ROBUST MODEL PREDICTIVE CONTROL FOR INPUT SATURATED AND SOFTENED STATE CONSTRAINTS

This paper starts with a brief review of robust model predictive control (RMPC) algorithsms for uncertain systems using linear matrix inequalities (LMIs) subject to input and/or output saturated constraints. However when RMPC has both input and state constraints, a difficulty will arise due to the inability of the optimizer to satisfy the state constraints due to the constraints on inputs. Therefore, a novel RMPC scheme is presented that softens the state constraints as penalty terms are added to its objective function. These terms maintain state violation at low values until a constrained solution is returned. The state violation can be regulated by changing the value of the weighting factor. A novel robust predictive controller for input saturated and softened state constraints for linear time varying (LTV) systems with polytopic model uncertainties is presented.     

Event‐triggered probabilistic robust control of linear systems with input constrains: By scenario optimization approach

This paper addresses the problem of probabilistic robust stabilization for uncertain systems subject to input saturation. A new probabilistic solution framework for robust control analysis and synthesis problems is addressed by a scenario optimization approach, in which the uncertainties are not assumed to be norm bounded. Furthermore, by expressing the saturated linear feedback law on a convex hull of a group of auxiliary linear feedback laws, we establish conditions under which the closed‐loop system is probabilistic stable. Based on these conditions, the problem of designing the state feedback gains for achieving the largest size of the domain of attraction is formulated and solved as a constrained optimization problem with linear matrix inequality constraints. The results are then illustrated by a numerical example.     

Robust model predictive control for polytopic uncertain systems with state saturation nonlinearities under Round‐Robin protocol

This paper is concerned with the robust model predictive control (RMPC) problem for polytopic uncertain systems with state saturation nonlinearities under the Round‐Robin (RR) protocol. With respect to the practical application, one of the most commonly encountered obstacles that stem from the physical limitation of system components, ie, state saturation, is adequately taken into consideration. In order to reduce the network transmission burden and improve the utilization of the network from the controller nodes to the actuator node, a so‐called RR protocol is employed to orchestrate the data transmission order. At each transmission instant, only one controller node that obtains the priority is accessible to the shared communication network. Our aim of the underlying problem is to design a set of controllers in the framework of RMPC such that the closed‐loop system is asymptotically stable. By taking the influence of the RR protocol and the state saturation precisely into account, some sufficient criteria are established in terms of the token‐dependent Lyapunov‐like approach. Then, an online optimization problem subjected to some matrix inequality constraints is provided, and the desired controllers can be obtained by solving the certain upper bound of the objective addressed. Finally, a distillation process example is provided to illustrate the effectiveness of the proposed RMPC approach.     

Robust feedback model predictive control of constrained uncertain systems

We propose a novel procedure for the solution to the problem of robust model predictive control (RMPC) of linear discrete time systems involving bounded disturbances and model-uncertainties along with hard constraints on the input and state. The RMPC (outer) controller – responsible for steering the uncertain system state to a designed invariant (terminal) set – has a mixed structure consisting of a state-feedback component as well as a control-perturbation. Both components are explicitly considered as decision variables in the online optimization and the nonlinearities commonly associated with such a state-feedback parameterization are avoided by adopting a sequential approach in the formulation. The RMPC controller minimizes an upper bound on an H₂/H_∞-based cost function. Moreover, the proposed algorithm does not require any offline calculation of (feasible) feedback gains for the computation of the RMPC controller. The optimal Robust Positively invariant set and the inner controller – responsible for keeping the state within the invariant set – are both computed in one step as solutions to an LMI optimization problem. We also provide conditions which guarantee the Lyapunov stability of the closed-loop system. Numerical examples, taken from the literature, demonstrate the advantages of the proposed scheme.     

