Predictive metamorphic control

In spite of its easy implementation, ability to handle constraints and nonlinearities, etc., model predictive control (MPC) does have drawbacks including tuning difficulties. In this paper, we propose a refinement to the basic MPC strategy by incorporating a tuning parameter such that one can move smoothly from an existing controller to a new MPC strategy. Each change of this tuning parameter leads to a new stabilising control law, therefore, allowing one to gradually move from an existing control law to a new and better one. For the infinite horizon case without constraints and for the general case with state and input constraints, stability results are established. We also examine the practical applicability of the proposed approach by employing it in the nominal prediction model of the tube-based output feedback robust MPC method. The merits of the proposed method are illustrated by examples.     

Stabilization of linear systems over networks with bounded packet loss and its use in model predictive control

This paper considers stabilization of discrete-time linear systems, where network exists for transmitting the sensor and controller information, and arbitrary bounded packet loss occurs in the sensor–controller link and the controller–actuator link. The stabilization of this system is transformed into the robust stabilization of a set of systems. The stability result for this system is specially applied on model predictive control (MPC) that explicitly considers the satisfaction of input and state constraints. Two synthesis approaches of MPC are presented, one parameterizing the infinite horizon control moves into a single state feedback law, the other into a free control move followed by the single state feedback law. Two simulation examples are given to illustrate the effectiveness of the proposed techniques.     

Adaptive receding horizon predictive control for constrained discrete-time linear systems with parameter uncertainties

This paper proposes a discrete-time model predictive control (MPC) scheme combined with an adaptive mechanism. To this end, first, an adaptive parameter estimation algorithm suitable for MPC is proposed, which uses the available input and output signals to estimate the unknown system parameters. It enables the prediction of a monotonically decreasing worst-case estimation error bound over the prediction horizon of MPC. These distinctive features allow for future model improvement to be explicitly considered in MPC. Thus, a less conservative adaptive-type MPC controller can be developed based on the proposed estimation method. Second, we show how the discrete-time adaptive-type state-feedback MPC controller is constructed by combining the on-line parameter estimation scheme with a modified robust MPC method based on the comparison model. The developed MPC controller guarantees feasibility and stability of the closed-loop system theoretically in the presence of input and state constraints. A numerical example is given to demonstrate its effectiveness.     

Synthesis of Mixed Objective Output Feedback Robust Model Predictive Control

Aiming at the constrained polytopic uncertain system with energy‐bounded disturbance and unmeasurable states, a novel synthesis scheme to design the output feedback robust model predictive control(MPC)is put forward by using mixed H₂/H_∞ design approach. The proposed scheme involves an offline design of a robust state observer using linear matrix inequalities(LMIs)and an online output feedback robust MPC algorithm using the estimated states in which the desired mixed objective robust output feedback controllers are cast into efficiently tractable LMI‐based convex optimization problems. In addition, the closed‐loop stability and the recursive feasibility of the proposed robust MPC are guaranteed through an appropriate reformulation of the estimation error bound (EEB). A numerical example subject to input constraints illustrates the effectiveness of the proposed controller.     

Integrating dynamic economic optimization and model predictive control for optimal operation of nonlinear process systems

In this work, we propose a conceptual framework for integrating dynamic economic optimization and model predictive control (MPC) for optimal operation of nonlinear process systems. First, we introduce the proposed two-layer integrated framework. The upper layer, consisting of an economic MPC (EMPC) system that receives state feedback and time-dependent economic information, computes economically optimal time-varying operating trajectories for the process by optimizing a time-dependent economic cost function over a finite prediction horizon subject to a nonlinear dynamic process model. The lower feedback control layer may utilize conventional MPC schemes or even classical control to compute feedback control actions that force the process state to track the time-varying operating trajectories computed by the upper layer EMPC. Such a framework takes advantage of the EMPC ability to compute optimal process time-varying operating policies using a dynamic process model instead of a steady-state model, and the incorporation of suitable constraints on the EMPC allows calculating operating process state trajectories that can be tracked by the control layer. Second, we prove practical closed-loop stability including an explicit characterization of the closed-loop stability region. Finally, we demonstrate through extensive simulations using a chemical process model that the proposed framework can both (1) achieve stability and (2) lead to improved economic closed-loop performance compared to real-time optimization (RTO) systems using steady-state models.     

