Predictive Control Of Nonlinear Systems Research Articles

Self‐triggered predictive control of nonlinear systems using approximation model

AbstractThis article studies discrete‐time model predictive control of continuous‐time nonlinear systems with measurement noises and exogenous disturbances. We consider the co‐design of discrete‐time finite horizon optimal control problem (FHOCP) and the associated self‐triggering schemes that schedule the time instants for sampling the state and computing the FHOCP. The state‐dependent nature of the self‐triggered scheduling can not only dynamically adjust the inter‐sampling period according to the system status, but dynamically discretize the model used in the FHOCP as well, in order to reduce the complexity of the FHOCP if designed appropriately. It is shown that the system can be stabilized with uniform ultimate boundedness, as long as the scheduling scheme matches the approximation model such that the one‐step approximation error between the predicted state and the actual state is below a threshold related to the cost function. These results can be applied to most existing model approximation methods with either fixed or time‐varying sampling rates.

Model-free predictive control of nonlinear systems under False Data Injection attacks

The control systems attacked by False Data Injection (FDI) force the equipment out of action. This paper presents a model-free predictive control framework based on polynomial regressors that attenuates adverse effects of FDI attacks on control systems modeled by the nonlinear systems. An FDI attacker targets at tampering the state estimation results, thereby destroy the security of control systems. In order to guarantee its stability, the polynomial regression vectors are considered. The novel point of this paper is the improvement of existing attack datasets by the polynomial regression which combines previous recorded datasets and attack datasets. The polynomial regression vectors can ensure the stable operation of the nonlinear systems guaranteed under FDI attacks. Finally, the simulation is employed to verify our points.

Multiple Model Predictive Control for Nonlinear Systems Based on Self-Balanced Multimodel Decomposition

Multiple Model Predictive Control for Nonlinear Systems Based on Self-Balanced Multimodel Decomposition

Hybrid Koopman model predictive control of nonlinear systems using multiple EDMD models: An application to a batch pulp digester with feed fluctuation

In the pulping process, feed fluctuations often occur due to the supply of raw materials from various and unconventional sources, such as recycle to meet the increasing market demand for paper, and strict environmental regulations. However, such feed fluctuation can significantly extend the operating range of the process, which may cause differing local dynamics that degrade the performance of a single model-based controller. Motivated by these concerns, in this work, a hybrid Koopman model predictive control (KMPC) framework for a batch pulping process is developed to regulate the Kappa number and the cell wall thickness (CWT) of fibers to produce pulp with desired properties in the presence of feed fluctuations. Specifically, multiple local models are constructed by clustering the time-series operation data from the pulping process and identifying lifted state–space models for each cluster using extended dynamic mode decomposition (EDMD). Subsequently, a local EDMD model-based controller for each cluster is developed. In the closed-loop system, one local controller is selected based on the current system state at every time step. Consequently, in the numerical experiments, the derived multiple EDMD models successfully predicted the local behavior of the batch pulping process, and the developed hybrid KMPC system was able to obtain the desired Kappa number and CWT values in the presence of feed fluctuations.

Membership-function-dependent model predictive control for nonlinear systems in a piecewise-fuzzy framework

This paper is concerned with the membership-function-dependent model predictive control (MPC) problem for a class of Takagi-Sugeno (T-S) fuzzy systems with hard constraints. In order to design a set of membership-function-dependent controllers in the framework of MPC, the original T-S fuzzy systems are equivalently converted into a piecewise-fuzzy model by means of the partition method of the premise variable space. Then, instead of calculating vertices to construct the fuzzy MPC controller as adopted in the traditional T-S fuzzy control strategies, some staircase membership functions are employed to approximate the continuous membership functions, such that the information of membership functions can be adequately considered in the control synthesis to reduce the conservatism of the controller design. Furthermore, associated with the piecewise-fuzzy model, an online optimization problem based on the membership-function-dependent terminal constraint set is formulated in terms of the piecewise-Lyapunov-function-based MPC to calculate the feedback gains. Besides, by employing polynomial constraints based on the shape information of the membership functions, errors between the staircase membership functions and the original continuous membership functions are taken into account for facilitating the feasibility investigation and the stability analysis. Finally, two illustrative examples are used to illustrate the validity of the proposed membership-function-dependent MPC strategy.