Robust Tracking Controller Design for a Class of Block Lower‐Triangular Systems

A class of multi‐input multi‐output (MIMO) block lower‐triangular systems are considered with the dynamic and static uncertainties related to the states of the former subsystems. A design procedure of robust tracking controller is presented, which avoids the problem of the “explosion of complexity” and can be implemented very simply. The closed‐loop system possesses robust properties that, 1) all signals involved are semi‐global uniformly ultimately bounded for bounded differentiable reference inputs; 2) for given initial tracking errors and uncertainty boundary, controller parameters can be found to guarantee that the tracking errors can be smaller than a specific positive constant after a limited time. Two numerical instances are given at last.     

Constrained control of uncertain nonhomogeneous Markovian jump systems

This paper addresses the problem of robust stabilization for uncertain systems subject to input saturation and nonhomogeneous Markovian jumps, where the uncertainties are assumed to be norm bounded and the transition probabilities are time‐varying and unknown. By expressing the saturated linear feedback law on a convex hull of a group of auxiliary linear feedback laws and the time‐varying transition probabilities inside a polytope, we establish conditions under which the closed‐loop system is asymptotically stable. On the basis of these conditions, the problem of designing the state feedback gains for achieving fast transience response with a guaranteed size of the domain of attraction is formulated and solved as a constrained optimization problem with linear matrix inequality constraints. The results are then illustrated by numerical examples including the application to a DC motor speed control example. Copyright © 2017 John Wiley & Sons, Ltd.     

Simultaneous design of AWC and nonlinear controller for uncertain nonlinear systems under input saturation

This article addresses a novel technique for the simultaneous design of a robust nonlinear controller and static anti‐windup compensator (AWC) for uncertain nonlinear systems under actuator saturation and exogenous bounded input. The system is presumed to have locally Lipschitz nonlinearities, time‐varying uncertainties (appearing both in the linear as well as nonlinear dynamics and both in the state in addition to the output equations), and external norm‐bounded inputs both in the state and the output equations. Several bilinear matrix inequality–based conditions are derived to simultaneously design the robust nonlinear controller and AWC gains for uncertain nonlinear systems by employing the Lyapunov functional, reformulated Lipschitz property, uncertainty bounds, linear parameter‐varying approach, modified local and global sector conditions, iterative linear matrix inequality algorithm, convex optimization procedure, and gain minimization. The proposed multiobjective AWC‐based dynamic robust nonlinear controller guarantees the mitigation of saturation effects, robustness against time‐varying parametric norm‐bounded uncertainties, the asymptotic stability of the closed‐loop nonlinear system under zero external disturbances, and the attenuation of disturbance effects under nonzero external disturbances. The effectiveness of the proposed AWC‐based dynamic robust nonlinear controller synthesis scheme is illustrated by simulation examples.     

Linearized min‐max robust model predictive control: Application to the control of a bioprocess

This work deals with the problem of trajectory tracking for a nonlinear system with unknown but bounded model parameter uncertainties. First, this work focuses on the design of a robust nonlinear model predictive control (RNMPC) law subject to model parameter uncertainties implying solving a min‐max optimization problem. Secondly, a new approach is proposed, consisting in relating the min‐max problem to a more tractable optimization problem based on the use of linearization techniques to ensure a good trade‐off between tracking accuracy and computation time. The developed strategy is applied in simulation to a simplified macroscopic continuous photobioreactor model and is compared to the RNMPC and nonlinear model predictive controllers. Its efficiency and its robustness against parameter uncertainties and/or perturbations are illustrated through numerical results.     

Tracking setpoint robust model predictive control for input saturated and softened state constraints

This paper starts with a brief review of robust model predictive control (RMPC) schemes for uncertain systems using linear matrix inequalities (LMIs) subject to input saturated and softened state constraints. However when RMPC has both input and state constraints, difficulties will arise due to the inability to satisfy the state constraints. In this paper, we develop two new tracking setpoint RMPC schemes with common Lyapunov function and with zero terminal equality subject to input saturated and softened state constraints. A brief comparative simulation of the two new RMPC schemes is implemented via examples to demonstrate the ability of the new RMPC schemes.     