Robust model predictive control for optimal continuous drug administration

In this paper the model predictive control (MPC) technology is used for tackling the optimal drug administration problem. The important advantage of MPC compared to other control technologies is that it explicitly takes into account the constraints of the system. In particular, for drug treatments of living organisms, MPC can guarantee satisfaction of the minimum toxic concentration (MTC) constraints. A whole-body physiologically-based pharmacokinetic (PBPK) model serves as the dynamic prediction model of the system after it is formulated as a discrete-time state-space model. Only plasma measurements are assumed to be measured on-line. The rest of the states (drug concentrations in other organs and tissues) are estimated in real time by designing an artificial observer. The complete system (observer and MPC controller) is able to drive the drug concentration to the desired levels at the organs of interest, while satisfying the imposed constraints, even in the presence of modelling errors, disturbances and noise.     

Stochastic model predictive control for probabilistically constrained Markovian jump linear systems with additive disturbance

Model predictive control (MPC) for Markovian jump linear systems with probabilistic constraints has received much attention in recent years. However, in existing results, the disturbance is usually assumed with infinite support, which is not considered reasonable in real applications. Thus, by considering random additive disturbance with finite support, this paper is devoted to a systematic approach to stochastic MPC for Markovian jump linear systems with probabilistic constraints. The adopted MPC law is parameterized by a mode‐dependent feedback control law superimposed with a perturbation generated by a dynamic controller. Probabilistic constraints can be guaranteed by confining the augmented system state to a maximal admissible set. Then, the MPC algorithm is given in the form of linearly constrained quadratic programming problems by optimizing the infinite sum of derivation of the stage cost from its steady‐state value. The proposed algorithm is proved to be recursively feasible and to guarantee constraints satisfaction, and the closed‐loop long‐run average cost is not more than that of the unconstrained closed‐loop system with static feedback. Finally, when adopting the optimal feedback gains in the predictive control law, the resulting MPC algorithm has been proved to converge in the mean square sense to the optimal control. A numerical example is given to verify the efficiency of the proposed results.     

Model predictive control of constrained LPV systems

This article considers robust model predictive control (MPC) schemes for linear parameter varying (LPV) systems in which the time-varying parameter is assumed to be measured online and exploited for feedback. A closed-loop MPC with a parameter-dependent control law is proposed first. The parameter-dependent control law reduces conservativeness of the existing results with a static control law at the cost of higher computational burden. Furthermore, an MPC scheme with prediction horizon ‘1’ is proposed to deal with the case of asymmetric constraints. Both approaches guarantee recursive feasibility and closed-loop stability if the considered optimisation problem is feasible at the initial time instant.     

基于滚动优化和能量回收的V2I电动汽车决策

通过对标准新欧洲汽车法规循环(NEDC)工况的分析,提取出NEDC工况中的实时交通信息,分析不同驾驶状态对于车辆能耗的影响,提出一种新的基于实时交通信息的适用于V2I车辆的测试工况;结合电动汽车能量回收的优点,考虑电池-电机-制动特性约束,设计多源信息融合框架下的制动力分配策略;结合模型预测控制(MPC)的滚动优化思想提出MPC软约束框架下的电动汽车V2I最优控制策略;在AMESim & Simulink联合仿真平台上进行高精度纯电动车整车建模和MPC最优控制器的设计;对优化后车辆和未优化的车辆进行仿真对比验证,结果表明:结合道路交通信息进行最优决策的V2I纯电动车辆可有效降低车辆运行中的启停频率,减少整车能耗、车辆加速度和冲击度幅度,并显著提高整车经济性和舒适性.     

Non-fragile observer-based output feedback control for polytopic uncertain system under distributed model predictive control approach

In this paper, a non-fragile observer-based output feedback control problem for the polytopic uncertain system under distributed model predictive control (MPC) approach is discussed. By decomposing the global system into some subsystems, the computation complexity is reduced, so it follows that the online designing time can be saved.Moreover, an observer-based output feedback control algorithm is proposed in the framework of distributed MPC to deal with the difficulties in obtaining the states measurements. In this way, the presented observer-based output-feedback MPC strategy is more flexible and applicable in practice than the traditional state-feedback one. What is more, the non-fragility of the controller has been taken into consideration in favour of increasing the robustness of the polytopic uncertain system. After that, a sufficient stability criterion is presented by using Lyapunov-like functional approach, meanwhile, the corresponding control law and the upper bound of the quadratic cost function are derived by solving an optimisation subject to convex constraints. Finally, some simulation examples are employed to show the effectiveness of the method.     

