Robust Model Predictive Control Method Research Articles

Tube-based robust output feedback model predictive control for autonomous rendezvous and docking with a tumbling target

In this paper, a tube-based robust output feedback model predictive control method (TRMPC) is proposed for controlling chaser spacecraft docking with a tumbling target in near-circular orbit. The controller contains a simple, stable, Luenberger state estimator and a tube-based robust model predictive controller. Several practical challenges are also considered under dock-enabling conditions, such as the control saturation, velocity constraint, approach corridor constraint, and collision avoidance constraint. Meanwhile, uncertainties are carefully analyzed when designing the controller, including dynamics uncertainty, measurement error, and control deviation. The TRMPC ensures that all possible state trajectories with uncertainties lie in the minimum robust positively invariant set (mRPI, i.e., the so-called tube in this paper). The tube center is the solution of a nominal (without uncertainties) system. Another important contribution of this paper is to propose a technique where it is unnecessary to calculate the mRPI explicitly. Thereby, the ‘curse of dimensionality’ can be avoided for a six-dimensional system. To verify the feasibility of the proposed TRMPC strategy in the presence of uncertainties, two scenarios of autonomous rendezvous and docking (AR&D) are simulated. The simulation results show that the TRMPC method is more efficient in minimizing the uncertainties, fuel consumption, and computational cost, compared to the classic model predictive control (MPC) method.

Model Predictive Control of Uninterruptible Power Supply with Robust Disturbance Observer

This paper presents a robust continuous control set model predictive control (CCS-MPC) method to control the output voltage of a three-phase inverter in uninterruptible power supplies (UPS). A robust disturbance observer (DOB) is proposed to estimate the load current of the three-phase UPS without a steady-state error, taking the effect of model uncertainties into account. A CCS-MPC is designed using the DOB for reference voltage tracking purpose, and input constraints are considered in the controller design to calculate the optimal control input. Model uncertainties are defined using polytopic uncertainty class, and a linear matrix inequality (LMI) optimization method is used to compute the optimal observer gain matrix. Another robust controller (RC) is designed based on the DOB and compared with CCS-MPC. The effectiveness of the proposed method (the DOB based CCS-MPC) is evaluated for resistive, inductive, and nonlinear loads then compared with other control methods using a three-phase 5-KVA laboratory experiment UPS system.

Robust model predictive control with randomly occurred networked packet loss in industrial cyber physical systems

for a class of linear discrete-time systems that is subject to randomly occurred networked packet loss in industrial cyber physical systems, a novel robust model predictive control method with active compensation mechanism was proposed. The probability distribution of packet loss is described as the Bernoulli distributed white sequences. By using the Lyapunov stability theory, the existing sufficient conditions of the controller are derived from solving a group of linear matrix inequalities. Moreover, dropout-rate with uncertainty and unknown dropout-rate are also considered, which can greatly reduce the conservativeness of the controller. The designed robust model predictive control method not only efficiently eliminates the negative effects of the networked data loss in industrial cyber physical systems but also ensures the stability of closed-loop system. Two examples were provided to illustrate the superiority and effectiveness of the proposed method.

Stabilization of uncertain nonlinear discrete-time switched systems with state delays: A constrained robust model predictive control approach

This paper studies the problem of robust stabilization for a class of nonlinear discrete-time switched systems with polytopic uncertainties and unknown state delay. Moreover, the control signal is assumed to be constrained. The objective of the proposed controller is to stabilize the switched system under arbitrary switching signals based on the switched Lyapunov function approach. Therefore, based on the constrained robust model predictive control method and an appropriate Lyapunov–Krasovskii functional, the sufficient conditions to guarantee the asymptotical stability of the switched system are developed as linear matrix inequalities. Through online solving an optimization problem, the predictive state-feedback controller is designed. Furthermore, in this delay-dependent approach, only the upper bound of time-delay should be known. Appropriate transient response, ability to handle constraints, and nonconstrained switching signal are the other advantages of the proposed method. Finally, the performance of the proposed approach is compared with a similar approach through a numerical example. As well as, to show the applicability of the proposed controller, it is applied to a drinking water supply network, as an application example.

