State Feedback Model Predictive Control Research Articles

Membership function‐dependent predictive control for interval type‐2 Takagi–Sugeno fuzzy system

AbstractIn this paper, the problem of membership function‐dependent model predictive control (MFD‐MPC) of interval type‐2 Takagi–Sugeno (IT2 T‐S) fuzzy system is investigated. An online MFD‐MPC optimization problem is formulated to minimize an infinite horizon objective function subject to hard constraints on control input and system state. By using the variable dimension expansion method and dividing the operation domain of independent variables into several subdomains, a subregion‐based state feedback model predictive controller that offers more design flexibility is designed to stabilize the open‐loop fuzzy system. Based on descriptor system theory, the variable mismatching phenomenon between MFs and the coupling between plant, controller, and Lyapunov matrix are eliminated. Then, using the piecewise linear approximation technology, MFD sufficient conditions of low conservatism on guaranteeing recursive feasibility and the stability of IT2 closed‐loop fuzzy system are deduced by tightening terminal constraint set. Finally, a numerical example is provided to further explain the advance of the proposed method.

A novel constraint‐tightening approach for robust data‐driven predictive control

In this paper, we present a data-driven model predictive control (MPC) scheme that is capable of stabilizing unknown linear time-invariant systems under the influence of process disturbances. To this end, Willems' lemma is used to predict the future behavior of the system. This allows the entire scheme to be set up using only a priori measured data and knowledge of an upper bound on the system order. First, we develop a state-feedback MPC scheme, based on input-state data, which guarantees closed-loop practical exponential stability and recursive feasibility as well as closed-loop constraint satisfaction. The scheme is extended by a suitable constraint tightening, which can also be constructed using only data. In order to control a priori unstable systems, the presented scheme contains a prestabilizing controller and an associated input constraint tightening. We first present the proposed data-driven MPC scheme for the case of full state measurements, and also provide extensions for obtaining similar closed-loop guarantees in case of output feedback. The presented scheme is applied to a numerical example.

Load frequency predictive control for power systems concerning wind turbine and communication delay

AbstractThis article addresses a model predictive control (MPC) technique for load frequency control (LFC) system in the presence of wind power, communication delay, and denial‐of‐service (DoS) attack. In this article, communication delay is incorporated into a single area control error transmission for simplicity, wind power and load disturbance are regarded as Lipschitz nonlinear terms, as for the randomly occurring DoS attack, it is modeled as Bernoulli processes with known conditional probability. Thinking all these adverse factors to stability and the limitation of input constraint synthetically, the stability of LFC system can be guaranteed by delay‐dependent Lyapunov function lemma and a state feedback MPC controller is designed to solve the LFC problems by minimizing the infinite‐horizon objective function. Although some scholars have studied the performance degradation and instability of LFC system caused by cyber attack and/or communication delay and some very nice results have been addressed, limited works have considered the MPC approach to deal with both the problems of cyber attack and communication delay which explicitly considers the physical constraints. In addition, the delay‐dependent Lyapunov function is adopted to deal with the problem of communication delay, which results in less conservatism of the presented method. Finally, the optimization problem with input constraint is solved and proven to be recursive feasibility, and the closed‐loop system turns out to be stable. The reasonability and validity of the provided strategy is verified through several groups of simulation experiments. It illustrates that the proposed control method can keep the system frequency steady in the standard range in spite of various attack conditions.

A predictive fault tolerant control method for qLPV systems subject to input faults and constraints

In this paper, we investigate the use of Model Predictive Control (MPC) applications for quasi-Linear Parameter Varying (qLPV) systems subject to faults along the input channels. We propose a Fault Tolerant Control (FTC) mechanism based on a robust state-feedback MPC synthesis, considering polytopic inclusions. In order to alleviate the numerical burden of the robust min-max procedure, we use small prediction horizons, in such a way that the solution becomes viable for real-time systems. The FTC system is able to tolerate time-varying saturation of the actuator, which may happen due to malfunctions. Recursive feasibility and poly-quadratic stability guarantees are ensured through the synthesis of adequate terminal ingredients. Accordingly, we present a catalogue of three different LMI remedies, considering: (a) parameter-independent ingredients, (b) a parameter-dependent terms and (c) a parameter-dependent maps that take into account bounded rates of parameter variation. An autonomous driving car example is used to illustrate the performances of the proposed technique, which is compared to other MPCs from the literature. The proposed FTC method is able to ensure good performances, obtained with reduced computational demand.

