Predictive Control Of Nonlinear Systems Research Articles

On the terminal region of model predictive control for non‐linear systems with input/state constraints

AbstractThis paper addresses the terminal region of model‐based predictive control (MPC) for non‐linear systems with control input and state constraints. Based on a stability condition of non‐linear MPC, a method to determine the terminal weighting term in the performance index and the terminal stabilizing control law to enlarge the terminal region and thus the domain of attraction of the non‐linear MPC is proposed. An LMI based optimization approach is developed to choose the terminal weighting item and fictitious terminal stabilizing control law so as to enlarge the terminal region of the non‐linear MPC method. The proposed method is illustrated by a numerical example and compares favourably with existing results. Copyright © 2003 John Wiley & Sons, Ltd.

Nonlinear Model-Based Predictive Control Using a Generalised Hammerstein Model and its Application to a Semi-Batch Reactor

In recent years, much attention has been focused upon predictive control of nonlinear systems. The implementation of such a control strategy for real processes has greatly improved their performance. This paper deals with a model-based predictive control (MBPC) strategy using a generalised Hammerstein model and its application to the temperature control of a semibatch reactor. Both unconstrained and constrained adaptive control problems are considered. A simple identification method based on the weighted recursive least squares method (WRLS) is used to estimate the model parameters on-line. An indirect adaptive nonlinear controller is designed by combining the predictive controller with an indirect parameter estimation algorithm. This adaptive scheme has been applied for the control of a semi-batch chemical reactor. Experimental results show that the performance of the generalised Hammerstein MBPC (NLMBPC) was significantly better than that of a linear model predictive controller (LMBPC).

Constrained receding horizon predictive control for nonlinear systems

The paper concerns the receding horizon predictive control of constrained nonlinear systems and presents an algorithm which relies on the online solution of a simple linear program (LP). Use is made of a finite control horizon in conjunction with a terminal inequality constraint and a predicted cost that includes a terminal penalty term. The optimization procedure is based on predictions made by linearized incremental models at points of a given seed trajectory and the effects of linearization error are taken into account to give a bound on the predicted tracking error. The algorithm is posed in the form of an LP and the proper selection of the terminal penalty term of the predicted cost guarantees the asymptotic stability. The results of the paper are illustrated by means of a simple example.

지연시간을 갖는 비선형 시스템을 위한 퍼지-신경망 기반 예측제어기 설계

본 논문에서는 지연시간을 갖는 비선형 시스템의 효율적 제어를 위해 퍼지-신경망에 기반한 지연시간 보상기를 제안하였다. 제안된 제어시스템은 ANFIS(Adaptive Neuro-Fuzzy Inference System)라고 불리는 두개의 퍼지-신경망으로 구성되며 이중 하나는 직-병렬 방식으로 동작하고 다른 하나는 병렬 방식으로 동작한다. 직-병렬 방식으로 동작하는 퍼지-신경망은 지연시간을 갖는 비선형 시스템의 응답을 추종하는 특성을 갖으며 병렬 방식으로 동작하는 퍼지-신경망은 지연시간을 보상하기 위한 시스템 출력을 예측하는 기능을 수행한다. 따라서 본 연구에서 제안된 시스템은 전형적인 Smith 예측기의 비선형 시스템에의 적용을 위한 확장이라고 생각할 수 있다. 본 논문에서는 제안된 지연시간 보상기의 상세한 설계과정을 보였으며 또한 제안된 제어기 설계 기법의 유용성 화인을 위해 비선형 수치데이터에 대한 컴퓨터 모의실험을 수행하였다. In this paper a design of neuro-fuzzy-based predictive controller for nonlinear systems with time-delay is proposed. The proposed control system contains two neuro-fuzzy systems called ANFIS(Adaptive Neuro-Fuzzy Inference System). One is run as a series-parallel mode and the other is run as a parallel mode. An ANFIS running in series-parallel mode emulates the response of the nonlinear system with time-delay. Another ANFIS running in parallel mode generates the predicted output of the nonlinear system to compensate for the time-delays. Therefore, the proposed control system can be thought of as an extension of Smith-predictor scheme to the nonlinear systems with time-delay. A detailed design Procedure is presented and finally computer simulations are executed for the effectiveness of the proposed control scheme.

