Dynamic Output Feedback Robust Model Research Articles

Dynamic output feedback model predictive control for asynchronous Markovian jump systems under try‐once‐discard protocol

AbstractThis paper is concerned with the dynamic output feedback robust model predictive control (RMPC) problem for a class of discrete‐time asynchronous Markovian jump systems (MJSs) subject to polytopic parameter uncertainties and hard constraints on states and inputs. A hidden Markov model is employed to describe the asynchronous phenomenon between the detected modes and the system modes. For the purpose of improving the network utilization as well as reducing the transmission burden and avoiding data collisions, the try‐once‐discard (TOD) protocol is deployed in the shared communication network between sensor nodes and the controller node. Considering the difficulty of obtaining the system state in the practice, the dynamic output‐feedback control in the framework of RMPC is adopted, and the worst‐case optimization problem over the infinite moving horizon is formulated for the performance analysis and control synthesis. By means of the Lyapunov‐like function approach, free weighting matrices and inequality techniques such as the ‐procedure are introduced to deal with the non‐convexity caused by couplings between decisive variables and the negative influence resulting from the data orchestration is mitigated. Based on the delicate establishments, a certain upper bound of the objective function is employed to construct an auxiliary optimization problem with solvability to find the desired controllers, and sufficient conditions are obtained to guarantee that the MJSs under the proposed RMPC‐based controllers are mean‐square stable. Finally, an illustrative example is used to demonstrate the validity of the proposed methods.

A Summary of Dynamic Output Feedback Robust MPC for Linear Polytopic Uncertainty Model with Bounded Disturbance

This paper is the summary and enhancement of the previous studies on dynamic output feedback robust model predictive control (MPC) for the linear parameter varying model (described in a polytope) with additive bounded disturbance. When the state is measurable and there is no bounded disturbance, the robust MPC has been developed with several paradigms and seems becoming mature. For the output feedback case for the LPV model with bounded disturbance, we have published a series of works. Anyway, it lacks a unification of these publications. This paper summarizes the existing results and exposes the ideas in a unified framework. Indeed there is a long way to go for the output feedback case for the LPV model with bounded disturbance. This paper can pave the way for further research on output feedback MPC.

A Convexity Approach to Dynamic Output Feedback Robust MPC for LPV Systems with Bounded Disturbances

A convexity approach to dynamic output feedback robust model predictive control (OFRMPC) is proposed for linear parameter varying (LPV) systems with bounded disturbances. At each sampling time, the model parameters and disturbances are assumed to be unknown but bounded within pre-specified convex sets. Robust stability conditions on the augmented closed-loop system are derived using the techniques of robust positively invariant (RPI) set and the S-procedure. A convexity method reformulates the non-convex bilinear matrix inequalities (BMIs) problem as a convex optimization one such that the on-line computational burden is significantly reduced. The on-line optimized dynamic output feedback controller parameters steer the augmented states to converge within RPI sets and recursive feasibility of the optimization problem is guaranteed. Furthermore, bounds of the estimation error set are refreshed by updating the shape matrix of the future ellipsoidal estimation error set. The dynamic OFRMPC approach guarantees that the disturbance-free augmented closed-loop system (without consideration of disturbances) converges to the origin. In addition, when the system is subject to bounded disturbances, the augmented closed-loop system converges to a neighborhood of the origin. Two simulation examples are given to verify the effectiveness of the approach.

Dynamic output-feedback RMPC for systems with polytopic uncertainties under Round-Robin protocol

This paper is concerned with the dynamic output-feedback robust model predictive control (RMPC) problem for systems with polytopic uncertainties under the Round-Robin (RR) protocol. In the backward channel, i.e., from the sensors to the controller, several sensors share a communication network to transmit the data to the remote controller, and thus data collision might happen if these sensors start transmissions together. In order to prevent data from collisions, a so-called RR protocol is utilized to orchestrate the data transmission order, where only one node with token is allowed to send data at each transmission instant. The aim of the problem addressed is to design a set of controllers in the framework of dynamic output-feedback RMPC (OFRMPC) so as to guarantee the asymptotical stability of the closed-loop system in terms of the token-dependent Lyapunov-like approach. By taking the influence of the underlying RR protocol into consideration, sufficient conditions with less conservatism are obtained by solving a time-varying terminal constraint set of an auxiliary optimization problem. Furthermore, an algorithm including both off-line and online parts is provided to find a sub-optimal solution. Finally, a numerical simulation result is exploited to illustrate the usefulness and effectiveness of the proposed RMPC strategy.

