Robust Constrained Fuzzy Affine Model Predictive Control With Application to a Fluidized Bed Combustion Plant

In this paper, we investigate a robust constrained model predictive control synthesis approach for discrete‐time Takagi‐Sugeno's (T‐S) fuzzy system with structured uncertainty. The key idea is to determine, at each sampling time, a state feedback fuzzy predictive controller that minimizes the performance objective function in the infinite time horizon by solving a class of linear matrix inequalities (LMIs) optimization problem. To do this, the fuzzy predictive controller is designed on the basis of non‐parallel distributed compensation (non‐PDC) control law, relaxed stability conditions of the closed‐loop fuzzy system are developed by employing an extended nonquadratic Lyapunov function and introducing additional slack and collection matrices. In addition, the presented approach is capable of ensuring the robust asymptotic stability as well as the recursive feasibility of the closed‐loop fuzzy system. Simulations on a highly nonlinear continuous stirred tank reactor (CSTR) are eventually presented to demonstrate the effectiveness of the developed theoretical approach.

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.

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.

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.

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

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.

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.

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.

Robust constrained model predictive control using linear matrix inequalities

ABSTRACTThis paper investigates the robust control of discrete‐time switched systems in the presence of parametric uncertainty and time‐varying delays. To accommodate a more general model, nonlinear Lipschitz functions are incorporated. Additionally, the system is modeled with constraints on both control inputs and outputs. To achieve the control objectives, static and dynamic output feedback controllers are designed using the robust model predictive control (RMPC) framework. The underlying optimization problem is formulated and solved, leveraging Lyapunov‐Krasovskii functionals (LKF) and switched Lyapunov functions (SLF). The asymptotic stability of the closed‐loop system under arbitrary switching signals is ensured by satisfying sufficient conditions expressed as linear matrix inequalities (LMIs). A key advantage of the proposed method lies in its low conservatism. Moreover, the time delay and state variables are assumed unknown, and they ensure an acceptable transient response of the closed‐loop system. To demonstrate the effectiveness of the designed controllers, simulation results are provided and compared against prior related works, highlighting the improvements achieved.

Constant-air-volume (CAV) air-conditioning systems consist mainly of two local processes: an air-handling process and a room temperature process. A robust model predictive control (RMPC) strategy was developed for CAV air-conditioning systems, which adopted two uncertain first-order plus time-delay models to describe the dynamics of the local processes and used a linear matrix inequality (LMI)-based optimisation technique to optimise the control law. This paper develops a new control design, which reformulates the prediction models by shifting the uncertainties of the first model into the second one, and then uses the reformulated prediction models in the RMPC strategy. This paper will show that compared with the original design, the new control design can enhance the feasibility of the optimisation of control law, reduce the computational burden of the optimisation and also remove the requirement of a sensor for supply air temperature in the original design. Practical applications: The new design method is a further development of a RMPC strategy presented in Xu et al.13 It inherits the benefits of the original control design for practical application, i.e. uncertainties and constraints can be dealt with simultaneously in the design and the robustness of the controlled system can be enhanced. The new design improves the optimisation feasibility, reduces the computational complexity and does not need to measure the supply air temperature. When the new design is adopted to replace the traditional PI control, there is no necessity to change the existent input structure of the PI control. Hence, the new design can be realised in practice easier than the original design.

T–S fuzzy affine model based non-synchronized state estimation for nonlinear Itô stochastic systems

Wide-area damping power system control based on robust self-triggered model predictive control

Nominal robustness of model predictive control for nonlinear systems is considered. It is shown, by examples, that when the optimization problem involves state constraints, or terminal constraints coupled with short optimization horizons, the asymptotic stability of the closed loop may have absolutely no robustness. Namely, it is possible for arbitrarily small disturbances to keep the closed loop strictly inside the interior of the feasibility region of the optimization problem and, at the same time, far from the desired set point. This phenomenon does not occur when using model predictive control for linear systems with convex constraint sets. It is emphasized that a necessary condition for the absence of nominal robustness in nonlinear model predictive control is that the value function and feedback law are discontinuous at some point(s) in the interior of the feasibility region.