Trajectory following for a flexible probe with state/input constraints: An approach based on model predictive control

This paper describes the trajectory following algorithm developed for a bio-inspired flexible probe, the direction of which can be controlled by means of an offset between interlocked probe segments which make up its body. The control approach employs model predictive control (MPC) to explicitly consider input and state constraints which arise from the unique mechanism of motion of the probe. For the sake of fast computation, a tracking error model is modified so that the nonlinear kinematic model of the probe is linearized, and the model is used to convert the optimization problem into a well-known quadratic programming (QP) problem. The input and state constraints are also converted into an inequality to be integrated into the QP problem. Simulated results demonstrate that the linearized tracking error model and the MPC control strategy are appropriate, handling large perturbations robustly, while satisfying all constraints. Experimental results in a gelatine sample, carried out with a 12 mm outer diameter prototype, demonstrate satisfactory two-dimensional trajectory following performance (0.52 mm average tracking error, with 1.49 mm STD). The experimental results also show that, given the probe’s constraints, the proposed controller provides more robust performance against large insertion perturbations than previously published control strategies developed for the probe.     

Resource-aware MPC for constrained nonlinear systems: A self-triggered control approach

In systems with resource constraints, such as actuation limitations or limited communication bandwidth, it is desired to obtain control signals that are either sparse or sporadically changing in time to reduce resource utilization. In this paper, we propose a resource-aware self-triggered MPC strategy for discrete-time nonlinear systems subject to state and input constraints that has three important features: Firstly, significant reductions in resource utilization can be realized without modifying the cost function by input regularization or explicitly penalizing resource usage. Secondly, the control laws and triggering mechanisms are synthesized so that a priori chosen performance levels (in terms of the original cost function) are guaranteed by design next to asymptotic stability and constraint satisfaction. Thirdly, we address the co-design problem of jointly designing the feedback law and the triggering condition. By means of numerical examples, we show the effectiveness of this novel strategy.     

A fast ellipsoidal MPC scheme for discrete-time polytopic linear parameter varying systems

This paper proposes a fast ellipsoidal Model Predictive Control (MPC) strategy to address feedback regulation problems for constrained polytopic Linear Parameter Varying (LPV) systems subject to bounded disturbances. In order to deal with the specific non-convex structure of the state prediction tubes arising in LPV contexts, a new convexification procedure is proposed and, based on the off-line computation of a sequence of inner ellipsoidal approximations of exact one-step controllable sets, a computationally low-demanding MPC algorithm is presented. Comparisons with state-of-the-art MPC control algorithms for LPV systems are reported in a final numerical example where several methods are contrasted in terms of achievable domains of attraction, control performance, numerical burdens and memory requirements.     

Design of networked control systems with bounded arbitrary time delays

This paper is mainly concerned with the model predictive control (MPC) of networked control systems (NCSs) with uncertain time delay and data packets disorder. The network-induced time delay is described as bounded and arbitrary process. For the usual state feedback controller, by considering all the possibilities of delays, an augmented state space model of the closed-loop system, which characterizes all the delay cases, is obtained. The stability conditions are given according to the Lyapunov method based on this augmented model. The stability property is inherited in MPC which explicitly considers the physical constraints. A numerical example is given to demonstrate the effectiveness of the proposed MPC.     

Planning under uncertainty using model predictive control for information gathering

This paper considers trajectory planning problems for autonomous robots in information gathering tasks. The objective of the planning is to maximize the information gathered within a finite time horizon. It is assumed that either the Extended Kalman Filter (EKF) or the Extended Information Filter (EIF) is applied to estimate the features of interest and the information gathered is expressed by the covariance matrix or information matrix. It is shown that the planning process can be formulated as an optimal control problem for a nonlinear control system with a gradually identified model. This naturally leads to the Model Predictive Control (MPC) planning strategy, which uses the updated knowledge about the model to solve a finite horizon optimal control problem at each time step and only executes the first control action. The proposed MPC framework is demonstrated through solutions to two challenging information gathering tasks: (1) Simultaneous planning, localization, and map building (SPLAM) and (2) Multi-robot Geolocation. It is shown that MPC can effectively deal with dynamic constraints, multiple robots/features and a range of objective functions.     

