Robust output feedback model predictive control of constrained linear systems

This paper provides a solution to the problem of robust output feedback model predictive control of constrained, linear, discrete-time systems in the presence of bounded state and output disturbances. The proposed output feedback controller consists of a simple, stable Luenberger state estimator and a recently developed, robustly stabilizing, tube-based, model predictive controller. The state estimation error is bounded by an invariant set. The tube-based controller ensures that all possible realizations of the state trajectory lie in a simple uncertainty tube the ‘center’ of which is the solution of a nominal (disturbance-free) system and the ‘cross-section’ of which is also invariant. Satisfaction of the state and input constraints for the original system is guaranteed by employing tighter constraint sets for the nominal system. The complexity of the resultant controller is similar to that required for nominal model predictive control.     

Robust output feedback model predictive control of constrained linear systems: Time varying case

The problem of output feedback model predictive control of discrete time systems in the presence of additive but bounded state and output disturbances is considered. The overall controller consists of two components, a stable state estimator and a tube based, robustly stabilizing model predictive controller. Earlier results are extended by allowing the estimator to be time varying. The proposed robust output feedback controller requires the online solution of a standard quadratic program. The closed loop system renders a specified invariant set robustly exponentially stable.     

Robust output feedback model predictive control using off-line linear matrix inequalities

A fundamental question about model predictive control (MPC) is its robustness to model uncertainty. In this paper, we present a robust constrained output feedback MPC algorithm that can stabilize plants with both polytopic uncertainty and norm-bound uncertainty. The design procedure involves off-line design of a robust constrained state feedback MPC law and a state estimator using linear matrix inequalities (LMIs). Since we employ an off-line approach for the controller design which gives a sequence of explicit control laws, we are able to analyze the robust stabilizability of the combined control laws and estimator, and by adjusting the design parameters, guarantee robust stability of the closed-loop system in the presence of constraints. The algorithm is illustrated with two examples.     

MPC for stable linear systems with model uncertainty

In this paper, we developed a model predictive controller, which is robust to model uncertainty. Systems with stable dynamics are treated. The paper is mainly focused on the output-tracking problem of a system with unknown steady state. The controller is based on a state-space model in which the output is represented as a continuous function of time. Taking advantage of this particular model form, the cost functions is defined in terms of the integral of the output error along an infinite prediction horizon. The model states are assumed perfectly known at each sampling instant (state feedback). The controller is robust for two classes of model uncertainty: the multi-model plant and polytopic input matrix. Simulations examples demonstrate that the approach can be useful for practical application.     

Output feedback MPC with guaranteed robust stability

This paper focuses on the issues of robust stability of model predictive control (MPC). The control problem is formulated as linear matrix inequalities (LMI) optimization problem. A suboptimal solution for the output feedback control problem is proposed. The size of the resulting MP controller is reduced by using a suitable state-space representation of the process. Guaranteed stability conditions for the output feedback MPC are enforced via a Lyapunov type constraint. An iterative algorithm is developed resulting in a pair of coupled LMI optimization problems which provide a robustly stable output feedback gain. Model uncertainties are considered via a polytopic set of process models. The methodology is illustrated with the simulation of the control problem of two chemical processes. The results show that the proposed strategy eliminates the need to detune the MP controller improving the performance for most of the cases considered.     

Robust adaptive output feedback control for uncertain nonlinear systems with quantized input

In this paper, we study the input quantization problem for a class of uncertain nonlinear systems. The quantizer adopted belongs to a class of sector‐bounded quantizers, which basically include all the currently available static quantizers. Different from the existing results, the quantized input signal, rather than the input signal itself, is used to design the state observers, which guarantees that the state estimation errors will eventually converge to zero. Because the resulting system may be discontinuous and non‐smooth, the existence of the solution in the classical sense is not guaranteed. To cope with this problem, we utilize the non‐smooth analysis techniques and consider the Filippov solutions. A robust way based on the sector bound property of the quantizers is used to handle the quantization errors such that certain restrictive conditions in the existing results are removed and the problem of output feedback control with input signal quantized by logarithmic (or hysteresis) quantizers is solved for the first time. The designed controller guarantees that all the closed‐loop signals are globally bounded and the tracking error exponentially converges towards a small region around zero, which is adjustable. Copyright © 2016 John Wiley & Sons, Ltd.     

