Robust hybrid predictive control of nonlinear systems

In this work, we consider nonlinear systems with input constraints and uncertain variables, and develop a robust hybrid predictive control structure that provides a safety net for the implementation of any model predictive control (MPC) formulation, designed with or without taking uncertainty into account. The key idea is to use a Lyapunov-based bounded robust controller, for which an explicit characterization of the region of robust closed-loop stability can be obtained, to provide a stability region within which any available MPC formulation can be implemented. This is achieved by devising a set of switching laws that orchestrate switching between MPC and the bounded robust controller in a way that exploits the performance of MPC whenever possible, while using the bounded controller as a fall-back controller that can be switched in at any time to maintain robust closed-loop stability in the event that the predictive controller fails to yield a control move (due, e.g., to computational difficulties in the optimization or infeasibility) or leads to instability (due, e.g., to inappropriate penalties and/or horizon length in the objective function). The implementation and efficacy of the robust hybrid predictive control structure are demonstrated through simulations using a chemical process example.     

Backstepping control integrated with Lyapunov-based model predictive control

In this study, backstepping control integrated with Lyapunov-based model predictive control (BS-MPC) is proposed for nonlinear systems in a strict-feedback form. The virtual input of the first step is designed by solving the finite-horizon optimal control problem (FHOCP), and the real input is designed by the backstepping method. BS-MPC guarantees (semiglobal) ultimate boundedness of the closed-loop system when the control is implemented in a zero-order hold manner. When the robustness of BS-MPC is analyzed for uniformly bounded disturbances, the ultimate boundedness of the solution of perturbed system is guaranteed. BS-MPC can provide a better desired value of the virtual input of the first step by solving the FHOCP, resulting in a faster stabilization of the system compared with the backstepping control. In addition, BS-MPC requires less computational load compared with MPC because the dimension of the states considered in the on-line optimization problem of BS-MPC is lower than that of MPC.     

Isolation and handling of actuator faults in nonlinear systems

This work considers the problem of control actuator fault detection and isolation and fault-tolerant control for a multi-input multi-output nonlinear system subject to constraints on the manipulated inputs and proposes a fault detection and isolation filter and controller reconfiguration design. The implementation of the fault detection and isolation filters and reconfiguration strategy are demonstrated via a chemical process example.     

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.     

Stabilization of max-plus-linear systems using model predictive control: The unconstrained case

Max-plus-linear (MPL) systems are a class of event-driven nonlinear dynamic systems that can be described by models that are “linear” in the max-plus algebra. In this paper we derive a solution to a finite-horizon model predictive control (MPC) problem for MPL systems where the cost is designed to provide a trade-off between minimizing the due date error and a just-in-time production. In general, MPC can deal with complex input and states constraints. However, in this paper we assume that these are not present and it is only required that the input should be a nondecreasing sequence, i.e. we consider the “unconstrained” case. Despite the fact that the controlled system is nonlinear, by employing recent results in max-plus theory we are able to provide sufficient conditions such that the MPC controller is determined analytically and moreover the stability in terms of Lyapunov and in terms of boundedness of the closed-loop system is guaranteed a priori.     

Uniting bounded control and MPC for stabilization of constrained linear systems

In this work, a hybrid control scheme, uniting bounded control with model predictive control (MPC), is proposed for the stabilization of linear time-invariant systems with input constraints. The scheme is predicated upon the idea of switching between a model predictive controller, that minimizes a given performance objective subject to constraints, and a bounded controller, for which the region of constrained closed-loop stability is explicitly characterized. Switching laws, implemented by a logic-based supervisor that constantly monitors the plant, are derived to orchestrate the transition between the two controllers in a way that safeguards against any possible instability or infeasibility under MPC, reconciles the stability and optimality properties of both controllers, and guarantees asymptotic closed-loop stability for all initial conditions within the stability region of the bounded controller. The hybrid control scheme is shown to provide, irrespective of the chosen MPC formulation, a safety net for the practical implementation of MPC, for open-loop unstable plants, by providing a priori knowledge, through off-line computations, of a large set of initial conditions for which closed-loop stability is guaranteed. The implementation of the proposed approach is illustrated, through numerical simulations, for an exponentially unstable linear system.     