Online optimal estimation and control for a common class of activated sludge plants

In this work, we design an output predictive controller that operates a common class of activated sludge plants. The controller solves a state-feedback model predictive control problem in which the process state and disturbances are determined by a moving horizon estimator. We illustrate the behaviour of the controller when operating the plant to produce an effluent water of varying nitrogen content. The close tracking of the effluent profiles is enforced by stabilizing the system around optimal steady-state points that satisfy the output reference trajectories. Considering the generality of the formulation, the predictive controller can be configured to operate this class of activated sludge plants to achieve alternative objectives.

Emerging approaches for nonlinear parameter varying systems

Emerging approaches for nonlinear parameter varying systems

Model Based Robust Predictive Control of Ship Roll/Yaw Motions with Input Constraints

A robust H∞-type state feedback model predictive control (H∞-SFMPC) with input constraints is proposed to optimize the control performance during the ship sailing. Specifically, the approach employed in this paper is able to optimize the closed-loop performance with respect to an H∞-type cost function which predicts the system performance based on the actual model instead of the ideal model. As a result, the effect caused by disturbances is attenuated. The state feedback control gain for the control input of the rudder-fin joint roll/yaw control system is obtained by solving a constrained convex optimization problem in terms of linear matrix inequalities. Simulations are carried out, which reveal that the proposed approach has outstanding control performance. Furthermore, it is found that the approach also has significant robustness with respect to parameter uncertainties.

Real-Time Multi-Rate Predictive Cascade Speed Control of Synchronous Machines in Automotive Electrical Traction Drives

A challenging task in automotive electrical traction drives is to control the speed of synchronous machines due to the existing physical and computational constraints. The goal of this paper is to find a control solution which can answer this problem. To this end, a multirate predictive cascade speed control structure suitable for real-time implementation is proposed. The focus in this paper is only on the design of the outer-loop controller. First, a suitable mathematical model for the outer-loop plant which includes also the dynamics of the inner control loop is obtained. Second, a one-step-ahead state-feedback model predictive controller based on flexible Lyapunov function concept is employed to control the rotor electrical speed. Third, a state and disturbance observer is employed to estimate the load torque and the unmeasured state. This ensures also offset-free operation of the closed-loop system. To illustrate its effectiveness, the proposed control solution is implemented in a real microcontroller and tested in real time on an industrial hardware-in-the-loop test bench and on a real traction test bench.

Model predictive control for constrained uncertain, time-varying systems

In this paper, a new state feedback model predictive control for polytopic uncertain and/or time-varying linear discrete-time systems with input and state constraints is proposed. The main idea is to incorporate state decomposition principle and model predictive control in order to obtain a large domain of attraction using a short prediction horizon. At each time instant a quadratic programming problem is solved on-line. Proofs of recursive feasibility and asymptotic stability are given.

Optimal Control Algorithm of Constrained Fuzzy System Integrating Sliding Mode Control and Model Predictive Control

The sliding mode control and the model predictive control are connected by the value function of the optimal control problem for constrained fuzzy system. New conditions for the existence and stability of a sliding mode are proposed. Those conditions are more general conditions for the existence and stability of a sliding mode. When it is applied to the controller design, the design procedures are different from other sliding mode control (SMC) methods in that only the decay rate of the sliding mode motion is specified. The obtained controllers are state-feedback model predictive control (MPC) and also SMC. From the viewpoint of SMC, sliding mode surface does not need to be specified previously and the sliding mode reaching conditions are not necessary in the controller design. From the viewpoint of MPC, the finite time horizon is extended to the infinite time horizon. The difference with other MPC schemes is that the dependence on the feasibility of the initial point is canceled and the control schemes can be implemented in real time. Pseudosliding mode model predictive controllers are also provided. Closed loop systems are proven to be asymptotically stable. Simulation examples are provided to demonstrate proposed methods.