A neural predictive controller for non-linear systems

Design and implementation are studied for a neural network-based predictive controller meant to govern the dynamics of non-linear processes. The advantages of using neural networks for modeling non-linear processes are shown together with the construction of neural predictors. The resulting implementation of the neural predictive controller is able to eliminate the most significant obstacles encountered in non-linear predictive control applications by facilitating the development of non-linear models and providing a rapid, reliable solution to the control algorithm. Controller design and implementation are illustrated for a plant frequently referred to in the literature. Results are given for simulation experiments, which demonstrate the effectiveness of the proposed approach.

Analytic predictive controllers for nonlinear systems with ill-defined relative degree

The paper addresses the problem of the control of nonlinear systems with ill-defined relative degree. The analytic solution to an optimal tracking problem in terms of a generalised predictive performance index is presented, where the output tracking error is predicted by Taylor series approximation up to an arbitrarily chosen order. It is shown that the optimal control for nonlinear systems with ill-defined relative degree is discontinuous, and the optimal control law is not unique when the system is within the singular point set. Approximate implementation of the optimal predictive control law is discussed. The nonlinear predictive controller presented is successfully demonstrated by an numerical example.

Model predictive control of nonlinear systems using piecewise linear models

We consider the problem of controlling nonlinear systems which are modeled as a set of piecewise linear (PL) or affine systems using a model predictive control (MPC). The paper reviews recent results on the analysis and control of PL systems, which can model a wide range of practically relevant nonlinear systems. Using techniques from the theory of linear matrix inequalities (LMIs), we develop a multiple model MPC technique involving a sequence of local state feedback matrices, which minimize an upper bound on the ‘worst-case’ objective function. The resulting problem, which utilizes a single quadratic Lyapunov function and multiple local state-feedback matrices, can be cast as a convex optimization problem involving LMIs. Several extensions of this technique involving approximating the local regions by ellipsoids or polytopes, and their respective advantages and disadvantages, are discussed.

Model predictive control of nonlinear systems: Computational burden and stability

Implementation of model predictive control (MPC) or nonlinear systems requires the online solution of a nonconvex, constrained nonlinear optimisation problem. Computational delay and loss of optimality arise in the optimisation procedures. The paper presents a practical MPC scheme for nonlinear systems with guaranteed asymptotic stability. It is shown that when an initial control profile is chosen to satisfy an inequality condition in each online optimisation procedure, the nonlinear system under the proposed nonlinear MPC is asymptotically stable. The stability condition presented in the paper enables the 'fictitious' terminal control to be nonlinear, rather than only linear, thus the stability region is greatly enlarged. Furthermore, it is pointed out that nominal stability is still guaranteed even though the global, or even the local, minimisation of the objective cost is not achieved within the prescribed computational time.

A stable one-step-ahead predictive control of non-linear systems

In this paper stability of one-step ahead predictive controllers based on non-linear models is established. It is shown that, under conditions which can be fulfilled by most industrial plants, the closed-loop system is robustly stable in the presence of plant uncertainties and input–output constraints. There is no requirement that the plant should be open-loop stable and the analysis is valid for general forms of non-linear system representation including the case out when the problem is constraint-free. The effectiveness of controllers designed according to the algorithm analyzed in this paper is demonstrated on a recognized benchmark problem and on a simulation of a continuous-stirred tank reactor (CSTR). In both examples a radial basis function neural network is employed as the non-linear system model.

Nonlinear generalised predictive control and optimal dynamical inversion control

Abstract This paper addresses nonlinear Generalised Predictive Control (GPC) for nonlinear mechanical systems and its relationship with dynamical inversion control. First continuous-time generalised predictive control for nonlinear systems is developed and the stability of the closed-loop systems is shown. It is pointed out that the dynamical inversion control is a special case of continuous-time nonlinear GPC. This result also provides an optimal design method for dynamical inversion control in term of the generalised predictive control performance index. The nonlinear GPC developed is successfully applied to the control of a two-link robotic manipulator.

