Robust Receding Horizon Control Research Articles

Data-Driven Digital Advertising with Uncertain Demand Model in Metro Networks

Nowadays most metro advertising systems schedule advertising slots on digital advertising screens to achieve the maximum exposure to passengers by exploring passenger demand models. However, our empirical results show that these passenger demand models experience uncertainty at fine temporal granularity (e.g., per min). As a result, for fine-grained advertisements (shorter than one minute), a scheduling based on these demand models cannot achieve the maximum advertisement exposure. To address this issue, we propose an online advertising approach, called FineUDM, based on the uncertain passenger demand modeling for both entering passengers and exiting passengers. FineUDM combines coarse-grained statistical demand modeling and fine-grained real-time demand modeling by leveraging historical passenger demands, real-time card-swiping records, and passenger mobility patterns. Based on this uncertain demand model, it schedules advertising time online based on robust receding horizon control to maximize the advertisement exposure. We evaluate the proposed approach based on an one-month sample from our 530 GB real-world metro fare dataset with 16 million cards. The results show that our approach provides a 61.5 percent lower traffic prediction error and 20 percent improvement on advertising efficiency on average.

Robust Receding Horizon Control with Free Control Moves for Polytopic Parametric Uncertainty Systems Subject to Multiple Input Delays

A robust receding horizon control (RHC) with free control moves is applied to polytopic parametric uncertainty systems with multiple input delays and unstable system matrices. A difficulty in the previous robust RHC work is that the free control moves are unsuitable for the system with input time delay, which is overcome in this paper by the design based on the augmented state. As a result, the synthesis of local control based on augmented feedback is given offline to alleviate the online computation burden. The free control moves before the augmented feedback are the online decision variables, which are solved by minimizing a sequence of nonnegative scalars online. The recursive feasibility is guaranteed by adopting the augmented state space equation. By adjusting the robust positively invariant set, the stability of the closed-loop system is guaranteed. Simulation results demonstrate that the proposed algorithm improves the control performance effectively.

Synchronous distributed receding horizon control for uncertain networked systems with time delays

This study investigates the problem of distributed receding horizon control (DRHC) for constrained networked systems with polytopic uncertainty description, subject to time delays. Considering the limited communication capacity of the network and computational complexity, the approach of this study is based on a synchronous and non-iterative structure. Thus, for each subsystem, assumed predictive state evolutions of the neighbours are used. To restrict the assumed evolutions not deviating much from the true ones, the compatibility condition is derived concerning global stability. Time delays are handled by introducing an augmented polytopic uncertainty description, and the local optimisation problem is properly formulated by means of the robust receding horizon control technique. Applying the DRHC approach of this study, the recursive feasibility of the optimisation problem and exponential stability of the global system are guaranteed. An example is provided to illustrate the effectiveness of the proposed approach.

Robust receding horizon control strategy for replenishment planning of pharmacy robotic dispensing systems

This paper presents a robust receding horizon control strategy (RHC-RO) to enhance replenishment planning and inventory control of robotic dispensing systems in central fill pharmacies (CFPs). Replenishment in CFPs is a key process greatly influenced by several stochastic factors, such as demand volume and process times. In this research, a robust mixed integer quadratic programming (RMIQP) model is proposed to determine the number of allocated canisters and the schedule of replenishment operations considering multiple scenarios. A receding horizon control (RHC) mechanism, which divides the optimization horizon into smaller time windows, is applied to enhance the solution quality and reduce the computational burden. The proposed RHC-RO strategy is evaluated using simulation against offline, robust optimization (RO), and RHC strategies in terms of total replenishment costs. The results indicate that RHC-RO outperforms the offline, RO, and RHC strategies by generating 19.7%, 18.3%, and 5.6% less replenishment costs on average, respectively. The results also show that the RHC-RO strategy enables timely, accurate, and robust replenishment decisions.