Dynamic output feedback robust MPC with convex optimisation for system with polytopic uncertainty

ABSTRACTThis paper proposes a dynamic output feedback robust model predictive control for system with polytopic model uncertainty. Earlier researches on this topic utilise iterative methods to solve the non-convex optimisation problem which are computationally demanding. In order to reduce the computational burden, we explore a new approach in this paper, where, by utilising some proper matrix transformations, a computationally more efficient but conservative convex optimisation problem is formulated which can be solved in terms of linear matrix inequalities. Furthermore, we try to reduce the conservativeness by introducing a nonsingular matrix as a degree of freedom. The recursive feasibility and the convergence of the augmented state to the equilibrium point are guaranteed. The effectiveness of the proposed approach is illustrated by two numerical examples.

Output feedback robust MPC using general polyhedral and ellipsoidal true state bounds for LPV model with bounded disturbance

ABSTRACTThis paper considers the dynamic output feedback robust model predictive control (MPC) for a system with both polytopic model parametric uncertainty and bounded disturbance. For this topic, the techniques for handling the unknown true state are crucial, and the strict guarantee of the input/output/state constraints requires replacing the true state by its bounds in the optimisation problems. Previously, in the separate works, we (i) gave the general polyhedral bound; (ii) proposed the general ellipsoidal bound; (iii) applied some special polyhedral bounds to tighten the ellipsoidal bound since the latter is crucial for guaranteeing recursive feasibility. In this paper, (i)–(iii) are unified, and the up-to-date least conservative treatment of the true state bound is given, so the control performance can be greatly improved. The contribution mainly lies in overcoming the difficulties in developing technical details for the unification. A numerical example is given to illustrate the effectiveness of the new method.

Synchronization for chaotic systems via mixed-objective dynamic output feedback robust model predictive control

This paper focuses on mixed-objective dynamic output feedback robust model predictive control (OFRMPC) for the synchronization of two identical discrete-time chaotic systems with polytopic uncertainties, energy bounded disturbances, and input constraint. Using active control strategy, the chaos synchronization is transformed into standard dynamic OFRMPC scenarios tractable through receding horizon min–max optimization. Utilizing the notion of quadratic boundedness, the augmented closed-loop stability is further characterized. Then, the concepts of mixed performance criteria are firstly incorporated into the dynamic OFRMPC scheme to guarantee both the robust stability and the disturbance attenuation ability while preserving better dynamical behaviors. Necessary and/or sufficient conditions for desired mixed-objective dynamic OFRMPC are formulated involving linear matrix inequalities (LMIs). Finally, two numerical examples are given to demonstrate the theoretical results.

Dynamic output feedback robust MPC for LPV systems subject to input saturation and bounded disturbance

For linear parameter varying (LPV) systems with unknown scheduling parameters and bounded disturbance, a synthesis approach of dynamic output feedback robust model predictive control (OFRMPC) with input saturation is investigated. By pre-specifying partial controller parameters, a main optimization problem is solved by convex optimization to reduce the on-line computational burden. The main optimization problem guarantees that the estimated state and estimation error converge within the corresponding invariant sets such that recursive feasibility and robust stability are guaranteed. The consideration of input saturation in the main optimization problem improves the control performance. Two numerical examples are given to illustrate the effectiveness of the approach.

Event-triggered dynamic output feedback RMPC for polytopic systems with redundant channels: Input-to-state stability

This paper is concerned with the event-triggered dynamic output feedback robust model predictive control (RMPC) problem for a class of polytopic systems subject to redundant channels and the constraints on states and inputs. The redundant channels are employed to deal with the unanticipated problems such as packet dropouts during the data transmission via network, where the investigated packet dropouts are supposed to occur in a random way modeled by a set of mutually independent Bernoulli distributed sequences. A novel event-triggered communication mechanism with the time-varying threshold is adopted when the data is transmitted from estimator side to controller side, which reduces the communication burden by canceling unnecessary data transmission and hence effectively saves energy. At each sampling instant, the optimized feedback control law is computed by minimizing the upper bound on the “worst-case” value of an event-dependent infinite horizon cost function subject to constraints on inputs and states. In virtue of the cone complementarity linearization (CCL) technique, the non-convex optimization problem is converted to a minimization problem including some linear matrix inequalities. Based on the invariant set theory, some sufficient conditions are established to guarantee the recursive feasibility and input-to-state stability (ISS) in mean square sense. An event-based dynamic output feedback RMPC algorithm is developed to implement the online computation. A numerical simulation example is given to demonstrate the validity in energy saving as well as the desirable performance insurance.