Robust Model Predictive Control for a Class of Discrete-Time Markovian Jump Linear Systems With Operation Mode Disordering

For a class of discrete-time Markovian jump linear systems subject to operation mode disordering, a robust model predictive control method can be proposed to solve this issue. A bijective mapping scheme between the original random process and a new random process is studied to cope with the problem of operation mode disordering. At each sampling time, the original “min-max” optimization problem is transformed into a convex optimization problem with linear matrix inequalities so that the complexity of solving the optimization problem can be greatly reduced. The sufficient stability condition of the Markovian jump linear systems can be achieved by using the Lyapunov stability theory. Moreover, a state feedback control law is obtained, which minimizes an infinite prediction horizon performance cost. Furthermore, the cases of uncertain and unknown transition probabilities are also considered in this paper. The simulation results show that the proposed method can guarantee the optimal control performance and the stability of Markovian jump linear systems.

Collision prediction and avoidance for satellite ultra-close relative motion with zonotope-based reachable sets

Collision prediction and avoidance are critical for satellite proximity operations, and the key is the treatment of satellites' motion uncertainties and shapes, especially for ultra-close autonomous systems. In this paper, the zonotope-based reachable sets are utilized to propagate the uncertainties. For satellites with slender structures (such as solar panels), their shapes are simplified as cuboids which is a special class of zonotopes, instead of the classical sphere approach. The domains in position subspace influenced by the uncertainties and shapes are determined, and the relative distance is estimated to assess the safety of satellites. Moreover, with the approximation of the domains, the worst-case uncertainties for path constraints are determined, and a robust model predictive control method is proposed to deal with the line of sight and obstacle avoidance constraints. With zonotope representations of satellites, the proposed robust model predictive control is capable of handling the shapes of the satellite and obstacle simultaneously. Numerical simulations demonstrate the effectiveness of the proposed methods with an elliptic reference orbit. 1

Robust Tube-Based Predictive Control for Visual Servoing of Constrained Differential-Drive Mobile Robots

This paper proposes a control strategy for the vision-based control problem of a nonholonomic constrained differential-drive mobile robots with bounded disturbance by using robust tube-based model predictive control (MPC) method. The proposed control strategy mainly consists of an ancillary state feedback controller and an MPC control for a nominal robotic system. First, the state-error kinematics of the nominal system is converted into a chained form system, and then its MPC optimization is computed to deal with a quadratic programming optimization problem by integrating a linear variable inequality-based primal-dual neural network (LVI-PDNN). Next, the gain scheduling of the ancillary state feedback is obtained via solving robust pole assignment using LVI-PDNN. An optimal state trajectory is thus generated for the nominal robotic system by the MPC without various uncertainties, the ancillary state feedback control forces the state variables to be constrained within an invariant designed tube. Finally, extensive experimental results on stabilization control of the nonholonomic mobile robot are provided to verify the effectiveness of the proposed robust tube-based MPC.

A new robust MPC using an approximate convex hull

A robust Model Predictive Control (MPC) method with a new model uncertainty characterization technique is studied for linear systems. The goal is to reduce the computational complexity of robust MPC. The main element of this method is to trade off the complexity of the representation of the uncertainty set with its accuracy, while still guaranteeing that input, state, and output constraints are met. The mechanism for the trade off is the computation of an approximate convex hull of the model set. This method is an effective tool to eliminate redundancy in the model set and decrease the number of extreme models in robust MPC approaches, resulting in decreased computational complexity. Simulation results illustrate the proposed method.

Robust Model Predictive Control: Implementation Issues with Comparative Analysis

Abstract Robust Model Predictive Control (RMPC) is related to a variety of methods designed to guarantee control performance using optimization algorithms while considering systems with uncertainties. Many RMPC methods were created with different formulations, however there is lack of studies comparing their performances using pre-established metrics. Thus, the objective of this paper is to analyze and compare different RMPC methods using a Continuous Stirred-Tank Reactor (CSTR) plant with parametric uncertainties as a case of study. The methods are sorted by Min-max MPC, Tube-based MPC and LMI-based MPC, which were carefully chosen based on their relevance in the current literature. The metrics used to compare the methods are separated in off-line, related to configuration of the controller prior to its use, and on-line, which are related to the computational cost of the algorithm and difficulties that may arise during its application. Based on simulation results, it will be shown that the LMI-based methods are slower for calculating the control signal, but are easier to implement. Whereas, both Min-max and Tube-based methods require calculation of robust control invariant sets which might be difficult for more complex systems, however they are much faster when comparing to LMI.