Robust RHC for wheeled vehicles with bounded disturbances

SummaryThe robust receding horizon control (RHC) synthesis approach is developed in this paper, for the simultaneous tracking and regulation problem (STRP) of wheeled vehicles with bounded disturbances. Considering the bounded disturbances, we firstly provide a robust positively invariant (RPI) set and associated feedback controller for the perturbed vehicles, which contribute to the foundation of the robust RHC synthesis approach. Then, by extending the tube‐based approach introduced in the article of Mayne et al (robust model predictive control of constrained linear systems with bounded disturbances in Automatica, 2005, vol. 41) to the STRP of wheeled vehicles, we employ the designed RPI set to determine the robust tube and terminal state region, and further construct a nominal optimal control problem. The actual control input is implemented by correcting the solved nominal input with the designed feedback controller. Following the contributed properties of the developed RPI set and extended tube‐based approach, a robust RHC algorithm is finally proposed with the guarantees of recursive feasibility and robust convergence, which can also be adapted for real‐time implementation. Additionally, due to the elaborate control design, the effect of disturbances can be completely nullified to achieve better tracking performance. The effectiveness and advantage of the proposed approach are illustrated by two simulation examples.

Robust receding horizon control for linear systems with state and input dependent disturbances

A robust model predictive controller is proposed for constrained linear systems with unknown disturbances that are subject to state and input dependent piecewise affine bounds. The formulation encompasses problems involving model uncertainty arising from unknown system parameters and linearisation errors. We propose a computationally efficient method for the online optimization of a receding horizon min-max cost over the class of feedback strategies subject robust constraint satisfaction and provide an illustrative numerical example.

이동 구간 제어기의 최근 기술 동향

Abstract: This article introduces recent trends in RHC (Receding Horizon Control), also known as MPC (Model Predictive Control), that has been well recognized in industry and academy as a systematic approach for optimal design and constraint management. Constrained and robust RHCs will be briefly reviewed with milestone results. Among the diverse developments and achievements of RHCs, implementation issues will be focused on, together with the latest applications. In particular, this article introduces results on how to solve a finite horizon open-loop optimal control problem in an efficient way, together with code generation for real-time execution and easy implementation. Instead of traditional applications such as refineries and petrochemical plants, this article highlights some selected emerging applications, such as energy management systems and mechatronics, that have resulted from state-of-the-art high performance computing power and advanced numerical schemes.Keywords: RHC (Receding Horizon Control), MPC (Model Predictive Control), constraint handling, robust, computation, implementation

Robust $H_{\infty}$ Receding Horizon Control for a Class of Coordinated Control Problems Involving Dynamically Decoupled Subsystems

This paper presents a robust receding-horizon-control (RHC)-based scheme for a class of coordinated control problems involving dynamically decoupled subsystems which are required to reach a consensus condition in some optimal way. A general case of constrained subsystems having possibly uncertain time-varying dynamics in addition to external disturbances is considered and a suitable H∞-based near-consensus condition is defined as the target condition to be achieved. The proposed scheme employs computationally efficient subsystem-level RHC policies in the H∞-based minmax-cost framework together with a distributed subgradient-based method to optimize and update the consensus signal and the subsystem control inputs at regular intervals. Furthermore, the proposed framework allows the incorporation of computational delays in the RHC policy formulation so that the desired control performance is always guaranteed. The performance of the proposed control scheme is illustrated with some simulation examples.

An active set solver for input-constrained robust receding horizon control

An efficient optimization procedure is proposed for computing a receding horizon control law for linear systems with linearly constrained control inputs and additive disturbances. The procedure uses an active set approach to solve the dynamic programming problem associated with the min–max optimization of an H∞ performance index. The active constraint set is determined at each sampling instant using first-order necessary conditions for optimality. The computational complexity of each iteration of the algorithm depends linearly on the prediction horizon length. We discuss convergence, closed loop stability and bounds on the disturbance l2-gain in closed loop operation.

Robust constrained economic receding horizon control applied to the two time‐scale dynamics problem of a greenhouse

SUMMARYThis paper discusses the formulation of an optimal control framework for a two time‐scale system modeled in terms of singular perturbation theory. The fast dynamics subsystem is controlled online by means of a robust receding horizon control approach considering economic objectives in the performance function and fulfilling state and input constraints. The formulation is addressed in general terms, so it can be adapted to different applications. A practical example is given, greenhouse crop growth control. Simulations comparing the proposed controller with another two time‐scale control strategy demonstrate constraints fulfillment and a proper performance, assuming uncertainty in the weather conditions during the predictions. Copyright © 2013 John Wiley & Sons, Ltd.