Finite-frequency output feedback MPC for Markov jump systems

This paper investigates a general design framework of dynamic output feedback model predictive control (DOFMPC) for Markov jump systems within both time and frequency domain. Such a design with guaranteed H_∞ and quadratic performance is formulated by a standard semi-definite programming (SDP), and it is achieved by employing a special congruence transformation. The SDP condition greatly reduces the computational effort by eliminating bilinear matrix inequalities or equation constraints reported in existing references. Specifically, the H_∞ norm of the transfer function is optimized within three types of frequency ranges on account of generalized Kalman–Yakubovic–Popov (GKYP) lemma. The quadratic index is optimized online via SDP. Finally, we verify the feasibility and effectiveness of the proposed method from both theoretical and practical point of view.     

Adaptive output feedback quantised tracking control for stochastic nonstrict-feedback nonlinear systems with input saturation

This paper is concerned with the problem of adaptive output feedback quantised tracking control for a class of stochastic nonstrict-feedback nonlinear systems with asymmetric input saturation. Especially, both input and output signals are quantised by two sector-bounded quantisers. In order to solve the technical difficulties originating from asymmetric saturation nonlinearities and sector-bounded quantisation errors, some special technique, approximation-based methods and Gaussian error function-based continuous differentiable model are exploited. Meanwhile, an observer including the quantised input and output signals is designed to estimate the states. Then, a novel output feedback adaptive quantised control scheme is proposed to ensure that all signals in the closed-loop system are 4-moment (2-moment) semi-globally uniformly ultimately bounded while the output signal follows a desired reference signal. Finally, the effectiveness and applicability of the design methodology is illustrated with two simulation examples.     

Distributed output feedback MPC with randomly occurring actuator saturation and packet loss

In 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.     

Leader-following fixed-time output feedback consensus for second-order multi-agent systems with input saturation

This paper investigates the leader-following fixed-time output feedback consensus problem for second-order multi-agent systems with input saturation. By combing fixed-time control technique and bi-limit homogeneous systems theory, a class of bounded fixed-time consensus protocols are developed for leader-following multi-agent systems. The protocol design is divided into two parts. First, when all the state information of the followers are measurable, a state feedback consensus protocol is designed to achieve fixed-time consensus. Then, when the velocity information is unmeasurable, an observer-based fixed-time consensus protocol is proposed. With the help of Lyapunov stability theorem and the property of a homogeneous function, it is theoretically shown that the states of all followers can track that of the leader in fixed-time in the presence of input saturation. Finally, numerical simulation is carried out to illustrate the effectiveness of theoretical results.     

Improved dynamic output feedback RMPC for linear uncertain systems with input constraints

In this work, we propose a dynamic output feedback robust model predictive control (RMPC) design method for linear uncertain systems with input constraints. In order to handle the input constraints, the control signals are permitted to saturate, which can fully utilize the capability of actuators and thus can reduce the conservatism. For the unavailable states, an ellipsoidal set is used to obtain an estimation, and it is updated at every time instant. A modified RMPC design requirement is used to ensure the recursive feasibility of the optimization problem. Then, the design method is formulated in terms of a convex optimization problem with linear matrix inequality constraints. The proposed output feedback RMPC design method is expected to further reduce the conservativeness. The improvements of the proposed algorithm over the other existing techniques is demonstrated by an example. Copyright © 2015 John Wiley & Sons, Ltd.     

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).     