Predictive control of switched nonlinear systems with scheduled mode transitions

In this work, a predictive control framework is proposed for the constrained stabilization of switched nonlinear systems that transit between their constituent modes at prescribed switching times. The main idea is to design a Lyapunov-based predictive controller for each constituent mode in which the switched system operates and incorporate constraints in the predictive controller design which upon satisfaction ensure that the prescribed transitions between the modes occur in a way that guarantees stability of the switched closed-loop system. This is achieved as follows: For each constituent mode, a Lyapunov-based model predictive controller (MPC) is designed, and an analytic bounded controller, using the same Lyapunov function, is used to explicitly characterize a set of initial conditions for which the MPC, irrespective of the controller parameters, is guaranteed to be feasible, and hence stabilizing. Then, constraints are incorporated in the MPC design which, upon satisfaction, ensure that: 1) the state of the closed-loop system, at the time of the transition, resides in the stability region of the mode that the system is switched into, and 2) the Lyapunov function for each mode is nonincreasing wherever the mode is reactivated, thereby guaranteeing stability. The proposed control method is demonstrated through application to a chemical process example.     

A robust gradient-based MPC for integrating real time optimizer (RTO) with control

A gradient-based model predictive control (MPC) strategy was recently proposed to reduce the computational burden derived from the explicit inclusion of an economic real time optimization (RTO). The main idea is to compute a suboptimal solution, which is the convex combination of a feasible solution and a solution of an approximated (linearized) problem. The main benefits of this strategy are that convergence is still guaranteed and good economic performances are obtained, according to several simulation scenarios. The formulation, however, is developed only for the nominal case, which significantly reduces its applicability. In this work, an extension of the gradient-based MPC to explicitly account for disturbances is made. The resulting robust formulation considers a nominal prediction model, but restricted constraints (in order to account for the effect of additive disturbances). The nominal economic performance is preserved and robust stability is ensured. An illustrative example shows the benefits of the proposal.     

Quasi-min-max output-feedback model predictive control for LPV systems with input saturation

In the research field of model predictive control (MPC), an output-feedback-type MPC method is consistently required for controlling a wide range of constrained systems. In this paper, we propose a two-stage control strategy for polytopic linear parameter varying (LPV) systems subject to input constraints. This strategy consists of a modified quasi-min-max output-feedback MPC method and a novel terminal output-feedback robust control technique. The proposed control mechanism involves the system states to be first controlled via the MPC method to be driven into a prescribed neighborhood of the origin, and then, the terminal output-feedback robust control method guaranteeing the input constraints is applied to make such states converge to the origin. It is also verified that our control method guarantees the closed-loop stability and feasibility in the presence of model uncertainties and input constraints. Finally, a numerical example is given to demonstrate its effectiveness.     

Model predictive control with robust feasibility

This paper presents a new model predictive control (MPC) method that provides robust feasibility with tractable, real-time computation. The method optimizes the closed-loop system dynamics, which involves models of the process (with parametric uncertainty) and controller at each step in the prediction horizon. Such problems are often formulated as a multi-stage stochastic program that suffers from the curse of dimensionality. This paper presents an alternative formulation that yields a bilevel stochastic optimization problem that is transformed by a series of reformulation steps into a tractable problem such that it can be solved through a limited number of second order cone programming sub-problems. The method addresses robust feasibility, manipulated saturation, state and output soft constraints, exogenous and endogenous uncertainty, and uncertainty in the state estimation in an integrated manner. Case study results demonstrate the advantages of the proposed robust MPC over nominal MPC and several other robust MPC formulations.     

Stochastic tube MPC with state estimation

An output feedback Model Predictive Control (MPC) strategy for linear systems with additive stochastic disturbances and probabilistic constraints is proposed. Given the probability distributions of the disturbance input, the measurement noise and the initial state estimation error, the distributions of future realizations of the constrained variables are predicted using the dynamics of the plant and a linear state estimator. From these distributions, a set of deterministic constraints is computed for the predictions of a nominal model. The constraints are incorporated in a receding horizon optimization of an expected quadratic cost, which is formulated as a quadratic program. The constraints are constructed so as to provide a guarantee of recursive feasibility, and the closed loop system is stable in a mean-square sense. All uncertainties in this paper are taken to be bounded—in most control applications this gives a more realistic representation of process and measurement noise than the more traditional Gaussian assumption.