Guaranteed Voronoi-based Deployment for Multi-Agent Systems under Uncertain Measurements

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.

摘要: 高效鲁棒预测控制 (ERPC) 是一种在线计算量较小, 且控制性能较好的鲁棒预测控制算法. 但采用单一椭圆不变集的设计方法存在保守性. 本文采用衰减集结策略, 通过离线设计在系统状态空间中投影彼此正交的两个椭圆不变集, 在线进行凸组合的方法设计 ERPC 控制器, 使系统初始可行域进一步扩大, 并在一定程度上改善了控制性能. 关键词: 模型预测控制 / 高效鲁棒预测控制器 / 衰减集结

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.

As a generalized input-output model, the state-dependent exogenous variable autoregressive (SD-ARX) model has been intensively utilized to model complex nonlinear systems. Considering that more freedom can be provided by the state feedback control with variable feedback gain for constructing robust controllers, we propose a robust model predictive control (RMPC) algorithm with variable feedback gain on the basis of the SD-ARX model. First, the polytopic state space models (SSMs) of the system are constructed and the prediction accuracy of the SSMs is further improved by using the parameter variation rate information of the SD-ARX model. Then, an RMPC algorithm with variable feedback gain is synthesized for increasing the design freedom and enhancing the control performance. Two simulation examples, that is, the modeling and control of a continuous stirred tank reactor (CSTR) and a water tank system, are provided to demonstrate the feasibility and effectiveness of the proposed RMPC algorithm.

An outlook on robust model predictive control algorithms: Reflections on performance and computational aspects

A systematic and complete method to design robust predictive controllers for unconstrained linear systems is proposed. The synthesis procedure is based on rigorous theoretical foundations, without resorting to approximations or ad hoc design guidelines, yet it remains a viable tool for practical application. A significant feature is that the robust predictive controller retains the servo performance of a nominal predictive controller designed using conventional methods. In addition, the robust predictive controller can be designed to guarantee perfect steady‐state rejection of asymptotically constant disturbances. The robust design method is developed for systems affected by unmodeled dynamics and is based on solving a discrete‐time model‐matching problem. It is shown that the robust controller can be classified legitimately as a predictive controller because it minimizes the same performance functional as the nominal predictive controller. An illustrative design example is given.

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.

In this paper, robust constrained model predictive control of uncertain fuzzy affine systems is considered. Based on piecewise quadratic Lyapunov functions, highly efficient robust constrained predictive control approaches are developed so that the closed-loop stability is guaranteed, and the transient control performance is improved even under input or state constraints. Moreover, by using approximate ellipsoid and S -procedure, the solution to the fuzzy affine model based predictive control can be cast as a convex optimization problem subject to some linear matrix inequalities, rather than a nonconvex problem via bilinear matrix inequalities as in conventional fuzzy affine model-based control. The proposed controllers are thus easier for real-time implementation in industry. Simulation results on the fluidized bed combustion plant have demonstrated the performance of the proposed approaches.

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

The Polyhedral Off-line Robust Model Predictive Control Strategy for Uncertain Polytopic Discrete-time Systems

In this paper, a robust model predictive control algorithm for polytope uncertain networked control systems with random time-delay and constrained input is presented. Considering the min-max infinite horizon cost function while the network delay is assumed as Markov chain, the mode-dependent state feedback controller is proposed, all the results are given by linear matrix inequality. The condition for the feasibility and robust stochastic stability of the algorithm is derived based on Lyapunov function method. The simulation shows the effectiveness of the proposed algorithm.

Unmanned underwater vehicle (UUV) has been applied for civil field all over the world. In technologies of UUV, the underwater recovery technology plays an essential part. And the superior precision control system is necessary for UUV underwater recovery. In this paper, the research background is the mother ship carries UUV recycling in piggyback method. And the important point is the method of dynamic positioning to line in process of UUV recovery and the UUV dynamic positioning to line strategy based on the robust model predictive control algorithm is proposed. Then, a digital simulation is made to verify the feasibility of the control algorithm. Through the simulation results, the conclusion of control algorithm is got.

On distributed model predictive control for vehicle platooning with a recursive feasibility guarantee

Wide-area damping power system control based on robust self-triggered model predictive control

Constant-air-volume (CAV) air-conditioning systems consist mainly of two local processes: an air-handling process and a room temperature process. A robust model predictive control (RMPC) strategy was developed for CAV air-conditioning systems, which adopted two uncertain first-order plus time-delay models to describe the dynamics of the local processes and used a linear matrix inequality (LMI)-based optimisation technique to optimise the control law. This paper develops a new control design, which reformulates the prediction models by shifting the uncertainties of the first model into the second one, and then uses the reformulated prediction models in the RMPC strategy. This paper will show that compared with the original design, the new control design can enhance the feasibility of the optimisation of control law, reduce the computational burden of the optimisation and also remove the requirement of a sensor for supply air temperature in the original design. Practical applications: The new design method is a further development of a RMPC strategy presented in Xu et al.13 It inherits the benefits of the original control design for practical application, i.e. uncertainties and constraints can be dealt with simultaneously in the design and the robustness of the controlled system can be enhanced. The new design improves the optimisation feasibility, reduces the computational complexity and does not need to measure the supply air temperature. When the new design is adopted to replace the traditional PI control, there is no necessity to change the existent input structure of the PI control. Hence, the new design can be realised in practice easier than the original design.