Sampled‐data MPC for LPV systems with input saturation

In this work, a sampled-data model predictive control (MPC) design method is proposed for continuous-time linear parameter varying (LPV) systems. The input saturation and parameter uncertainties are both considered. Using a method to deal with actuator saturation, the MPC controller is permitted to saturate. Using the measurable parameter vector, a scheduled state-feedback MPC controller is computed at each time instant which fully exploits the real-time information on the variations of the plant characteristics. By modelling the closed-loop systems of the continuous-time LPV systems with a piecewise constant sampled-data control input as linear impulsive systems, the stability properties of the proposed MPC are studied. The sampling interval in this work is not required to be periodic. The proposed MPC design method is expected to further reduce the conservativeness. The improvements of the proposed sampled-data MPC method w.r.t. other existing MPC techniques are demonstrated by an example.

Stabilizing model predictive control of time-varying non-linear systems using linear matrix inequalities

The paper presents a stabilizing model predictive control (MPC) scheme for time-varying non-linear systems subject to input constraints. A state-feedback MPC law is computed by minimizing an upper bound of infinite horizon performance objective, which is formulated as a convex optimization involving linear matrix inequalities constraints. Time-varying linear dynamic approximation is used to derive the stability of the closed-loop system. In particular, a suboptimal algorithm of stabilizing MPC for timevarying non-linear systems is provided to decrease the online computation burden. The performance and effectiveness of the proposed approaches is illustrated by some comparisons with MPC algorithms based on linear polytopic descriptions.

Output‐feedback model predictive controller for voltage regulation of a DC/DC converter

In this study, an output-feedback model predictive controller (MPC) is presented for capacitor voltage regulation on the basis of a non-linear DC/DC converter. The proposed output-feedback MPC scheme is constructed by combining a state-feedback MPC scheme with a Luenberger-type observer. The proposed MPC does not carry out any online optimisation. Although the converter model is non-linear, the proposed observer gain ensures global exponential convergence of the state estimation errors. On the basis of this observer, an output-feedback MPC scheme is designed by certainty equivalence. It is also shown that the capacitor voltage globally converges to its reference while fulfilling input constraints. In order to eliminate the capacitor voltage offset error, a PI controller is employed in the outer loop. The experiment results demonstrate that the closed-loop performance is satisfactory despite the load resistance variations.

Least-restrictive robust periodic model predictive control applied to room temperature regulation

State-feedback model predictive control (MPC) of constrained discrete-time periodic affine systems is considered. The periodic systems’ states and inputs are subject to periodically time-dependent, hard, polyhedral constraints. Disturbances are additive, bounded and subject to periodically time-dependent bounds. The objective is to design MPC laws that robustly enforce constraint satisfaction in a manner that is least-restrictive, i.e., have the largest possible domain. The proposed design method is demonstrated on a building climate control example. The proposed method is directly applicable to time-invariant MPC.

Output feedback predictive control for constrained linear systems with intermittent measurements

This paper studies the robust output feedback model predictive control (MPC) problem for a constrained linear system subject to periodical measurement losses and external disturbances. The overall robust output feedback model predictive controller consists of a robust observer that can accommodate the lost measurement and a new state feedback model predictive controller fulfilling the input and state constraints. Based on the designed observer, the error bounds of the system state estimate are established. By incorporating the estimation error bounds and the external disturbances, the input and state constraints are augmented and further tightened for the new state feedback model predictive controller. Furthermore, the iterative feasibility of the proposed robust output feedback MPC algorithm is proved. It is shown that the closed-loop system is asymptotically stable and the system state will periodically converge to several compact sets. Finally, simulation results and comparison studies are provided to verify effectiveness of the proposed robust output feedback MPC algorithm.

