Distributed model predictive control of constrained nonlinear systems with communication delays

Distributed model predictive control (MPC), having been proven to be efficient for large-scale control systems, is essentially enabled by communication network connections among involved subsystems (agents). This paper studies the distributed MPC problem for a class of continuous-time decoupled nonlinear systems subject to communication delays. By using a robustness constraint and designing a waiting mechanism, a delay-involved distributed MPC scheme is proposed. Furthermore, the iterative feasibility and stability properties are analyzed. It is shown that, if the communication delays are bounded by an upper bound, and the cooperation weights and the sampling period are designed appropriately, the overall system state converges to the equilibrium point. The theoretical results are verified by a simulation study.     

Distributed predictive control of continuous-time systems

In the last years focus has been put in the development of distributed Model Predictive Control (MPC) algorithms. With a few exceptions, they have been mostly developed in the discrete-time framework. However, discretization of large-scale systems may destroy the sparsity of the original continuous-time models, making distributed control design and implementation more difficult. Also, more in general, discrete-time control of continuous-time systems does not allow to consider the process inter-sampling behavior. In this paper we present a novel non-cooperative distributed predictive control algorithm for continuous-time systems based on robust MPC concepts. The convergence properties of the proposed control scheme are stated, and its realizability is tested through a simulation case study.     

Robust model predictive control for continuous uncertain systems with state delay

This paper is concerned with robust model predictive control for linear continuous uncertain systems with state delay and control constraints. A piecewise constant control sequence is calculated by minimizing the upper-bound of the infinite horizon quadratic cost function. At each sampling time, the sufficient conditions for the existence of the model predictive control are derived, and expressed as a set of linear matrix inequalities. The robust stability of the closed-loop systems is guaranteed by the proposed design method. A numerical example is given to illustrate the main results.     

Robust model predictive control for continuous uncertain systems with state delay

This paper is concerned with robust model predictive control for linear continuous uncertain systems with state delay and control constraints, A piecewise constant control sequence is calculated by minimizing the upper-bound of the infinite horizon quadratic cost function, At each sampling time, the sufficient conditions for the existence of the model predictive control are derived, and expressed as a set of linear matrix inequalities. The robust stability of the closed-loop svstems is guaranteed bv the proposed design method. A numerical example is given to illustrate the main results.     

A switching robust model predictive control approach for nonlinear systems

This work considers enhancing the stability and improving the economic performance of nonlinear model predictive control in the presence of disturbances or model uncertainties. First, a robust control Lyapunov function (RCLF)-based predictive control strategy is proposed. Second, the approximate dynamic programming (ADP) is employed to further improve regulation performance. Finally, the ADP and RCLF-MPC are combined to provide a switching control scheme, which is illustrated on a CSTR example to show its effectiveness.     

Robust model predictive control for constrained continuous-time nonlinear systems

In this paper, a robust model predictive control (MPC) is designed for a class of constrained continuous-time nonlinear systems with bounded additive disturbances. The robust MPC consists of a nonlinear feedback control and a continuous-time model-based dual-mode MPC. The nonlinear feedback control guarantees the actual trajectory being contained in a tube centred at the nominal trajectory. The dual-mode MPC is designed to ensure asymptotic convergence of the nominal trajectory to zero. This paper extends current results on discrete-time model-based tube MPC and linear system model-based tube MPC to continuous-time nonlinear model-based tube MPC. The feasibility and robustness of the proposed robust MPC have been demonstrated by theoretical analysis and applications to a cart-damper springer system and a one-link robot manipulator.     

Realization of robust nonlinear model predictive control by offline optimisation

This paper describes a new method for increasing the computational efficiency of nonlinear robust model-based predictive control. It is based on the application of neuro-fuzzy networks and improves the computation efficiency by arranging the online optimisation to be done offline. The offline optimisation is realized by offline training a neuro-fuzzy network, consisting of zero-order T–S fuzzy rules, which is designed to approximate the input–output relationship of a robust model-based predictive controller. The design and the training of the neuro-fuzzy network are described, and the corresponding control algorithm is developed. Experiment results performed on the temperature control loop of an experimental air-handling unit (AHU) demonstrate the effectiveness of this approach.     

Economic model predictive control of nonlinear singularly perturbed systems

We focus on the development of a Lyapunov-based economic model predictive control (LEMPC) method for nonlinear singularly perturbed systems in standard form arising naturally in the modeling of two-time-scale chemical processes. A composite control structure is proposed in which, a “fast” Lyapunov-based model predictive controller (LMPC) using a quadratic cost function which penalizes the deviation of the fast states from their equilibrium slow manifold and the corresponding manipulated inputs, is used to stabilize the fast dynamics while a two-mode “slow” LEMPC design is used on the slow subsystem that addresses economic considerations as well as desired closed-loop stability properties by utilizing an economic (typically non-quadratic) cost function in its formulation and possibly dictating a time-varying process operation. Through a multirate measurement sampling scheme, fast sampling of the fast state variables is used in the fast LMPC while slow-sampling of the slow state variables is used in the slow LEMPC. Appropriate stabilizability assumptions are made and suitable constraints are imposed on the proposed control scheme to guarantee the closed-loop stability and singular perturbation theory is used to analyze the closed-loop system. The proposed control method is demonstrated through a nonlinear chemical process example.     

