Robust Time-Varying Model Predictive Control with Application to Mobile Robot Unmanned Path Tracking

In this paper, the problem of optimal time-varying attitude tracking control for rigid spacecraft with system constraints and unknown additive disturbances is considered. Through the design of a new non-linear tube-based robust model predictive control (TRMPC) algorithm, a dual-loop cascaded tracking control framework is established. The proposed TRMPC algorithm explicitly considers the effect of disturbances and applies tightened system constraints to predict the motion of the nominal system. The obtained optimal control action is then combined with a non-linear feedback law such that the actual system trajectories can always be steered within a tube region centred around the nominal solution. To facilitate the recursive feasibility of the optimization process and guarantee the input-to-state stability of the tracking control process, the terminal controller and the corresponding terminal invariant set are also constructed. The effectiveness of using the proposed dual-loop TRMPC control scheme to track reference attitude trajectories is validated by experimental studies. A number of comparative studies were carried out, and the obtained results reveal that the proposed design is able to achieve more promising constraint handling and attitude tracking performance than that of the other newly developed methods investigated in this research.

This paper addresses a computationally efficient robust tube-based model predictive control (RTBMPC) strategy of linear systems in the presence of bounded disturbance. In the RTBMPC strategy, a nominal system is introduced by ignoring the disturbances of uncertain system, and then the uncertain system will be controlled in a robust manner through its nominal system as well as an additional feedback term which rejects a bounded additive disturbance. In this paper, the tracking problem is converted into the regulation problem by introducing an extra system called regulation nominal system that its constraints are translated from tracking into regulation. It leads to a reduction in complexity of the objective function and simplification of driving the stability theory. On the other hand, RTBMPC strategy solves optimization problem for nominal system which ignores the disturbances. Since in the absence of disturbances, the state measured at the following sample will be the same as the one predicted by model, a variable prediction horizon is suggested to reduce the computational burden. In addition, new constraints are introduced to prove the recursive feasibility, local and asymptotic stability. The constrained sampled double integrator is presented to illustrate the effectiveness of the proposed RTBMPC.

In this study, an approach to design robust distributed model predictive control (MPC) is proposed for polytopic uncertain networked control systems with time delays. To reduce the computational complexity and improve the flexibility, the entire system is decomposed into multiple smaller dimensional subsystems. For each subsystem, the proposed robust distributed MPC algorithm requires solving multiple linear matrix inequality optimisation problems to minimise an upper bound on a robust performance objective. An augmented polytopic uncertainty description is invoked to handle the input delays. The conservativeness of distributed MPC algorithm is reduced by utilising a sequence of feedback control laws. An iterative on‐line algorithm for robust distributed MPC is developed to coordinate the distributed MPC controllers. Convergence and robust stability of the proposed distributed MPC are investigated. A numerical example is carried out to demonstrate the effectiveness of the proposed algorithm.

This paper focuses on the design of a robust tube-based Model Predictive Control law for the control of constrained mobile robots. A time-varying trajectory tracking error model has been used, where uncertainties are assumed to be bounded and additive. The proposed solution to the control problem is a tube-based MPC ensuring robustness and stability. A comparative simulation example is presented showing the promising behavior of the robust MPC controller.

A novel robust model predictive control strategy is presented for a class of discrete-time time-varying system with delays. The modified quadratic Lyapunov-Krasovskii functionals for uncertain discrete-time system with both states and input delays is proposed. A robust model predictive control law is derived such that the closed-loop system is asymptotically stable and a dasiaworst-casepsila infinite horizon performance objective is minimized. A feasible state feedback model predictive control law is obtained by using linear matrix inequalities approach. And then, a convex optimization problem is formulated to design the robust model predictive controller which minimizes the upper bound of the closed-loop performance objective. The robust model predictive controller design is illustrated with numerical examples.

In this paper, a decentralized robust tube-based model predictive control algorithm is used for two-dimensional Voronoi-based deployment of a multi-agent system in a bounded convex area, where the planar motion of each agent is subject to uncertain measurements. A bias bounded by a rectangle is thus considered for each agent's position measurement. The convex area of deployment is then partitioned into guaranteed Voronoi cells separated by a bounded unauthorized corridor. By using a decentralized robust predictive control, each agent is guaranteed to evolve inside the safety region defined by the agent's guaranteed Voronoi cell and to converge to a point in a set centered on the Chebyshev center of this cell, driving the multi-agent system into a static configuration. Simulation results show the effectiveness of the proposed decentralized control strategy on a fleet of quadrotors when one of the agents is subject to a measurement bias due to a sensor fault.