Emerging approaches for nonlinear parameter varying systems

Emerging approaches for nonlinear parameter varying systems

An efficient algorithm for collaborative learning model predictive control of nonlinear systems

This paper contributes to an efficiently computational algorithm of collaborative learning model predictive control for nonlinear systems and explores the potential of subsystems to accomplish the task collaboratively. The collaboration problem in the control field is usually to track a given reference over a finite time interval by using a set of systems. These subsystems work together to find the optimal trajectory under given constraints in this study. We implement the collaboration idea into the learning model predictive control framework and reduce the computational burden by modifying the barycentric function. The properties, including recursive feasibility, stability, convergence, and optimality, are proved. The simulation is presented to show the system performance with the proposed collaborative learning model predictive control strategy.

Model Predictive Control of Nonlinear System Based on GA-RBP Neural Network and Improved Gradient Descent Method

A model predictive control (MPC) method based on recursive backpropagation (RBP) neural network and genetic algorithm (GA) is proposed for a class of nonlinear systems with time delays and uncertainties. In the offline modeling stage, a multistep-ahead predictor with GA-RBP neural network is designed, where GA-BP neural network is used as a one-step prediction model and GA is employed to train the initial weights and bias of the BP neural network. The incorporation of GA into RBP can reduce the possibility of the BP neural network falling into a local optimum instead of reaching global optimization. In the online optimizing stage, a multistep-ahead GA-RBP neural network predictor and an improved gradient descent method (IGDM) are proposed to efficiently solve the online optimization problem of nonlinear MPC by minimizing a modified quadratic criterion. The designed MPC strategy can avoid information loss while linearizing the controlled system and computing the Hessian matrix and its inverse matrix. Experimental results show that the proposed approach can reduce the computational burden and improve the performance of MPC (i.e., the maximum overshoots, calculation time, rise time, and RMSE tracking error value) for the solution of nonlinear controlled systems.

Predictive Control using LPV Techniques for Fast Discrete Time Nonlinear Systems with Changing Setpoints

Abstract An approach to model predictive control of nonlinear systems with fast dynamics, disturbances, as well as polytopic state and input constraints is presented. Techniques based on linear parameter varying (LPV) systems are used to obtain multiple polyhedral invariant sets to establish stability constraints and to allow for linear prediction models for fast online computation. The presented approach enables switching between setpoints in different operating regions without the need of re-computing the sets online.

Model predictive control for nonlinear systems with time‐varying dynamics and guaranteed Lyapunov stability

SummaryThis article focuses on model predictive control (MPC) of nonlinear systems in the case that the system parameters are inaccurate due to equipment wear or environmental changes. An MPC where the parameters of the predictive model are recursive estimated is proposed for nonlinear continuous time systems. The range of initial state that is able to guarantee the state always bounded in an allowable stability region, even when there does not exist any robust control law designed based on the mismatched initial model, is deduced. The corresponding optimization problem is designed based on Lyapunov controller techniques and includes parameter estimation parts. By this method, the state will eventually converge to a small neighborhood of the desired set‐point. Stability analysis is performed and an application of the proposed method to the chemical process is presented to show the effectiveness of the proposed method.

Explicit multiobjective model predictive control for nonlinear systems with symmetries

SummaryModel predictive control is a prominent approach to construct a feedback control loop for dynamical systems. Due to real‐time constraints, solving model‐based optimal control problems in a very short amount of time can be challenging. For linear‐quadratic problems, Bemporad et al have proposed an explicit formulation where the underlying optimization problems are solved a priori in an offline phase. In this article, we present an extension of this concept in two significant ways. We consider nonlinear problems and—more importantly—problems with multiple conflicting objective functions. In the offline phase, we build a library of Pareto optimal solutions from which we then obtain a valid compromise solution in the online phase according to a decision maker's preference. Since the standard multiparametric programming approach is no longer valid in the nonlinear situation, we instead use interpolation between different entries of the library. To reduce the number of problems that have to be solved in the offline phase, we exploit symmetries in the dynamical system and the corresponding multiobjective optimal control problem. The results are verified using two different examples from autonomous driving.

