Predictive Control For Linear Systems Research Articles

An improved state space model predictive control for linear systems with input disturbance

This paper presents an improved model predictive control (MPC) algorithm for linear systems with input disturbance. Based on the developed extended non-minimum state space input disturbance (ENMSS-ID) model, the input disturbance model structure is incorporated into the MPC framework and the objective function of the MPC optimization problem is improved to weigh the system output increments. This enables the algorithm simultaneously to achieve good input disturbance rejection performance for systems with known input disturbances and reduce the controllers’ sensitivity to model mismatch. An existing optimal estimation method is introduced to estimate the input disturbance, together with the proposed strategy to improve estimation convergence. Offset-free property is also proven to show the steady-state performance of the designed control scheme. Finally, two benchmark plants are studied to illustrate the effectiveness and advantages of the proposed algorithm.

Tube-based model predictive control for linear systems with bounded disturbances and input delay

This paper proposes a tube-based model predictive control strategy for linear systems with bounded disturbances and input delay to ensure input-to-state stability. Firstly, the actual disturbed system is decomposed into a nominal system without disturbances and an error system. For the nominal system, solving an optimization problem, where the delayed control input is set as an optimization variable, yields a nominal control law that enables the nominal state signal to approach to zero. Then, for the error system, the Razumikhin approach is used to identify a robust control invariant set. Using the set invariance theorem, an ancillary control law is developed to confine the error state signal in the invariant set. Combining the two results, we obtain a control law that enables the state signal to remain within a robustly invariant tube. Finally, the effectiveness of the developed control strategy is validated by simulations.

Output Feedback Stochastic Model Predictive Control for Linear Systems with Convex Optimization Approach

Output Feedback Stochastic Model Predictive Control for Linear Systems with Convex Optimization Approach

Minimal Constraint Violation Probability in Model Predictive Control for Linear Systems

Minimal Constraint Violation Probability in Model Predictive Control for Linear Systems