Dynamic Output Feedback Robust MPC with Input Saturation Based on Zonotopic Set-Membership Estimation

For quasi-linear parameter varying (quasi-LPV) systems with bounded disturbance, a synthesis approach of dynamic output feedback robust model predictive control (OFRMPC) with the consideration of input saturation is investigated. The saturated dynamic output feedback controller is represented by a convex hull involving the actual dynamic output controller and an introduced auxiliary controller. By taking both the actual output feedback controller and the auxiliary controller with a parameter-dependent form, the main optimization problem can be formulated as convex optimization. The consideration of input saturation in the main optimization problem reduces the conservatism of dynamic output feedback controller design. The estimation error set and bounded disturbance are represented by zonotopes and refreshed by zonotopic set-membership estimation. Compared with the previous results, the proposed algorithm can not only guarantee the recursive feasibility of the optimization problem, but also improve the control performance at the cost of higher computational burden. A nonlinear continuous stirred tank reactor (CSTR) example is given to illustrate the effectiveness of the approach.

Improved dynamic output feedback RMPC for linear uncertain systems with input constraints

SummaryIn this work, we propose a dynamic output feedback robust model predictive control (RMPC) design method for linear uncertain systems with input constraints. In order to handle the input constraints, the control signals are permitted to saturate, which can fully utilize the capability of actuators and thus can reduce the conservatism. For the unavailable states, an ellipsoidal set is used to obtain an estimation, and it is updated at every time instant. A modified RMPC design requirement is used to ensure the recursive feasibility of the optimization problem. Then, the design method is formulated in terms of a convex optimization problem with linear matrix inequality constraints. The proposed output feedback RMPC design method is expected to further reduce the conservativeness. The improvements of the proposed algorithm over the other existing techniques is demonstrated by an example. Copyright © 2015 John Wiley & Sons, Ltd.

Dynamic Output Feedback Robust MPC Using General Polyhedral State Bounds for the Polytopic Uncertain System With Bounded Disturbance

AbstractThis paper considers the dynamic output feedback robust model predictive control (MPC) for a system with both polytopic model parametric uncertainty and bounded disturbance. For this topic, the techniques for handling the unknown true state are crucial, and the strict guarantee of the input/output/state constraints favors replacing the true state by its bound in the optimization problems. The previous utilized polyhedral bounds, constructed by virtue of the error signals which are some linear combinations of the true state, the estimated state and the output, are generalized, where a bias item is utilized. Based on this unified bounding approach, new techniques for handling the unknown true state are given for both the main and the auxiliary optimization problems. As before, the main optimization problem calculates the control law parameters conditionally, and the auxiliary optimization problem determines the time to refresh these parameters. By applying the proposed method, the augmented state of the closed‐loop system is guaranteed to converge to the neighborhood of the equilibrium point. A numerical example is given to illustrate the effectiveness of the new method.

Dynamic Output Feedback Robust Model Predictive Control via Zonotopic Set-Membership Estimation for Constrained Quasi-LPV Systems

For the quasi-linear parameter varying (quasi-LPV) system with bounded disturbance, a synthesis approach of dynamic output feedback robust model predictive control (OFRMPC) is investigated. The estimation error set is represented by a zonotope and refreshed by the zonotopic set-membership estimation method. By properly refreshing the estimation error set online, the bounds of true state at the next sampling time can be obtained. Furthermore, the feasibility of the main optimization problem at the next sampling time can be determined at the current time. A numerical example is given to illustrate the effectiveness of the approach.