Electrospinning Sedimentary Microstructure Feedback Control by Tuning Substrate Linear Machine Velocity

These years have witnessed increasing research works and new technologies on manufacture of micro-/nanoscale flexible and tractile electronic devices. Orderly bead-on-string microstructures fabricated by electrospinning processes have applications in flexible and tractile sensors, artificial tissues and energy harvesters. In this paper, a feedback control system is established for sedimentary microstructures produced by electrospinning processes. This system is composed of a high-speed camera, an National Instruments (NI) image processor, an NI controller, and a linear machine regulating the substrate velocity. A robust model predictive control (MPC) method is developed on practical electrospinning processes to improve the regularity of the sedimentary bead-on-string pattern suffered by external disturbances and system uncertainties. Extensive experimental results have verified that the interbead gap becomes tunable and stabilized by the closed-loop MPC controller actuated by the linear machine. This controller is beneficial to enhance the consistency and controllability of the microelectrical elements. More significantly, the adjustability of the interbead gap enables the manufacturing of uniform microstructures widely used in microscale sensors and electrical units manufacturing and tissue engineering.

Robust model predictive control for path-following of underactuated surface vessels with roll constraints

Abrupt maneuvering or strong disturbances from sea waves probably lead to large roll motion of underactuated surface vessels, which severely affects stability of surface vessels. A novel path-following control for vessels with roll constraints is proposed by combining Kalman filter, disturbance observer and robust constrained model predictive control method. Firstly, a switched linear uncertain model with coupled surge, sway, roll and yaw is constructed for underactuated surface vessels. Then, an improved Sage-Husa Adaptive Kalman Filter is proposed to estimate vessels' full states by partial states information and eliminate the effects of measurement noises. Next, the disturbance observer, which is used to estimate low-frequency disturbances from wind, waves and oceans, is combined with constrained model predictive control to improve the robustness of the closed-loop control system. In this paper, the effectiveness of the proposed algorithm is verified by theoretical analysis, simulations and experiments.

Robust Feedback Model Predictive Control of Sea Wave Energy Converters

This paper presents a robust feedback model predictive control (MPC) strategy for a sea wave energy converter (WEC). The control objective is to maximise the energy output while reducing the potential risk of device damage subject to sea wave excitation forces as persistent external disturbance. The robust feedback MPC proposed in this paper has the following prominent advantages: (i) the robust feasibility and stability can be guaranteed. (ii) the robust MPC method does not rely on the real time wave prediction. These features can not only reduce the unit cost of energy generation but also increase the reliability of the MPC controller.

Linear programming‐based robust model predictive control for positive systems

This study investigates the problem of robust model predictive control for positive systems under a new model predictive control framework. A robust model predictive control method is presented in this study for uncertain positive systems. A state-feedback control law that robustly stabilises the underlying system is designed by using linear programming. Different from the traditional model predictive control technique, the authors' proposed model predictive control framework employs a linear infinite horizon objective function and a linear Lyapunov function rather than quadratic performance indices and quadratic Lyapunov functions commonly used in the literature. Compared with existing design techniques for positive systems, the present approach owns the following advantages: (i) it gives a locally optimal control strategy which approaches to actual operation conditions and the control law is designed by solving a locally optimal control problem at each time step, (ii) it can explicitly deal with constraints of the systems, and (iii) the controller can be easily designed via linear programming without any additional constraints. An practical example is provided to verify the validity of the theoretical findings.

Robust static output feedback infinite horizon RMPC for linear uncertain systems

This work studies the problem of static output feedback (SOF) infinite horizon robust model predictive control (RMPC) for linear uncertain systems with input constraints. In contrast with the existing RMPC design methods, this approach computes the vector of control actions directly from the observed variables while the system states are unmeasurable. For the unavailable states, an ellipsoidal set is used to obtain an estimation and applied in the RMPC optimization problem. This set is updated at every time instant which may cause the loss of the recursive feasibility. In order to handle this drawback, a new design condition is adopted. Then, the design method is formulated in terms of a convex optimization problem with linear matrix inequality (LMI) constraints. The effectiveness of the proposed RMPC method is demonstrated by a numerical example.