不确定广义系统的输出反馈鲁棒预测控制

针对一类具有范数有界不确定性的广义系统,当系统状态不可测时,提出了一种基于输出反馈的鲁棒预测控制器综合算法．采用ＬＭＩ方法以及变量变换思想,将无限时域“最小最大”优化问题转化为线性规划问题．确定出一组分段连续的输出反馈控制序列,给出了输出反馈控制律存在的充分条件,证明了优化问题在初始时刻的可行解可以保证广义闭环系统是渐近稳定且正则无脉冲的．仿真实例验证了所提出方法的有效性．     

On dynamic output feedback robust MPC for constrained quasi-LPV systems

This paper considers the dynamic output feedback robust model predictive control (MPC) of a quasi-linear parameter varying (quasi-LPV) system with bounded noise. In our previous works, for the unknown true state, either its ellipsoidal bounds or its polyhedral bounds were solely applied in the main optimisation problem. The recursive feasibility of the main optimisation problem was guaranteed by a simple refreshment of the ellipsoidal bound, but might be lost by applying the polyhedral bounds. This paper shows how and to what extent the recursive feasibility can be restored when the polyhedral bounds are still utilised. First, we propose a new approach which, at each sampling time, utilises either the ellipsoidal bound or the polyhedral bound in the main optimisation problem, the latter being used if and only if it is contained in the former. Then, we show the sufficient conditions under which the approaches based on polyhedral bounds preserve the property of recursive feasibility. A numerical example is given to illustrate the effectiveness of the controller.     

输出反馈实现一类带不确定输入动态非线性系统的鲁棒几乎干扰解耦

研究一类带不确定输入动态非线性系统的输出反馈干扰抑制问题并基于观测器给出了输出反馈控制器 构造性的设计方法.所设计的控制器具有对可允许不确定动态的鲁棒性.不仅在L₂增益意义上抑制了干扰对输出 的影响,同时在ISS镇定意义上抑制了干扰对状态的影响.     

A gradient flow approach to on-line robust pole assignment for synthesizing output feedback control systems

Pole assignment is a basic design method for synthesis of feedback control systems. In this paper, a gradient flow approach is presented for robust pole assignment in synthesizing output feedback control systems. The proposed approach is shown to be capable of synthesizing linear output feedback control systems via on-line robust pole assignment. Convergence of the gradient flow can be guaranteed. Moreover, with appropriate design parameters the gradient flow converges exponentially to an optimal solution to the robust pole assignment problem and the closed-loop control system based on the gradient flow is globally exponentially stable. These desired properties make it possible to apply the proposed approach to slowly time-varying linear control systems. Simulation results are shown to demonstrate the effectiveness and advantages of the proposed approach.     

Semi-global output regulation for linear systems with input saturation by composite nonlinear feedback control

To improve transient performance of output response, this paper applies composite nonlinear feedback (CNF) control technique to investigate semi-global output regulation problems for linear systems with input saturation. Based on a linear state feedback control law for a semi-global output regulation problem, a state feedback CNF control law is constructed by adding a nonlinear feedback part. The extra nonlinear feedback part can be applied to improve the transient performance of the closed-loop system. Moreover, an observer is designed to construct an output feedback CNF control law that also solves the semi-global output regulation problem. The sufficient solvability condition of the semi-global output regulation problem by CNF control is the same as that by linear control, but the CNF control technique can improve the transient performance. The effectiveness of the proposed method is illustrated by a disturbance rejection problem of a translational oscillator with rotational actuator system.     

Robust nonlinear output feedback control for brake by wire control systems

This work proposes a nonlinear output feedback control law for active braking control systems. The control law guarantees bounded control action and can cope also with input constraints. Moreover, the closed-loop system properties are such that the control algorithm allows to detect—without the need of a friction estimator—if the closed-loop system is operating in the unstable region of the friction curve, thereby allowing to enhance both braking performance and safety. The design is performed via Lyapunov-based methods and its effectiveness is assessed via simulations on a multibody vehicle simulator.