An Off-line Approach to Dynamic Output Feedback Robust Model Predictive Control

摘要: 研究具有多包不确定性和有界噪声系统的动态输出反馈鲁棒模型预测控制(Robust model predictive control, RMPC)的离线方法. 先前的在线方法中, 在估计状态和估计误差集合已知的情况下, 在每一采样时刻通过近似最优算法求解控制器参数. 本文采用先前的方法计算离线控制器参数和吸引域. 首先, 选定一系列估计状态, 其中,每个估计状态对应同样一组嵌套的估计误差集合. 然后,针对每一估计状态和每一估计误差集合的组合,离线计算唯一的控制器参数和对应的吸引域. 这些控制器参数和对应的吸引域存储在表中. 如果离线确定的吸引域包含实时的扩展状态, 则该离线控制器参数是实时可行的. 在线时, 根据实时估计状态和选取实时估计误差集合, 在表中搜索包含实时扩展状态且优化性能指标最小的吸引域所对应的控制器参数. 通过连续搅拌釜式反应器控制系统验证了该方法的有效性. 关键词: 动态输出反馈 / 模型预测控制 / 不确定系统 / 离线方法

On dynamic output feedback robust MPC for constrained quasi-LPV systems

This paper considers the dynamic output feedback robust model predictive control (MPC) of a quasi-linear parameter varying (quasi-LPV) system with bounded noise. In our previous works, for the unknown true state, either its ellipsoidal bounds or its polyhedral bounds were solely applied in the main optimisation problem. The recursive feasibility of the main optimisation problem was guaranteed by a simple refreshment of the ellipsoidal bound, but might be lost by applying the polyhedral bounds. This paper shows how and to what extent the recursive feasibility can be restored when the polyhedral bounds are still utilised. First, we propose a new approach which, at each sampling time, utilises either the ellipsoidal bound or the polyhedral bound in the main optimisation problem, the latter being used if and only if it is contained in the former. Then, we show the sufficient conditions under which the approaches based on polyhedral bounds preserve the property of recursive feasibility. A numerical example is given to illustrate the effectiveness of the controller.

Off-line approach to dynamic output feedback robust model predictive control

This paper presents an off-line approach to the dynamic output feedback robust model predictive control (OFRMPC) for a system with both polytopic uncertainty and bounded disturbance. For the off-line optimization, a sequence of controller parameters and the corresponding regions of attraction are calculated for all combinations of the pre-specified estimated states and estimation error sets (EESs). These controller parameters and the corresponding regions of attraction are stored in a look-up table. On-line, the controller parameters are searched in this look-up table corresponding to real-time EES, and to the region of attraction with the closest containment of real-time estimated state. This method considerably reduces the on-line computational burden. Two numerical examples are given to illustrate the effectiveness of the approach.

Dynamic Output Feedback Robust Model Predictive Control

This paper addresses the synthesis approach of dynamic output feedback robust model predictive control for systems with both polytopic uncertainty and bounded disturbance.The system is quasi-linear parameter varing,i.e.,the time-varing parameters of the system are exactly known at the current time but unknown in the future.The notion of quadratic boundedness is utilized to characterize the stability properties of the augmented closed-loop system.The primary contribution of this paper is to propose a method for the auxiliary optimization to provide reliable bounds of true state for the main optimization problem at the next sampling time.A continuous stirred tank reactor control system is given to illustrate the e?ectiveness of the approach.

New Formulation of Dynamic Output Feedback Robust Model Predictive Control with Guaranteed Quadratic Boundedness

AbstractThe dynamic output feedback robust model predictive controller for a system with both polytopic uncertainty and bounded disturbance is addressed in this paper. This controller utilizes a main optimization problem to find the control law and a simple auxiliary optimization problem to refresh the bounds on the true state. The main optimization problem, which is not necessarily solved at each sampling instant, achieves the near‐optimal solution. The auxiliary optimization, which is solved at each sampling instant, is followed with a simple criterion which determines whether or not to solve the main optimization problem at the next sampling time. By applying the proposed method, the augmented state of the closed‐loop system is guaranteed to converge to the neighborhood of the equilibrium point.

Dynamic output feedback robust model predictive control

The synthesis approach for dynamic output feedback robust model predictive control is considered. The notion of quadratic boundedness is utilised to characterise the stability properties of the augmented closed-loop system. A finite horizon performance cost, which corresponds to the worst case of both the polytopic uncertainty and the bounded disturbance/noise, is utilised. It is not required to specify the horizon length. A numerical example is given to illustrate the effectiveness of the proposed controller.