Robust model predictive control of constrained non‐linear systems: adopting the non‐squared integrand objective function

This study presents a novel robust model predictive control (MPC) method for constrained non-linear systems with control constraints and external disturbances. The control signal is obtained by optimising an objective function consisting of two terms: an integral non-squared stage cost and a non-squared terminal cost. The terminal weighting matrix is designed appropriately such that: (i) the terminal cost serves as a control Lyapunov function; and (ii) the resultant finite horizon cost can be treated as a quasi-infinite horizon cost. Provided that the Jacobian linearisation of the system to be controlled is stabilisable and the optimisation is initially feasible, sufficient conditions ensuring the recursive feasibility of the optimisation and the robust stability of the closed-loop system are established. It is shown that the conditions rely on an appropriate design of the sampling interval with respect to a certain given disturbance level. The effectiveness of the proposed method is illustrated through a numerical example.

Robust On-Line Model Predictive Control for a Constrained Image Based Visual Servoing

This paper presents an online image-based visual servoing (IBVS) controller for a 6-degrees-of-freedom (DOF) robotic system based on the robust model predictive control (RMPC) method. The controller is designed considering the robotic visual servoing system’s input and output constraints, such as robot physical limitations and visibility constraints. The proposed IBVS controller avoids the inverse of the image Jacobian matrix and hence can solve the intractable problems for the classical IBVS controller, such as large displacements between the initial and the desired positions of the camera. To verify the effectiveness of the proposed algorithm, real-time experimental results on a 6-DOF robot manipulator with eye-in-hand configuration are presented and discussed.

The Stochastic Robust Model Predictive Control of Shimmy Vibration in Aircraft Landing Gears

AbstractThis paper considers robust model predictive control (RMPC) methods for a linear parameter varying (LPV) system that has both probabilistic uncertain and time‐varying parameters. The parameters are considered to be measured online. In this regard, the aircraft landing gear system is considered as an LPV system whose parameters variation can affect both stability and performance. By transforming this system into a convex combination of linear time‐invariant vertices form with the tensor‐product (TP) model transformation method, the landing gear system is represented as a polytopic linear parameter‐varying system. A computationally efficient RMPC control signal law is calculated online by carrying out the convex optimization involving linear matrix inequalities (LMIs) in MPC which leads to finding the solutions that can guarantee the closed‐loop robust stability and performance. The proposed controller can effectively suppress the shimmy vibration of the landing gear with variable taxiing velocity and wheel caster length, also with the probabilistic uncertain torsional spring stiffness.

Modeling and Model Predictive Power and Rate Control of Wireless Communication Networks

A novel power and rate control system model for wireless communication networks is presented, which includes uncertainties, input constraints, and time-varying delays in both state and control input. A robust delay-dependent model predictive power and rate control method is proposed, and the state feedback control law is obtained by solving an optimization problem that is derived by using linear matrix inequality (LMI) techniques. Simulation results are given to illustrate the effectiveness of the proposed method.

Predictive metamorphic control

In spite of its easy implementation, ability to handle constraints and nonlinearities, etc., model predictive control (MPC) does have drawbacks including tuning difficulties. In this paper, we propose a refinement to the basic MPC strategy by incorporating a tuning parameter such that one can move smoothly from an existing controller to a new MPC strategy. Each change of this tuning parameter leads to a new stabilising control law, therefore, allowing one to gradually move from an existing control law to a new and better one. For the infinite horizon case without constraints and for the general case with state and input constraints, stability results are established. We also examine the practical applicability of the proposed approach by employing it in the nominal prediction model of the tube-based output feedback robust MPC method. The merits of the proposed method are illustrated by examples.

Parameterized Tube Model Predictive Control

This paper develops a parameterized tube model predictive control (MPC) synthesis method. The most relevant novel feature of our proposal is the online use of a single tractable linear program that optimizes parameterized, Minkowski decomposable, state and control tubes and an associated, fully separable, nonlinear, control policy. The induced control policy enjoys a higher degree of nonlinearity than existing tube MPC and robust MPC using disturbance affine control policy. Our proposal offers greater generality than the state of the art robust MPC methods. It is conjectured, and also established in three cases, that our proposal is equivalent, feasibility-wise, to dynamic programming (DP). It is also shown that, under natural assumptions, our method is computationally efficient while it possesses rather strong system theoretic properties.