Designing of non-fragile robust model predictive control for constrained uncertain systems and its application in process control

A non-fragile robust model predictive control (RMPC) is designed in the uncertain systems under bounded control signals. To this aim, a class of the nonlinear systems with additive uncertainty is considered in its general form. The RMPC synthesis could lead to the proper selection of the controller’s gains. Thus, the non-fragile RMPC design is translated into a minimization problem subjected to some constraints in terms of linear matrix inequality (LMI). Hence, the controller’s gains are computed by solving such a minimization problem. In some numerical examples, the suggested non-fragile RMPC is compared with the other methods. The simulation results demonstrate the effectiveness of the proposed RMPC in comparison with similar techniques.     

Nonlinear Adaptive Model Predictive Control of Constrained Systems with Offset‐Free Tracking Behavior

In this paper, a nonlinear model‐based predictive control strategy for constrained systems based on an adaptive neural network (NN) predictor is proposed. The proposed controller is robust against the model uncertainties and external bounded disturbances. Moreover, it provides offset‐free tracking behavior using the adaptive structure in the model. Based on the uncertainties bounds, the restriction of the system constraints causes robust feasibility and stability of the closed‐loop system. It is shown that the output of the NN predictor converges to the system output. Moreover, offset‐free behavior of the closed‐loop system is investigated using the Lyapunov theorem. Simulation results show the effectiveness of the proposed method as compared to the recently proposed model predictive control methods in the literature.     

具有自适应噪声边界的Tube可达集鲁棒预测控制

针对过程噪声设定边界与真实噪声边界失配的有界干扰离散线性不确定系统,提出一种具有自适应噪声边界的Tube可达集鲁棒模型预测控制方法.首先,该算法引入基于MIT规则的自适应集员滤波在线估计系统状态和噪声边界.其次,基于估计值,通过迭代自适应集员滤波的时间更新部分计算出预测时域内闭环不确定系统状态的可达集.最后,用可达集代替不变集并根据Tube鲁棒模型预测控制策略,给出了实际不确定系统的控制律,确保系统状态鲁棒渐近稳定,并收敛于终端干扰不变集.仿真结果验证了该控制方法的有效性.     

Robust MPC for Linear Systems with Structured Time‐Varying Uncertainties and Saturating Actuator

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.     

H∞ fault estimation with randomly occurring uncertainties,quantization effects and successive packet dropouts: The finite‐horizon case

In this paper, the finite‐horizon H_∞ fault estimation problem is investigated for a class of uncertain nonlinear time‐varying systems subject to multiple stochastic delays. The randomly occurring uncertainties (ROUs) enter into the system due to the random fluctuations of network conditions. The measured output is quantized by a logarithmic quantizer before being transmitted to the fault estimator. Also, successive packet dropouts (SPDs) happen when the quantized signals are transmitted through an unreliable network medium. Three mutually independent sets of Bernoulli‐distributed white sequences are introduced to govern the multiple stochastic delays, ROUs and SPDs. By employing the stochastic analysis approach, some sufficient conditions are established for the desired finite‐horizon fault estimator to achieve the specified H_∞ performance. The time‐varying parameters of the fault estimator are obtained by solving a set of recursive linear matrix inequalities. Finally, an illustrative numerical example is provided to show the effectiveness of the proposed fault estimation approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Improved model prediction and RMPC design for LPV systems with bounded parameter changes

This paper studies the future model prediction and robust model predictive control (RMPC) design for linear parameter varying systems with bounded parameter changes. By developing tight bound estimations for varying parameters, we construct a set-valued map as the predicted family of future models. This construction attains accurate estimations and thus reduces conservativeness. Based on model predictions, we use a parameter-dependent feedback to design RMPC that achieves an enhanced performance with guaranteed robust and stability properties.     

