Robust Constrained Model Predictive Control for Discrete‐Time Uncertain System in Takagi‐Sugeno's Form

In this paper, a robust constrained model predictive control approach for discrete-time uncertain Takagi-Sugeno (T-S) fuzzy systems is developed. Based on the non-parallel distributed compensation law (non-PDC), a fuzzy predictive controller is designed to stabilize the resulting closed-loop system via an extended non-quadratic Lyapunov function. Slack matrices and collection matrix are employed to obtain less conservative results and sufficient conditions for the solvability of this problem is provided in the form of linear matrix inequalities, the real-time fuzzy predictive control law is easily calculated and implemented, at each sampling time, which minimizes the objective function over infinite moving horizon subjects to input and output constraints. To demonstrate the effectiveness and applicability, the simulation results on a continuous stirred tank reactors (CSTR) is illustrated by the fuzzy model predictive control approach we proposed.

In this paper, robust constrained model predictive control of uncertain fuzzy affine systems is considered. Based on piecewise quadratic Lyapunov functions, highly efficient robust constrained predictive control approaches are developed so that the closed-loop stability is guaranteed, and the transient control performance is improved even under input or state constraints. Moreover, by using approximate ellipsoid and S -procedure, the solution to the fuzzy affine model based predictive control can be cast as a convex optimization problem subject to some linear matrix inequalities, rather than a nonconvex problem via bilinear matrix inequalities as in conventional fuzzy affine model-based control. The proposed controllers are thus easier for real-time implementation in industry. Simulation results on the fluidized bed combustion plant have demonstrated the performance of the proposed approaches.

A synthesis approach of constrained robust model predictive control (SCRMPC) for systems with polytopic description is proposed. This proposal uses time-varying sequences of models in a polytope to forecast the model uncertainties and optimizes the terminal constrained set, the local controller and the terminal cost on-line. Using standard techniques, the problem is reduced to a convex optimization involving linear matrix inequalities (LMIs). We compare the proposed algorithm with the existing algorithms via an example and the simulation results demonstrate that our algorithm enlarges the feasible region and improves the control performance.

The problem of robust constrained model predictive control (MFC) of systems with polytopic uncertainty is considered in this paper. New sufficient conditions for the existence of parameter-dependent Lyapunov functions are proposed in terms of linear matrix inequalities (LMIs), which will reduce the conservativeness resulting from using a single Lyapunov function. At each sampling instant, the corresponding parameter-dependent Lyapunov function is an upper bound for a worst-case objective function, which can be minimized using the LMI convex optimization approach. Based on the solution of optimization at each sampling instant, the corresponding state feedback controller is designed, which can guarantee that the resulting closed-loop system is robustly asymptotically stable. In addition, the feedback controller will meet the specifications for systems with input or output constraints, for all admissible time-varying parameter uncertainties. Numerical examples are presented to demonstrate the effectiveness of the proposed techniques.

For the input and output constraints and uncertainties in batch processes, a 2D output feedback robust constrained model predictive control (MPC) method is designed by combining iterative learning control (ILC), MPC and output feedback. Firstly, an equivalent 2D-FM closed-loop prediction model is established by combining with the proposed output feedback controller. Then an optimization performance index function with terminal constraint is constructed to study its control optimization. According to the designed optimization performance index and Lyapunov stability theory, the feasible MPC problem is obtained by solving the linear matrix inequalities (LMIs). At the same time, the gain of the new output feedback control law is given to ensure that the performance index reaches the minimum upper bound under the constraints of input and output. In order to solve the manual adjustment problem of some parameters in the performance index function, the particle swarm optimization (PSO) algorithm is introduced, and a better solution is found near the controller by using the search optimization method. Finally, taking the injection molding process as an example and comparing with the existing method without using PSO algorithms, it is proved that the above method is more feasible.

The Polyhedral Off-line Robust Model Predictive Control Strategy for Uncertain Polytopic Discrete-time Systems

In this paper, a synthesis of model predictive control (MPC) algorithm is presented for uncertain systems subject to structured time‐varying uncertainties and actuator saturation. The system matrices are not exactly known, but are affine functions of a time varying parameter vector. To deal with the nonlinear actuator saturation, a saturated linear feedback control law is expressed into a convex hull of a group of auxiliary linear feedback laws. At each time instant, a state feedback law is designed to ensure the robust stability of the closed‐loop system. The robust MPC controller design problem is formulated into solving a minimization problem of a worst‐case performance index with respect to model uncertainties. The design of controller is then cast into solving a feasibility of linear matrix inequality (LMI) optimization problem. Then, the result is further extended to saturation dependent robust MPC approach by introducing additional variables. A saturation dependent quadratic function is used to reduce the conservatism of controller design. To show the effectiveness, the proposed robust MPC algorithms are applied to a continuous‐time stirred tank reactor (CSTR) process.