Explicit multiobjective model predictive control for nonlinear systems under uncertainty

SummaryIn real‐world problems, uncertainties (eg, errors in the measurement, precision errors, among others) often lead to poor performance of numerical algorithms when not explicitly taken into account. This is also the case for control problems, where in the case of uncertainties, optimal solutions can degrade in quality or they can even become unfeasible. Thus, there is the need to design methods that can handle uncertainty. In this work, we consider nonlinear multiobjective optimal control problems with uncertainty on the initial conditions, and in particular their incorporation into a feedback loop via model predictive control. For such problems, not much has been reported in terms of uncertainties. To address this problem class, we design an offline/online framework to compute an approximation of efficient control strategies. In order to reduce the numerical cost of the offline phase—which grows exponentially with the parameter dimension—we exploit symmetries in the control problems. Furthermore, in order to ensure optimality of the solutions, we include an additional online optimization step, which is considerably cheaper than the original multiobjective optimization problem. We test our framework on a car maneuvering problem where safety and speed are the objectives. The multiobjective framework allows for online adaptations of the desired objective. Our results show that the method is capable of designing driving strategies that deal better with uncertainties in the initial conditions, which translates into potentially safer and faster driving strategies.

Nonlinear predictive control employing Carleman bilinearization and fixed search directions

AbstractThis work is concerned with the predictive control of nonlinear systems using the Carleman bilinearization technique. Given a nonlinear system model with sufficient regularity, a bilinear approximation can be obtained by means of Carleman's technique. After discretizing the continuous time model, several algorithms exist to tackle the bilinear model predictive control (BMPC) problem. More specifically, the present work exploits the combination of Carleman's approximation with a fixed search directions algorithm previously proposed within the context of BMPC. Simulations are carried out in order to compare predictive controllers designed using bilinear and linear plant models, but acting on the original nonlinear system. Moreover, the fixed search directions algorithm is compared with the use of a standard interior point optimizer. As a result, the proposed method is shown to provide improvements in terms of either stability, constraint satisfaction or reduced computational effort.

Model Predictive Control of Non-Linear Systems Using Tensor Flow-Based Models

The present paper proposes an approach for the development of a non-linear model-based predictive controller (NMPC) using a non-linear process model based on Artificial Neural Networks (ANNs). This work exploits recent trends on ANN literature using a TensorFlow implementation and shows how they can be efficiently used as support for closed-loop control systems. Furthermore, it evaluates how the generalization capability problems of neural networks can be efficiently overcome when the model that supports the control algorithm is used outside of its initial training conditions. The process’s transient response performance and steady-state error are parameters under focus and will be evaluated using a MATLAB’s Simulink implementation of a Coupled Tank Liquid Level controller and a Yeast Fermentation Reaction Temperature controller, two well-known benchmark systems for non-linear control problems.

Model predictive control for nonlinear systems in Takagi-Sugeno’s form under round-robin protocol

In this paper, we focus on the investigation of the fuzzy model predictive control (FMPC) problem for nonlinear systems characterized by Takagi-Sugeno (T-S) fuzzy form with hard constraints on the control input and the state. To reduce the data transmission burden and improve the network utilization, a so-called Round-Robin (RR) communication protocol is employed to orchestrate data transmission orders via the shared communication network, which is located from controller nodes to the actuator node. In light of the token-dependent quadratic function approach, a switching system is constructed based on the data transmission period regarding the adopted RR protocol. Then, with respect to system nonlinearities in the case of the T-S fuzzy form, a “min-max” problem is formulated by resorting to the objective function over the infinite horizon. Our purpose is to find a series of desired controllers in terms of FMPC approach such that the underlying T-S fuzzy system is asymptotically stable. With taking the T-S fuzzy nonlinearities and the RR protocol fully into consideration, sufficient conditions are provided through an online auxiliary optimization problem. Finally, two simulation examples are used to demonstrate the effectiveness and the validity of the proposed methods.