A new robust model predictive control method I: theory and computation

The success of the single-model MPC (SMPC) controller depends on the accuracy of the process model. Modeling errors cause sub-optimal control performance and may cause the control system to become closed-loop unstable. The goal of this paper is to examine the control performance of the robust MPC (RMPC) method proposed by Wang and Rawlings [34] on several illustrative examples. In this paper, we show the RMPC method successfully controls systems with time-varying uncertainties in the process gain, time constant and time delay and achieves offset-free non-zero set point tracking and non-zero disturbance rejection subject to input and output constraints.     

Robust neural network–based tracking control and stabilization of a wheeled mobile robot with input saturation

This paper presents a robust neural network–based control scheme to deal with the problem of tracking and stabilization simultaneously for a wheeled mobile robot subject to parametric uncertainties, external disturbances, and input saturation. At first, a new error‐state transformation scheme is designed by introducing some auxiliary variables as an additional virtual control signals to reduce the adverse effect caused by the underactuation. These variables can change their structures for different desired trajectories to be tracked. Then, a robust control law is proposed combining with a kinematic controller and a dynamic controller, while a three‐layer neural network system is applied to approximate model uncertainties. Stability analysis via the Lyapunov theory shows that the proposed controller can make tracking errors converge to bounded neighborhoods of the origin. Finally, some simulation results are illustrated to verify the effectiveness of the proposed control strategy.     

H∞ Control of Linear Discrete‐Time Systems With Norm‐Bounded Nonlinear Uncertainties

In this paper, robust H_∞ control of a class of discrete‐time uncertain systems in state‐space form with linear nominal parts and norm‐bounded nonlinear uncertainties in both state and output equations is discussed. Such systems have a unique characterisic; that is, the two norm‐bounded nonlinear uncertainties have the equivalent representation by means of time‐varying and norm‐bounded linear uncertainties. To overcome the conservativenss of [5], the two nonlinear uncertainty sets are considered to be different. Then, by converting such systems into related discrete‐time linear systems with time‐varying and norm‐bounded linear uncertainties, we obtain that a sufficient condition for robust H_∞ control of such systems is equivalent to the solvability of the same problem of the related linear uncertain systems, which is solvable by means of a linear algebraic Riccati inequality.     

Robust adaptive output feedback control of a class of discrete‐time nonlinear systems with nonlinear uncertainties and unknown control directions

In this paper, robust adaptive output feedback control is studied for a class of discrete‐time nonlinear systems with functional nonlinear uncertainties of the Lipschitz type and unknown control directions. In order to construct an output feedback control, the system is transformed into the form of a nonlinear autoregressive moving average with eXogenous inputs (NARMAX) model. In order to avoid the noncausal problem in the control design, future output prediction laws and parameter update laws with the dead‐zone technique are constructed on the basis of the NARMAX model. With the employment of the predicted future outputs, a constructive output feedback adaptive control is proposed, where the discrete Nussbaum gain technique and the dead‐zone technique are used in parameter update laws. The effect of the functional nonlinear uncertainties is compensated for, such that an asymptotic tracking performance is achieved, whereas other signals in the closed‐loop systems are guaranteed to be bounded. Simulation studies are performed to demonstrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

ROBUST CONTROL FOR A CLASS OF UNCERTAIN STATE‐DELAYED SINGULARLY PERTURBED SYSTEMS

This paper considers the problem of robust control for a class of uncertain state‐delayed singularly perturbed systems with norm‐bounded nonlinear uncertainties. The system under consideration involves state time‐delay and norm‐bounded nonlinear uncertainties in the slow state variable. It is shown that the state feedback gain matrices can be determined to guarantee the stability of the closed‐loop system for all ∞ ∞ (0, ∞00) and independently of the time‐delay. Based on this key result and some standard Riccati inequality approaches for robust control of singularly perturbed systems, a constructive design procedure is developed. We present an illustrative example to demonstrate the applicability of the proposed design approach.