Fast model predictive control for linear periodic systems with state and control constraints

The design of stabilizing model predictive control laws for discrete‐time linear periodic systems with state and control constraints is considered. Two algorithms are presented. The first one is based on interpolation between several unconstrained periodic controllers. Among them, one controller is chosen for the performance while the rest are used to extend the domain of attraction. The second algorithm aims to improve the performance by combining model predictive control and interpolating control. The proposed approaches not only guarantee recursive feasibility and asymptotic stability but also are optimal for states near the origin. Copyright © 2017 John Wiley & Sons, Ltd.     

Parameter governors for discrete-time nonlinear systems with pointwise-in-time state and control constraints

Parameter governors are add-on control schemes that adjust parameters (such as gains or offsets) in the nominal control laws to avoid violation of pointwise-in-time state and control constraints and to improve the overall system transient performance via the receding horizon minimization of a cost functional. As compared to more general model predictive controllers, parameter governors tend to be more conservative but the computational effort needed to implement them on-line can be relatively modest because the few parameters to be optimized remain constant over the prediction horizon. In this paper, we discuss the properties of several classes of parameter governors which have a common property in that the governed parameters do not shift the steady-state equilibrium of the states on which the incremental cost function explicitly depends on. This property facilitates the application of meaningful cost functionals. An example, together with simulation results, is reported to provide additional insights into the operation of the proposed parameter governor schemes.     

具有时变通信受限非线性信息物理系统的网络化预测控制

针对具有时变通信受限的一类非线性信息物理系统,本文采用网络化预测控制策略,对于时变通信时延和数据丢失,不是使用常规的被动方式抑制,而是进行主动补偿.为了使补偿时变通信受限的方式简单、主动和通用,提出了一种新颖的网络化非线性预测控制方法.所设计的网络化非线性预测控制器能达到具有与无网络的本地闭环控制系统完全相同的期望控制...     

Adaptive control Lyapunov function based model predictive control for continuous nonlinear systems

A design of adaptive model predictive control (MPC) based on adaptive control Lyapunov function (aCLF) is proposed in this article for nonlinear continuous systems with part of its dynamics being unknown at the starting time. Specifically, to guarantee the convergence of the closed-loop system with online predictive model updating, a stability constraint is designed. It limits the aCLF of the system under the MPC to be less than that under an online updated auxiliary adaptive control. The auxiliary adaptive control which implements in a sampling-hold fashion can guarantee the convergence of the controlled system. The sufficient conditions that guarantee the states to be steered to a small region near the equilibrium by the proposed MPC are provided. The calculation of the proposed algorithm does not depend on the model mismatch at the starting time. And it does not require the Lyapunov function of the state of the real system always to be reduced at each time. These provide the potential to improve the performance of the closed-loop system. The effectiveness of the proposed method is illustrated through a chemical process example.     

State transfer based on decoherence-free target state by Lyapunov-based control

We propose a Lyapunov-based control approach for state transfer based on the decoherence-free target state.The expected target state is constructed to be a decoherence-free state in a decoherence-free subspace(DFS) by an external laser fieldⅠ,so that the system state can be decoupled from the environment,and no more decoherence process will occur.With the decoherence-free target state,we design a Lyapunov-based control fieldⅡto steer the given initial state to the decoherence-free state of open quantum systems as completely as possible,and decouple the system state from the environment at the same time.In the end,it is verified that the state transfer control designed comes true on a∧-type four-level atomic system,and the system can stay on the decoherence-free target state without coupling to environment.     

Transient average constraints in economic model predictive control

In this paper, an economic model predictive control algorithm is proposed which ensures satisfaction of transient average constraints, i.e., constraints on input and state variables averaged over some finite time period. We believe that this stricter form of average constraints (compared to previously proposed asymptotic average constraints) is of independent interest in various applications such as the operation of a chemical reactor, where e.g. the amount of inflow or the heat flux during some fixed period of time must not exceed a certain value. Besides guaranteeing fulfillment of transient average constraints for the closed-loop system, we show that closed-loop average performance bounds and convergence results established in the setting of asymptotic average constraints also hold in case of transient average constraints. Furthermore, we illustrate our results with a chemical reactor example.     