In this paper, we present a method for synthesizing a robust constrained model predictive control for uncertain time-varying systems. The goal is to design, at each sampling time, a state feedback control law that minimizes an upper bound of the worst-case objective function subject to constraints of control inputs and plant outputs. The worst-case performance is defined as an infinite-horizon quadratic function of states and control inputs. In order to guarantee robust performance, the method uses multiple Lyapunov functions each of which corresponds to a different vertex of the uncertainty polytope. The state feedback design problem is cast as convex optimization involving linear matrix inequalities which can be efficiently solved. The proposed technique yields an improved performance and less conservative than the robust MPC technique using a single Lyapunov function. Numerical examples based on a two-mass-spring system are given to illustrate the effectiveness of the control algorithm.

A new method to address constrained robust model predictive control for systems with polytopic description is proposed. Inheriting from an earlier method, we split the infinite-horizon control moves into a set of free control moves over a fixed horizon and a state feedback law in the terminal region, all on-line optimized. Then, the basic idea is to utilize, at each sampling instant, a fixed number of free control moves to drive (implicitly) the terminal state into a terminal constraint set changing with time. However, a nominal, instead of worst-case, infinite horizon performance cost is adopted. This can reduce the computational burden and improve feasibility and optimality. Simulation result illustrates the advantages of the new technique.

In this paper, a novel predictive controller based on minimal resource allocation network for non-linear system is presented. The controller combines the advantages of MRAN and neural predictor. The implemented neural predictive controller not only effectively eliminates the most significant obstacles but also be very robustness. At last, the algorithm is applied in a high nonlinear continuous stirred tank reactor (CSTR) pH process model and presents a better real-time control effect.

Gain-scheduled Composite Non linear Feedback (CNF) control has been implemented to Continuous Stirred Tank Reactor (CSTR) in this work. Chemical reaction takes place inside the CSTR, which is adjured from high residual concentration to low residual concentration. Control of CSTR is a bit complex, as it requires complete dynamic study and its implementation. During the entire process, the reaction kinetics changes from stable-unstable-stable range with the decrease in residual concentration. To stabilize the reaction, appropriate cooling is necessary, to ensure that overheating of the CSTR doesn't occur. Gain-scheduled composite non linear feedback controller has been implemented successfully for better tracking performance and error has been computed in terms of Integral of Absolute Error (IAE). The novelty of the work lies in lesser error obtained for this particular model of CSTR. Comparison of the IAE has been done with Model Reference Adaptive Control (MRAC) MIT control in CSTR.

This paper presents an observer-based robust model predictive control (RMPC) for a class of nonlinear systems with both state and input delays. The observer is invoked to estimate the states of system when the states are not completely measurable. The MPC problem is formulated with a memory-less observer-based feedback control law to minimize the upper bound of the infinite horizon cost that satisfies the sufficient stability conditions. Novel delay dependent sufficient conditions are proposed for the existence of such controllers in the form of a linear matrix inequality (LMI) optimization problem. A numerical example is included to illustrate the effectiveness of the proposed method.

Robust constrained model predictive control using linear matrix inequalities

In this study, an approach to design robust distributed model predictive control (MPC) is proposed for polytopic uncertain networked control systems with time delays. To reduce the computational complexity and improve the flexibility, the entire system is decomposed into multiple smaller dimensional subsystems. For each subsystem, the proposed robust distributed MPC algorithm requires solving multiple linear matrix inequality optimisation problems to minimise an upper bound on a robust performance objective. An augmented polytopic uncertainty description is invoked to handle the input delays. The conservativeness of distributed MPC algorithm is reduced by utilising a sequence of feedback control laws. An iterative on‐line algorithm for robust distributed MPC is developed to coordinate the distributed MPC controllers. Convergence and robust stability of the proposed distributed MPC are investigated. A numerical example is carried out to demonstrate the effectiveness of the proposed algorithm.

An extended model predictive control algorithm is proposed to address constrained robust model predictive control. New upper bounds on arbitrarily long time intervals are derived by introducing two external parameters, which can relax the requirements for the increments of the Lyapunov function. The main merit of this new approach compared to other well-known techniques is the reduced conservativeness. The proposed method is proved to be effective for a class of uncertain fuzzy Markov jump systems with partially unknown transition probabilities. A single pendulum example is given to illustrate the advantages and effectiveness of the proposed controller design method.