Control predictivo robusto descentralizado basado en tubos: aplicación a un sistema de cuatro tanques

This paper presents a decentralized model predictive controller for nonlinear systems that considers interaction between control inputs. The controller is based on a centralized robust tube-based nonlinear model predictive controller. The main contribution is a procedure to split the process model into s subsystems in order to construct s robust tube-based controllers ensuring a bounded linearization error. In order to show the applicability and effectiveness of the development, the proposed controller is tested on a coupled-tank system and the results are compared with a centralized nonlinear model predictive controller.

Integral-Type Event-Triggered Model Predictive Control of Nonlinear Systems With Additive Disturbance.

This article studies integral-type event-triggered model predictive control (MPC) of continuous-time nonlinear systems. An integral-type event-triggered mechanism is proposed by incorporating the integral of errors between the actual and predicted state sequences, leading to reduced average sampling frequency. Besides, a new and improved robustness constraint is introduced to handle the additive disturbance, rendering the MPC problem with a potentially enlarged initial feasible region. Furthermore, the feasibility of the designed MPC and the stability of the closed-loop system are rigorously investigated. Several sufficient conditions to guarantee these properties are established, which is related to factors, such as the prediction horizon, the disturbance bound, the triggering level, and the contraction rate for the robustness constraint. The effectiveness of the proposed algorithm is illustrated by numerical examples and comparisons.

PolyMPC: An efficient and extensible tool for real‐time nonlinear model predictive tracking and path following for fast mechatronic systems

SummaryThis paper presents PolyMPC, an open‐source C++ library for pseudospectral‐based real‐time predictive control of nonlinear systems. It provides a necessary background on the computational aspects of the pseudospectral approximation of optimal control problems and explains how various model predictive control and parameter estimation algorithms can be implemented using the software. We discuss the key algorithmic modules and architectural features of the PolyMPC library. The workflow of a path following controller design for a highly nonlinear mechatronic system is demonstrated in a tutorial example. Another example illustrates how the core functionality might be used to approximate and solve a custom optimal control problem.

Control Lyapunov-Barrier function-based model predictive control of nonlinear systems

In this paper, we propose a Control Lyapunov-Barrier Function-based model predictive control (CLBF-MPC) method for solving the problem of stabilization of nonlinear systems with input constraint satisfaction and guaranteed safety for all times. Specifically, considering the input constraints, a constrained Control Lyapunov-Barrier Function is initially employed to design an explicit control law and characterize a set of initial conditions, starting from which the solution of the nonlinear system is guaranteed to converge to the steady-state without entering a specified unsafe region in the state space. Then, the CLBF-MPC is proposed and is shown to be recursively feasible, and stabilizing and to ensure the avoidance of a set of states in state–space associated with unsafe operating conditions under sample-and-hold control action implementation. Finally, we demonstrate the efficacy of the proposed CLBF-MPC method through application to a chemical process example.

Self‐triggered robust model predictive control for nonlinear systems with bounded disturbances

A self-triggered model predictive control (MPC) scheme for continuous-time perturbed nonlinear systems subject to bounded disturbances is investigated in this study. A self-triggered strategy is designed to obtain the inter-execution time before the next trigger using the current sampled state. An optimisation problem is addressed to obtain the optimal control trajectory at each triggered instant. The so-called dual-mode approach is used to stabilise the perturbed closed-loop system. Furthermore, sufficient conditions are derived to ensure the feasibility and stability, respectively. It is shown that with a properly designed prediction horizon, the feasibility of the proposed self-triggered MPC algorithm can be guaranteed if the disturbance is bounded in a small enough area. Meanwhile, the stability is proved under the self-triggered condition. Finally, a numerical example is given to illustrate the efficacy of the authors proposed scheme.