Output feedback model predictive control for nonlinear systems represented by Hammerstein–Wiener model

This paper studies the synthesis approach of dynamic output feedback model predictive control (OFMPC) for nonlinear networked control systems (NCSs), which can be described by interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy model. The Bernoulli random binary distribution is exploited to describe the process of packet loss in NCSs. Compared with the existed output feedback model predictive controller based on traditional state observer, the parameter dependent dynamic OFMPC which minimizes the upper bound of a quadratic objective function in an infinite horizon is designed by applying the notion of quadratic boundedness. A numerical example is given to demonstrate the effectiveness of the proposed new design techniques.

Algorithms for improved fixed-time performance of Lyapunov-based economic model predictive control of nonlinear systems

This paper addresses the output feedback predictive control for a Takagi-Sugeno (T-S) fuzzy system with bounded noise. The controller optimizes an infinite-horizon objective function respecting the input and state constraints. The control law is parameterized as a dynamic output feedback that is dependent on the membership functions, and the closed-loop stability is specified by the notion of quadratic boundedness. Online algorithms that guarantee the recursive feasibility of the convex optimization problem and the convergence of the augmented state to a neighborhood of the equilibrium point are proposed in this paper. A numerical example is given to illustrate the effectiveness of the proposed output feedback controllers.

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SummaryIn this paper, a distributed output feedback model predictive control (OFMPC) algorithm is presented for the polytopic uncertain system subject to randomly occurring actuator saturation and packet loss. Compared with the intensively applied state feedback control in MPC, the OFMPC is more feasible to the real world because the system states are often unmeasurable. With taking both actuator saturation and packet loss into account, the presented OFMPC algorithm is more practical. Moreover, by splitting the controller inputs into two independent parts, the presented dynamic output feedback control (DOFC) strategy provides more freedom to the controller design. With the global system decomposed into some subsystems, the computation complexity is reduced, thus the online designing time can be saved. By defining the estimation error function and forming an augmented system to handle the DOFC and by transforming the nonlinear feedback law into a convex hull of linear feedback laws, the distributed controllers are obtained by solving a linear matrix inequality (LMI) optimization problem. Finally, some simulation examples are employed to show the effectiveness of the techniques proposed in this paper. Copyright © 2015 John Wiley & Sons, Ltd.

This study investigates the problem of fuzzy predictive control of non-linear systems with imperfect communication links. Packet loss (which appears typically in a network environment) is assumed to happen intermittently between the physical plant and the controller, and stochastic variables satisfying the Bernoulli random binary distribution are utilised to describe the imperfect communication phenomenon. The formulation is mathematically transformed into a stochastic Takagi-Sugeno fuzzy model. Attention is focused on the design of fuzzy predictive controllers such that the closed-loop system is stochastically stable, optimising an objective function value at every step in an infinite time horizon subject to input constraints and packet dropouts. A piecewise Lyapunov function approach is utilised, which is effective for fuzzy systems with trapezoidal membership functions; for continuous membership functions, the quadratic Lyapunov function approach is employed. A set of linear matrix inequalities is given to solve the corresponding controller optimisation problem. Two examples are provided to illustrate the usefulness and applicability of the developed theoretical results.

In this paper, we consider learning-based modeling and predictive control of nonlinear systems subject to multimodal uncertainties. A Gaussian mixture Koopman operator, which learns the evolution of the observable distribution in a higher-dimensional space, is proposed to characterize the dynamics of the underlying nonlinear systems. Based on the learned probabilistic Koopman model, a stochastic model predictive control method with chance constraints is introduced for the nonlinear systems with state constraints. Finally, a simulated chemical process is used to illustrate the effectiveness of the proposed method.

Frequency Domain Tuning Method for Unconstrained Linear Output Feedback 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.

A stabilizing output feedback model predictive control algorithm is proposed for linear systems with input constraints. Dual mode control strategy is adopted: the state observer, linear feedback controller and terminal constraint set are pre-computed; if the state is contained in terminal constraint set, linear feedback controller is used; otherwise a linear control structure with free vector is used, and control law can be obtained by solving an Second Order Cone Programming (SOCP) problem. The system with bounded disturbance is considered and bounded stability is shown. Simulations results show the effectiveness of the control algorithm.

A constrained multivariable Generalised Predictive Control (GPC), which is based upon the T-S fuzzy model, is proposed for a class of non-linear systems. The proposed method can deal with the case of rate and amplitude constraints for the control signal with a way different from the classical constrained multivariable GPC, so the computation burden cut down with a degree and the control scheme can be used in the high speed sampled control systems. The simulation results demonstrate the effectiveness of the proposed algorithm.

This note proposes a model predictive control (MPC) algorithm for the solution of a robust control problem for continuous-time systems. Discontinuous feedback strategies are allowed in the solution of the min-max problems to be solved. The use of such strategies allows MPC to address a large class of nonlinear systems, including among others nonholonomic systems. Robust stability conditions to ensure steering to a certain set under bounded disturbances are established. The use of bang-bang feedbacks described by a small number of parameters is proposed, reducing considerably the computational burden associated with solving a differential game. The applicability of the proposed algorithm is tested to control a unicycle mobile robot.

This paper presents a distributionally robust tube‐based model predictive control method for nonlinear systems affected by external random disturbances. The reference trajectory is computed by solving a rolling optimization problem for the nominal system, while an auxiliary controller with chance constraints is solved in real time to guarantee that the trajectory of the disturbed system remains within an invariant tube centered on the reference trajectory. Since the distribution information of disturbances is unknown, a distributionally robust ambiguity set is constructed based on disturbance samples collected online to reformulate the chance constraints, thereby ensuring that the state of the disturbed system satisfies the state constraints with a certain probability. It is demonstrated that this method can ensure the disturbed system remains stable, with its state staying near the reference trajectory. Furthermore, its robustness and compliance with constraints have been validated on a nonlinear continuous stirred‐tank reactor.

ABSTRACTThis paper addresses the problem of fuzzy model predictive control (FMPC) for a class of nonlinear systems represented by Takagi‐Sugeno (T‐S) fuzzy models, subject to both hard constraints on control inputs and states, as well as communication network limitations. To mitigate data collisions and improve the reliability of data transmission, a random multiaccess protocol (RMP) is integrated into the FMPC framework, resulting in the proposed RMP‐based FMPC approach. Specifically, a unified representation is developed to model the interplay between T‐S fuzzy nonlinearities and the RMP for nonlinear systems with hard constraints. Utilizing a scheduling signal‐dependent fuzzy quadratic function approach, a “min‐max” problem is formulated by resorting to the objective function over the infinite horizon. The primary objective is to design a series of controllers using the FMPC approach, ensuring that the T‐S fuzzy system remains mean‐square stable under the prescribed constraints. By incorporating both the nonlinearities of the T‐S fuzzy system and the dynamics of the RMP, sufficient stability conditions are derived via an auxiliary online optimization problem. Finally, the efficacy and applicability of the proposed approach are validated through two simulation examples, which demonstrate the robustness and effectiveness of the RMP‐based FMPC strategy in handling both the network constraints and the system's nonlinear characteristics.

We propose a novel output feedback model predictive control scheme for linear discrete-time systems incorporating a set-valued estimator based on a fixed finite number of recent measurements. Recursive feasibility is established by basing predictions that are farther in the future on fewer measurements. The resulting optimization problem is convex with linear constraints. We demonstrate in a numerical example that the proposed model predictive control scheme allows an enlargement of the feasible set beyond what is possible with earlier schemes using linear estimators.