This study proposes a layered hybrid control framework for automation and robotics systems that combines Tube-based Robust MPC (RMPC) as a safety envelope, adaptive parameter estimation to narrow online uncertainty, Sliding Mode Control (SMC) as a high-resilience fail-safe, and Reinforcement Learning (RL) as a performance booster through a warm-start/residual policy scheme that is always constrained by Control Barrier Functions (CBF). The study aims to achieve better tracking performance and computational efficiency without sacrificing safety and constraint compliance. The methodology includes constrained nonlinear plant modeling, design of tube invariance-based RMPC with constraint tightening, RLS/concurrent learning-based adaptive estimator, SMC for infeasibility/model drift conditions, and a CBF-based safety filter formulated as an online small QP. Evaluation is done through ablation studies on multi-domain benchmarks and HIL-style tests, with finite-horizon cost, ITAE, constraint violation rate, and computational latency (average and WCET) metrics. The results show that the RL+CBF configuration reduces the finite-horizon cost by about 15.7% compared to pure RMPC, maintaining a violation rate of ~0.35% (better than RMPC: 0.80%) and significantly below that of unfiltered RL (4.20%). The warm-start RL scheme accelerates the completion time of the MPC solver by ≈15–18% over various prediction horizons and reduces the WCET (26.4 → 23.3 ms), supporting real-time implementation. These findings confirm that the integration of RMPC–Adaptive–SMC–RL(+CBF) effectively bridges model-based optimality, online adaptivity, robust resilience, and learning from data in a single architecture that is safety-certified and feasible for real-world applications demanding high uptime.

ABSTRACTIn this work, synthesis of robust distributed model predictive control (MPC) is presented for a class of linear systems subject to structured time-varying uncertainties. By decomposing a global system into smaller dimensional subsystems, a set of distributed MPC controllers, instead of a centralised controller, are designed. To ensure the robust stability of the closed-loop system with respect to model uncertainties, distributed state feedback laws are obtained by solving a min–max optimisation problem. The design of robust distributed MPC is then transformed into solving a minimisation optimisation problem with linear matrix inequality constraints. An iterative online algorithm with adjustable maximum iteration is proposed to coordinate the distributed controllers to achieve a global performance. The simulation results show the effectiveness of the proposed robust distributed MPC algorithm.

Tube-based robust model predictive control for spacecraft proximity operations in the presence of persistent disturbance

This paper extends efficient, robust model predictive control (MPC) approaches for linear parameter varying (LPV) systems to tracking scenarios. A dual mode approach is used and future information about target changes is included in the optimisation tracking problem. The controller guarantees recursive feasibility by adding an artificial target as an extra degree of freedom. Convergence to admissible targets is ensured by constructing a robustly invariant set to track any admissible target. The efficacy of the proposed algorithm is demonstrated by MATLAB simulations.

The robust model predictive control (RMPC) based on extended state observer (ESO) is proposed for autonomous underwater vehicle (AUV) by considering the complexity and uncertainty of the marine environment and the strong nonlinearity and coupling. Based on the dynamics of the AUV, a nominal system is given by neglecting uncertainties and disturbances. Then, a robust model predictive control algorithm is designed for the nominal system and the robustness of the system is analyzed for the system uncertainty. The controller acting on the real system is designed by the feedback linearization method and the remained disturbances are estimated and compensated by the extended state observer. The asymptotic stability of the system is analyzed using Lyapunov theory and the input state stability of the error system is analyzed. It is demonstrated through simulation experiments that the extended state observer based robust model predictive controller has a better trajectory tracking performance and anti-disturbance capability than the common model predictive controller.

This paper presents a self-triggered model predictive control (MPC) algorithm for constrained linear discrete-time systems in the presence of bounded state and output disturbances, when only the system output can be measured at triggering instants. The proposed algorithm mainly relies on a state estimator whose estimation error is bounded by an invariant set, and on the self-triggered robust model predictive control of a nominal system, in which the cost function penalizes the nominal system state and control effort as well as the triggering interval. The proposed algorithm is proved to drive the system to an invariant set with respect to the disturbances. Numerical examples are also provided to validate the proposed algorithm and to further illustrate better performance compared with the periodic MPC.

Design and experimental validation of a robust model predictive control for the optimal trajectory tracking of a small-scale autonomous bulldozer

Dynamic Output Disturbance Models for Robust Constraint Satisfaction

This paper presents the performance evaluation of robust model predictive control (robust MPC) for a mobile robot. The mobile robot is affected by stationary or moving obstacles and exogenous disturbances, which are road surface slipperiness, fluid resistance under water and current disturbance. Since these disturbances make it difficult to accurately control the trajectory of the mobile robot, robustness is required in the control framework. The robust MPC is one of the methods for mobile robot control. Several previous studies about the robust MPC have mainly focused on Gaussian noise. We conduct a simulation to test mobile robot obstacle avoidance under three different non-Gaussian noise environments, and confirm that the robust MPC is effective given the exogenous disturbances of affecting the mobile robot.