control for a class of soft manipulators with fluidic actuation

Homothetic Tube Model Predictive Control With Multi-Step Predictors

Homothetic Tube Model Predictive Control With Multi-Step Predictors

Scalable tube model predictive control of uncertain linear systems using ellipsoidal sets

Scalable tube model predictive control of uncertain linear systems using ellipsoidal sets

Dynamic Tube Model Predictive Control for Powered-Descent Guidance

In this paper, a dynamic tube nonlinear model predictive control (NMPC) scheme is developed to solve the powered-descent guidance (PDG) problem in the presence of bounded disturbances and no-fly zones. First, owing to its simplicity and robustness, time-varying boundary layer sliding mode control (SMC) is used as an ancillary controller to compensate for external disturbances. Consequently, the tube geometry dynamics can be established as first-order differential equations to calculate the robust control invariant tube. Hence, the nominal trajectory and tube geometry are optimized simultaneously to improve the control performance by augmenting the tube geometry dynamics in open-loop MPC optimization. Moreover, the tube can be shrunk to reduce the conservativeness and enhance optimization feasibility by exploiting the tube geometry and tracking error dynamics. In addition, a constraint-tightening method is employed to ensure that the PDG problem satisfies all the constraints while accounting for the uncertainty caused by the disturbance. Finally, numerical case studies and Monte Carlo simulations validate the effectiveness and performance of the proposed strategy.