Multi-objective nonlinear predictive control of process systems: A dual-mode tracking control approach

There typically exist different and often conflicting control objectives, e.g., reference tracking, robustness and economic performance, in many chemical processes. The current work considers the multi-objective control problems of continuous-time nonlinear systems subject to state and input constraints and multiple conflicting objectives. We propose a new multi-objective nonlinear model predictive control (NMPC) design within the dual-mode paradigm, which guarantees stability and constraint satisfaction. The notions of utopia point and compromise solution are used to reconcile the confliction of the multiple objectives. The designed controller minimizes the distance of its cost vector to a vector of independently minimized objectives, i.e., the steady-state utopia point. Recursive feasibility is established via a particular terminal region formulation while stabilizing the closed-loop system to the compromise solution via the dual-mode control principle. In order to derive the terminal region as large as possible, a terminal control law with free-parameters is constructed by using the control Lyapunov functions (CLFs) technique. Two examples of multi-objective control of a CSTR and a free-radical polymerization process are used to illustrate the effectiveness of the new multi-objective NMPC and to compare their performance.     

Distributed model predictive control of dynamically decoupled systems with coupled cost

This paper considers the distributed model predictive control (DMPC) of systems with interacting subsystems having decoupled dynamics and constraints but coupled costs. An easily-verifiable constraint is introduced to ensure asymptotic stability of the overall system in the absence of disturbance. The constraint introduced has a parameter which allows for the performance of the DMPC system to approach that controlled by a centralized model predictive controller. When the subsystems are linear and additive disturbance is present, the added constraint ensures the state of each subsystem converges to its respective minimal disturbance invariant set. The approach is demonstrated via several numerical examples.     

Reconfigurable predictive control for redundantly actuated systems with parameterised input constraints

A method is proposed for on-line reconfiguration of the terminal constraint used to provide theoretical nominal stability guarantees in linear model predictive control (MPC). By parameterising the terminal constraint, its complete reconstruction is avoided when input constraints are modified to accommodate faults. To enlarge the region of feasibility of the terminal control law for a certain class of input faults with redundantly actuated plants, the linear terminal controller is defined in terms of virtual commands. A suitable terminal cost weighting for the reconfigurable MPC is obtained by means of an upper bound on the cost for all feasible realisations of the virtual commands from the terminal controller. Conditions are proposed that guarantee feasibility recovery for a defined subset of faults. The proposed method is demonstrated by means of a numerical example.     

Fault-tolerant control of a polyethylene reactor

This work focuses on fault-tolerant control of a gas phase polyethylene reactor. Initially, a family of candidate control configurations, characterized by different manipulated inputs, is identified. For each control configuration, a bounded nonlinear feedback controller, that enforces asymptotic closed-loop stability in the presence of constraints, is designed, and the constrained stability region associated with it is explicitly characterized using Lyapunov-based tools. Next, a fault-detection filter is designed to detect the occurrence of a fault in the control actuator by observing the deviation of the process states from the expected closed-loop behavior. A switching policy is then derived, on the basis of the stability regions, to orchestrate the activation/deactivation of the constituent control configurations in a way that guarantees closed-loop stability in the event of control system faults. Closed-loop system simulations demonstrate the effectiveness of the fault-tolerant control strategy.     

Multi-model predictive control with local constraints based on model switching

Because model switching system is a typical form of Takagi-Sugeno(T-S) model which is an univer sal approximator of continuous nonlinear systems,we describe the model switching system as mixed logical dynamical (MLD) system and use it in model predictive control (MPC) in this paper.Considering t hat each local model is only valid in each l ocal region,we add local constraints to local models.The stability of proposed multi-model predictiv e control (MMPC) algorithm is analyzed, and the p erformance of MMPC is also demonstrated on an in ulti-multi-output(MIMO) simulated pH neutralization process.     

Multi-model predictive control with local constraints based on model switching

Because model switching system is a typical form of Takagi-Sugeno（T-S） model which is an universal approximator of continuous nonlinear systems, we describe the model switching system as mixed logical dynamical （MLD） system and use it in model predictive control （MPC） in this paper. Considering that each local model is only valid in each local region,we add local constraints to local models. The stability of proposed multi-model predictive control （MMPC） algorithm is analyzed, and the performance of MMPC is also demonstrated on an inulti-multi-output（MIMO） simulated pH neutralization process.     

Fuzzy robust constrained model predictive control for nonlinear systems

This paper addresses robust constrained model predictive control (MPC) for a class of nonlinear systems with structured time‐varying uncertainties. First, the Takagi‐Sugeno (T‐S) fuzzy model is employed to represent a nonlinear system. Then, we develop some techniques for designing fuzzy control which guarantees the system stabilization subject to input and output constraints. Both parallel and nonparallel distributed compensation control laws (PDC and non‐PDC) are considered. Sufficient conditions for the solvability of the controller design problem are given in the form of linear matrix inequalities. A simulation example is presented to illustrate the design procedures and performances of the proposed methods. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society