Synthesizing scheduled robust model predictive control with target tracking

Systems with large operating regions and non-zero state target tracking have limited the industrial application of robust model predictive control (RMPC) with synthetic action. To overcome the problem, this paper presents a novel formulation of synthesizing scheduled RMPC for linear time varying (LTV) systems. Off-line, we compute the matrix that transforms target output into steady state first. Then a set of stabilizing state feedback laws which are corresponding to a set of estimated regions of stability covering the desired operating region are provided. On-line, these control laws are implemented as a single scheduled state feedback model predictive control (MPC) which switches between the set of local controllers and achieve the desired target at last. Finally, the algorithm is illustrated with an example.

Nonlinear predictive control based on T-S fuzzy model and particle-swarm optimization

A new constrained state feedback model predictive control approach of nonlinear system based on T-S fuzzy model is developed by combining T-S fuzzy model with constrained state feedback model predictive control based on particle-swarm optimization(PSO).It is used to solve the control problems of process such as CSTR reactor with highly nonlinear and constrains.A constrained state feedback model predictive controller is devised for each subsystem of T-S fuzzy model.In terms of parallel distributed compensation(PDC)fuzzy control theory,control movement and membership function of each subsystem can be calculated and used synthetically to calculate the fuzzy control movement of the whole control system.The control system of a continuous stirred tank reactor is simulated with different initial states,setpoint values and predict steps.The simulation results show that the proposed approach is effective and feasible.

MPC of constrained discrete-time linear periodic systems — A framework for asynchronous control: Strong feasibility, stability and optimality via periodic invariance

State-feedback model predictive control (MPC) of discrete-time linear periodic systems with time-dependent state and input dimensions is considered. The states and inputs are subject to periodically time-dependent, hard, convex, polyhedral constraints. First, periodic controlled and positively invariant sets are characterized, and a method to determine the maximum periodic controlled and positively invariant sets is derived. The proposed periodic controlled invariant sets are then employed in the design of least-restrictive strongly feasible reference-tracking MPC problems. The proposed periodic positively invariant sets are employed in combination with well-known results on optimal unconstrained periodic linear-quadratic regulation (LQR) to yield constrained periodic LQR control laws that are stabilizing and optimal. One motivation for systems with time-dependent dimensions is efficient control law synthesis for discrete-time systems with asynchronous inputs, for which a novel modeling framework resulting in low dimensional models is proposed. The presented methods are applied to a multirate nano-positioning system.

Robust memory state feedback model predictive control for discrete-time uncertain state delayed systems

In this paper, we propose a memory state feedback model predictive control (MPC) law for a discrete-time uncertain state delayed system with input constraints. The model uncertainty is assumed to be polytopic, and the delay is assumed to be unknown, but with a known upper bound. We derive a sufficient condition for cost monotonicity in terms of LMI, which can be easily solved by an efficient convex optimization algorithm. A delayed state dependent quadratic function with an estimated delay index is considered for incorporating MPC problem formulation. The MPC problem is formulated to minimize the upper bound of infinite horizon cost that satisfies the sufficient conditions. Therefore, a less conservative sufficient conditions in terms of linear matrix inequality (LMI) can be derived to design a more robust MPC algorithm. A numerical example is included to illustrate the effectiveness of the proposed method.

Model predictive control of glucose concentration in type I diabetic patients: An in silico trial

In this paper, the feedback control of glucose concentration in type I diabetic patients using subcutaneous insulin delivery and subcutaneous continuous glucose monitoring is considered. A recently developed in silico model of glucose metabolism is employed to generate virtual patients on which control algorithms can be validated against interindividual variability. An in silico trial consisting of 100 patients is used to assess the performances of a linear output feedback and a nonlinear state-feedback model predictive controller, designed on the basis of the in silico model. More than satisfactory results are obtained in the great majority of virtual patients. The experiments highlight the crucial role of the anticipative feedforward action driven by the meal announcement information. Preliminary results indicate that further improvements may be achieved by means of a nonlinear model predictive control scheme.