Suboptimality analysis of receding horizon predictive control with terminal constraints

In this paper, the suboptimality of predictive control with terminal constraints is analyzed. and compared with traditional optimal control. First, by studying the property of receding finite-horizon optimization, the upper bound of suboptimality of predictive control for nonlinear system is deduced. The result is then applied to linear system, and a quantitative measure of suboptimality is obtained.

Dynamically scheduled MPC of nonlinear processes using hinging hyperplane models

AbstractThis article deals with the issues associated with designing scheduled model predictive controllers for nonlinear systems within the multiple‐linear‐model‐based control framework. The issues of model set generation from empirical data and closed‐loop application of the generated model set are considered. A method of hinging hyperplanes is proposed as a way to construct a piecewise linear dynamic model, conducive to dynamic scheduling of linear MFC controllers. The design and implementation of dynamically scheduled MFC using a hinge function model are discussed, as well as its advantages. Alternate MFC formulations considered here require more computation, but utilize the hinge function model as a global model. Simulated examples of isothermal CSTRs and a batch fermenter are also presented to illustrate the proposed methodologies.

Predictive control for non-linear systems using neural networks

A neural network based predictive controller design algorithm is introduced for non-linear control systems. It is shown that the use of non-linear programming techniques can be avoided by using a set of affine non-linear predictors to predict the output of the non-linear process. The new predictive controller based on this design is both simple and easy to implement in practice. An on-line weight-learning algorithm for 9 neural networks is introduced, and convergence of both the weights and estimation errors is established. Predictive controller design based on the new procedure is illustrated using a growing network example.

Extended Horizon Predictive Control of Non-Linear Systems - Multi-Dimensional Optimisation and Suboptimal Solution

Predictive control strategies have been proved effective and robust in practice. These algorithms were developed mainly for linear processes. The main idea is to determine the control signal minimising the deviation between a reference signal and the predicted process output in a given prediction horizon. A simplified version is one-step-ahead predictive control, where prediction horizon is restricted to one future point. Extended horizon control proposed by Ydstie (1984) is enlengthened one-step-ahead control which lets more time for the settling process than the dead time. Extended horizon predictive control strategy is derived here for a class of nonlinear systems. Some simulation results show the effect of the tuning parameters for the reference signal tracking performance of the nonlinear system.

Robust Model Predictive Control for Nonlinear Systems with Constraints

A technique is introduced for the design of a robustly stabilizing model predictive output feedback controller for continuous time-varying nonlinear constrained systems. The controller is easily implementable and computationally inexpensive. A family of first order approximations of the plant is used for computation of the optimal control moves, which allows the optimization problem to be posed as a quadratic programming problem. Through the use of a “stability constraint” the resulting control algorithm can be made asymptotically stable and is able to handle unknown time-varying disturbances and parameters, measurement bias and structural model/plant mismatch.

Generalized predictive control of nonlinear systems of the Hammerstein form

A noolinear generalized predictive control scheme based on a Hammerstein model is prasented in this peper.The stability of the closed-lop system is analyzed with the control horizon equal to one.An adaptive nonlinear generalized predictive control algorithm with a linear estimator is proosed.The simulation examples demonstrate the effusiveness of the algorithm.

Adaptive general predictive controller for nonlinear systems

A nonlinear general predictive controller (NLGPC) is described which is based on the use of a Hammerstein model within a recursive control algorithm. A key contribution of the paper is the use of a novel, one-step simple root solving procedure for the Hammerstein model, this being a fundamental part of the overall tuning algorithm. A comparison is made between NLGPC and nonlinear deadbeat control (NLDBC) using the same one-step nonlinear components, in order to investigate NLGPC advantages and disadvantages.

Long-range Predictive Control of Nonlinear Systems given by Volterra Series

The unknown nonlinear process is approximated by a Volterra series model which is a nonparametric description. The parameters of the Volterra series can be approximated recursively. Because of the large number of the parameters the usage of scalar convergence coefficients is recommended. The control algorithm is an extension of Brujin's predictive control algorithm, based on the weighting function series of linear systems, to the Volterra weighting function series model. The control signal is assumed constant during the control horizon and the calculation is repeated in every control interval. The above strategy results in a very robust algorithm