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     

A scheduling quasi–min-max model predictive control algorithm for nonlinear systems

In this paper, a model predictive control algorithm is designed for nonlinear systems. Combination of a linear model with a linear parameter varying model approximates the nonlinear behavior. The linear model is used to express the current nonlinear dynamics, and the linear parameter varying model is used to cover the future nonlinear behavior. In the algorithm, a “quasi-worst-case” value of an infinite horizon objective function is minimized. Closed-loop stability is guaranteed when the algorithm is implemented in a receding horizon fashion by including a Lyapunov constraint in the formulation. The proposed approach is applied to control a jacketed styrene polymerization reactor.     

LMI-based model predictive control for switched nonlinear systems

This paper proposes an LMI approach to model predictive control of nonlinear systems with switching between multiple modes. In this approach, at each mode, the nonlinear system is divided to a linearized model in addition to a nonlinear term. A sum of squares (SOS) optimization problem is presented to find a quadratic bound for the nonlinear part. The stability condition of the switching system is obtained by using a discrete Lyapunov function and then the sufficient state feedback control law is achieved so that guarantees the stability of the system and also minimizes an infinite prediction horizon performance index. Moreover, two other LMI optimization problems are solved at each mode in order to find the maximum area region of convergence of the nonlinear system inscribed in the region of stability. The performance and effectiveness of the proposed MPC approach are illustrated by two case studies.     

On the explicit dead-time compensation for robust model predictive control

Computational simplicity is one of the most important aspects to take into account in robust model predictive control (MPC). In dead-time processes, it is common to use an augmented state-space representation in order to apply robust MPC strategies but, this procedure may affect computational aspects. In this paper, explicit dead-time compensation will be used to avoid augmented representation. This technique will be analyzed in terms of robust stability and constraint satisfaction for discrete-time linear systems. The results of this discussion will be applied to a robust tube-based MPC strategy which is able to guarantee robust stability and constraint satisfaction of a dead-time system by considering a prediction model without dead-time. Moreover, taking advantage of the proposed scheme, the robust MPC will be particularized for first-order plus dead-time models which simplifies significantly controller synthesis. The proposed dead-time compensation method will be applied to different robust MPC strategies in two case studies: (i) a simulated quadruple-tank system, and (ii) an experimental scaled laboratory heater process.     

Robust discrete-time set-based adaptive predictive control for nonlinear systems

The problem of robust adaptive predictive control for a class of discrete-time nonlinear systems is considered. First, a parameter estimation technique, based on an uncertainty set estimation, is formulated. This technique is able to provide robust performance for nonlinear systems subject to exogenous variables. Second, an adaptive MPC is developed to use the uncertainty estimation in a framework of min–max robust control. A Lipschitz-based approach, which provides a conservative approximation for the min–max problem, is used to solve the control problem, retaining the computational complexity of nominal MPC formulations and the robustness of the min–max approach. Finally, the set-based estimation algorithm and the robust predictive controller are successfully applied in two case studies. The first one is the control of anonisothermal CSTR governed by the van de Vusse reaction. Concentration and temperature regulation is considered with the simultaneous estimation of the frequency (or pre-exponential) factors of the Arrhenius equation. In the second example, a biomedical model for chemotherapy control is simulated using control actions provided by the proposed algorithm. The methods for estimation and control were tested using different disturbances scenarios.     

Stabilizing decentralized model predictive control of nonlinear systems

This note presents a stabilizing decentralized model predictive control (MPC) algorithm for nonlinear discrete time systems. No information is assumed to be exchanged between local control laws. The stability proof relies on the inclusion of a contractive constraint in the formulation of the MPC problem.     

Stochastic closed-loop model predictive control of continuous nonlinear chemical processes

A new predictive control framework for chemical processes is presented, that has a number of fundamental differences to classical MPC. Both future disturbances and future process measurements are explicitly introduced in the model prediction, while back-off prevents violation of the inequality constraints. A feedforward trajectory, used for constraint pushing, is optimized simultaneously with a linear time-varying feedback controller, used to minimize the back-off. No feedback is generated by the receding horizon implementation itself. Via several transformations, the resulting optimization problem is rendered convex. For nonlinear processes, this applies to the sub-problem in a sequential conic optimization approach. A two stage LQG approach reduces the complexity even further for large scale systems. The method is illustrated on a HDPE reactor example and compared to a LTV-MPC.     

基于遗传算法的非线性模型预测控制方法

介绍了非线性模型预调控制算法结构，提出了基于遗传算法的非线性模型预测控制方法，将遗传算法作为优化技术用于受限非线性模型预测控制器的设计。算法采用双模控制策略，将保证预测控制算法稳定性的终点等式约束转化为终点不等式约束，以利于遗传算法的实施。基于不变集理论，给出了非线性模型预测控制算法的稳定性定理。仿真结果表明了所提出控制算法的可行性和有效性。     

Constrained output feedback model predictive control for nonlinear systems

A constrained output feedback model predictive control approach for nonlinear systems is presented in this paper. The state variables are observed using an unscented Kalman filter, which offers some advantages over an extended Kalman filter. A nonlinear dynamic model of the system, considered in this investigation, is developed considering all possible effective elements. The model is then adaptively linearized along the prediction horizon using a state-dependent state space representation. In order to improve the performance of the control system as many linearized models as the number of prediction horizons are obtained at each sample time. The optimum results of the previous sample time are utilized for linearization at the current sample time. Subsequently, a linear quadratic objective function with constraints is formulated using the developed governing equations of the plant. The performance and effectiveness of the proposed control approach is validated both in simulation and through real-time experimentation using a constrained highly nonlinear aerodynamic test rig, a twin rotor MIMO system (TRMS).     

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.