Receding Horizon Control for Uncertain Markov Jump Linear Systems with Time Delay and Actuator Saturation

A robust receding horizon control (RHC) scheme is developed for uncertain discrete-time Markov Jump Linear Systems (MJLS) with time delay and actuator saturation where the system uncertainties and jumping transition probabilities are assumed to belong to some convex sets. Firstly, when time delay is considered, a sufficient condition of minimizing upper bound of the cost function and mean square stability of the closed-loop system are established based on the Lyapunov Krasovskii function which depend on the current time jump mode. At each sampling time, an optimal control gain can be obtained by solving the semi-definite programming (SDP) problem. Then, the proposed strategy is extended to design robust RHC scheme for uncertain MJLS with both time delay and actuator saturation. Moreover, the domain of attraction can be estimated through a modified invariant ellipsoid. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.

Robust nonlinear receding-horizon control of induction motors

Nonlinear robust receding-horizon control is designed and applied to fifth-order model of induction motor in cascade structure. The controller is based on a finite horizon continuous time minimization of the predicted tracking errors and no online optimization is needed. The initial system is decomposed into two sub-systems (mechanical and electromagnetic sub-systems) in cascade form. An integral action is incorporated in external loop to increase the robustness of the controller with respect to unknown time-varying load torque and mechanical parameters uncertainties. The control uses only measurement of the rotor speed and stator currents. The rotor flux is estimated by Kalman filter. The proposed nonlinear controller permits to achieve asymptotic speed and flux tracking in presence of mechanical parameters uncertainties, unknown variable load torque and resistances variations. In addition, it assures asymptotic decoupling of the speed and flux subsystems. The controller is applied, via simulation, to a benchmark example.

Numerical optimization method for HJI equations derived from robust receding horizon control schemes and controller design

This paper addresses how to numerically solve the Hamilton-Jacobin-Isaac (HJI) equations derived from the robust receding horizon control schemes. The developed numerical method, the finite difference scheme with sigmoidal transformation, is a stable and convergent algorithm for HJI equations. A boundary value iteration procedure is developed to increase the calculation accuracy with less time consumption. The obtained value function can be applied to the robust receding horizon controller design of some kind of uncertain nonlinear systems. In the controller design, the finite time horizon is extended into the infinite time horizon and the controller can be implemented in real time. It can avoid the on-line repeated optimization and the dependence on the feasibility of the initial state which are encountered in the traditional robust receding horizon control schemes.

鲁棒后退时域控制中HJI 方程的数值解法及控制器设计

This paper addresses how to numerically solve the Hamilton-Jacobin-Isaac (HJI) equations derived from the robust receding horizon control schemes. The developed numerical method, the finite difference scheme with sigmoidal transformation, is a stable and convergent algorithm for HJI equations. A boundary value iteration procedure is developed to increase the calculation accuracy with less time consumption. The obtained value function can be applied to the robust receding horizon controller design of some kind of uncertain nonlinear systems. In the controller design, the finite time horizon is extended into the infinite time horizon and the controller can be implemented in real time. It can avoid the on-line repeated optimization and the dependence on the feasibility of the initial state which are encountered in the traditional robust receding horizon control schemes.

Robust receding horizon control of uncertain fuzzy systems

The optimal control of uncertain fuzzy systems with constraints is still an open problem. One candidate to deal with this problem is robust receding horizon control (RRHC) schemes, which can be formulated as a differential game. Our focus concerns numerically solving Hamilton–Jacobi–Issac (HJI) equations derived from RRHC schemes for uncertain fuzzy systems. The developed finite difference approximation scheme with sigmoidal transformation is a stable and convergent algorithm for HJI equations. Accelerated procedures with boundary value iteration are developed to increase the calculation accuracy with less time consumption. Then, the state-feedback RRHC controller is designed for some class of uncertain fuzzy systems with constraints. The value function calculated by numerical methods acts as the design parameter. The closed-loop system is proven to be asymptotically stable. An engineering implementation of the controller is discussed.

Dividing Genetic Computation Method for Robust Receding Horizon Control Design

A new robust Receding Horizon Control (RHC) design approach for the sampled-data systems is proposed. The approach is based on a dividing genetic computation of minimax optimization for a robust finite receding horizon control problem. Numerical example is given to show the effectiveness of the proposed method.

Input-to-state stability of robust receding horizon control with an expected value cost

This paper is concerned with the stability of a class of receding horizon control (RHC) laws for constrained linear discrete-time systems subject to bounded state disturbances and convex state and input constraints. The paper considers the class of finite horizon feedback control policies parameterized as affine functions of the system state, calculation of which can be shown to be tractable via a convex reparameterization. When minimizing the expected value of a finite horizon quadratic cost, we show that the value function is convex. When solving this optimal control problem at each time step and implementing the result in a receding horizon fashion, we provide sufficient conditions under which the closed-loop system is input-to-state stable (ISS).

Robust receding horizon control for constrained linear fractional transformation parameter-dependent systems

A robust receding horizon control (RHC) scheme is proposed for parameter-dependent linear systems with linear fractional parameter dependency and input–output constraints. The cost function is defined over a moving finite horizon as the quadratic performance for future parameter trajectories. The robust stability of the proposed RHC scheme is guaranteed using a parameter-dependent control Lyapunov function as the terminal penalty term, which is available through off-line synthesis procedure. Moreover, it is shown that the domain of attraction will be enlarged and the controlled performance of the RHC scheme will be gradually improved as the upper bound of performance is monotonically decreasing on-line. Both off-line robust control synthesis and on-line RHC computation are formulated and solved using linear matrix inequality optimisation techniques.

Distributed Robust Receding Horizon Control for Multivehicle Guidance

This paper presents a new distributed robust model predictive control algorithm for multivehicle trajectory optimization and demonstrates the approach with numerical simulations and multivehicle experiments. The technique builds on the robust-safe-but-knowledgeable (RSBK) algorithm, which is developed in this paper for the multivehicle case. RSBK uses constraint tightening to achieve robustness to external disturbances, an invariant set to ensure safety in the presence of changes to the environment, and a cost-to-go function to generate an intelligent trajectory around known obstacles. The key advantage of this RSBK algorithm is that it enables the use of much shorter planning horizons while still preserving the robust feasibility guarantees of previously proposed approaches. The second contribution of this paper is a distributed version of the RSBK algorithm, which is more suitable for real-time execution. In the distributed RSBK (DRSBK) algorithm, each vehicle only optimizes for its own decisions by solving a subproblem of reduced size, which results in shorter computation times. Furthermore, the algorithm retains the robust feasibility guarantees of the centralized approach while requiring that each agent only have local knowledge of the environment and neighbor vehicles' plans. This new approach also facilitates the use of a significantly more general implementation architecture for the distributed trajectory optimization, which further decreases the delay due to computation time.

Output feedback receding horizon control of constrained systems

This paper considers output feedback control of linear discrete-time systems with convex state and input constraints which are subject to bounded state disturbances and output measurement errors. We show that the non-convex problem of finding a constraint admissible affine output feedback policy over a finite horizon, to be used in conjunction with a fixed linear state observer, can be converted to an equivalent convex problem. When used in the design of a time-varying robust receding horizon control law, we derive conditions under which the resulting closed-loop system is guaranteed to satisfy the system constraints for all time, given an initial state estimate and bound on the state estimation error. When the state estimation error bound matches the minimal robust positively invariant (mRPI) set for the system error dynamics, we show that this control law is time-invariant, but its calculation generally requires solution of an infinite-dimensional optimization problem. Finally, using an invariant outer approximation to the mRPI error set, we develop a time-invariant control law that can be computed by solving a finite-dimensional tractable optimization problem at each time step that guarantees that the closed-loop system satisfies the constraints for all time.