Analysis and design of control systems via parameter‐based approach

Control laws can be constructed in systems design by introducing parameters to obtain good system performance or robustness. A typical example of such a class of design approaches is the high-gain design approach. In the design of high-gain controllers, an introduction of a parameter results in a family of feedback control laws. Such a feedback law is given by a parametrized gain matrix which approaches infinity as the introduced parameter approaches its extreme value. Such a class of design approach can be called a parameter-based approach. Another case of the parameter-based approach is to establish mathematical models by introducing some extra parameters. A typical example is to derive the mathematical model of a spacecraft by unit quaternions which are constructed by introducing three extra parameters i, j and k with the properties i 2 = j 2 = k 2 = − 1 ${i^2} = {j^2} = {k^2} = - 1$ , i j = k $ij\; = {\rm{\;}}k$ , j k = i $jk\; = {\rm{\;}}i$ and k i = j $ki\; = {\rm{\;}}j$ . This Special Issue aims to present the recent development of the parameter-based approach in analysing and designing control systems. The theme of this special issue can be divided into three parts: Model construction by introducing parameters, control law design by introducing parameters and parametric solutions to control-related matrix equations. This topic includes 6 papers. Qi et al., in their paper ‘Finite-time attitude consensus control for multiple rigid spacecraft based on distributed observers’, use unit quaternions, which are constructed by, to investigate attitude consensus control for multiple rigid spacecraft. Based on this model, a group of distributed finite-time observers is constructed for each follower, and then an attitude control protocol based on a fast nonsingular terminal sliding mode is proposed by using the observed information. In the papers ‘Adaptive dual model predictive control for linear systems with parametric uncertainties’ by Lin et al. and ‘Generalized predictive controller (GPC) design on single-phase full-bridge inverter with a novel identification method’ by Ghamari et al., regressive models including the unknown parameters are used, and the dual adaptive model predictive control (MPC) and the generalized MPC are respectively proposed by incorporating least squares identification algorithms. In the paper ‘A recursive identification algorithm for linear discrete periodic systems’ by Lv et al., a periodic autoregressive and moving average (ARMA) model of a linear discrete-time periodically time-varying system is transformed into a time-invariant ARMA model by adopting cyclic lifting techniques. With this model, the considered system is described by a regressive form with the unknown coefficients as parameters, and then the corresponding least squares identification algorithm is proposed. Cai et al., in their paper ‘Design of LPV controller for morphing aircraft using inexact scheduling parameters’, establish a linear parameter-varying model for a morphing aircraft by Jacobian linearization. In this model, there exist a group of scheduling parameters. With such a model, Cai et al. investigate the design problem of gain-scheduled output-feedback controllers by using inexact scheduling parameters for morphing aircraft during the wing transition process. Liu et al., in their paper ‘Event-triggered fuzzy output feedback fault-tolerant control for interval type-2 Takagi-Sugeno large-scale systems with time delays’, propose an observer-based event-triggered fault-tolerant control law for a class of T-S fuzzy systems. In order to obtain the desired control laws, the considered T-S fuzzy system is represented as a linearly-parameterized dynamical system by introducing a set of parameters related to the membership functions. This topic includes 6 papers. Jin et al., in their paper ‘Optimal control of nonlinear Markov jump systems by control parametrization technique’, investigate the optimal control problem for nonlinear Markov jump systems with continuous state inequality constraints. In this paper, the control parametrization technique is used to represent the control function by a piecewise constant function. In such a representation, the heights of the piecewise constant function on the subintervals are the introduced parameters, and can be taken as decision variables to be optimized. With such an efficient treatment, the original problem is converted into an approximate finite-dimensional optimization problem. Huang et al., in their paper ‘Fixed-time fault-tolerance attitude tracking control for spacecraft without unwinding’, propose a disturbance-observer-based fixed-time fault-tolerance control law for rigid spacecraft by adopting backstepping techniques. Some design parameters exist in the part of the observer and the part of the fixed-time control law. In addition, the singularity problem in traditional fixed-time controllers based on signal function is eliminated with the aid of the arctangent function in the proposed controller. Wu et al., in their paper ‘Fractional-order sliding mode attitude coordinated control for spacecraft formation flying with unreliable wireless communication’, present two types of fractional order sliding mode control protocols to solve the coordinated attitude control problem for spacecraft formation flying. The introduced design parameters in these protocols can be appropriately chosen to improve convergence speed. It should be pointed out that a set of weighting parameters are introduced in the first class control protocol such that some nonlinear functions can be approximated by Chebyshev neural network. In the paper ‘Asymptotic stabilization for nonlinear systems with time-varying delays’, Li et al. present a novel output feedback control law for a class of nonlinear systems with unknown time-varying delays by introducing the static gain functions as parameters. In addition, in the control law there also exists another positive parameter which can be adjusted to improve system performance. Bi, in his paper ‘Neural networks adaptive control for fractional-order nonlinear with unmodelled dynamics and actuator faults’, investigate the problem of fault-tolerant control for fractional-order nonlinear systems. Two groups of parameters are introduced to construct the control law. The first group of parameters are introduced in the neural networks to approximate unknown nonlinear functions in the system, and the second group of parameters are dynamic, and its evolution law is given by a fractional-order adaptation law. Hou et al., in their paper ‘Fuzzy linear extended states observer based iteration learning fault-tolerant control for autonomous underwater vehicle trajectory tracking system’, develops a fault-tolerant control law based on a linear extended state observer (LESO) for autonomous underwater vehicles. In this control law, the LESO includes some parameters to be adjusted. This topic includes two papers. In these two papers, two classes of matrix equations with their applications in systems control are investigated. Cao et al., in their paper ‘Output feedback based poles configuration for LDP systems with varying state and input dimension’, convert the problem of poles configuration via periodic output feedback for linear discrete periodic systems into the problem of solving a class of special Sylvester matrix equations. A parametric solution to this class of matrix equations is presented in this paper, and then the output feedback gains for the periodic system are provided based on this parametric solution. Lei Zhang et al., in their paper ‘On the solutions to Sylvester-conjugate periodic matrix equations via iteration’, develop an iterative algorithm to solve the so-called Sylvester-conjugate periodic matrix equations. In this algorithm, two scalar parameters are involved. When the gradient principle is applied to a quadratic index function related to the considered matrix equations, the explicit expressions for these two scalars are determined, and in this case the developed algorithm is finite-time convergent. All of the papers selected for this Special Issue show that the parameter-based approach plays an importantly instrumental role in the analysis and design of control systems. It can be observed from these papers and some existing results that many control problems can be cast into such a framework. It is expected that this parameter-based approach can be further applied in more aspects of control systems design. Ai-Guo Wu was born in Gong'an, Hubei, China, in 1980. He received the B.Eng. degree in automation, an M.Eng. degree in navigation, guidance and control, and the Ph.D. degree in control science and engineering from the Harbin Institute of Technology, in 2002, 2004, and 2008, respectively. In 2008, he joinedthe Shenzhen Graduate School, Harbin Institute of Technology as an Assistant Professor, where he was promoted to Professor in 2012. He was a Research Fellow with the Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, from 2009 to 2011. He was a Visiting Professor with the Department of Electrical, Electronic and Computer Engineering, The University of Western Australia, Australia, from 2013 to 2014. Since 2018, he has been a Professor at Harbin Institute of Technology (Shenzhen). His research interests include spacecraft control, time delay systems, fully actuated systems theory, and robust control. He has authored/co-authored one English monograph and over 100 SCI journal papers. He received the National Natural Science Award (Second Prize) from China in 2015, and the National Excellent Doctoral Dissertation Award from the Academic Degrees Committee of the State Council and the Ministry of Education of China in 2011. He was supported by the Program for New Century Excellent Talents in Universities in 2011, and by the National Natural Science Foundation of China for Excellent Young Scholars in 2018. He has been serving as a Regional Editor for Nonlinear Dynamics and Systems Theory since 2015, and an International Subject Editor for Applied Mathematical Modeling since 2017. Zheng-Guang Wu (Member, IEEE) was born in 1982. He received the B.S. and M.S. degrees in mathematics from Zhejiang Normal University, Jinhua, China, in 2004 and 2007, respectively, and the Ph.D. degree in control science and engineering from Zhejiang University, Hangzhou, China,in 2011. He has authored or co-authored over 100 papers in refereed international journals. His current research interests include hybrid systems, Markov jump systems, sampled-data systems, fuzzy systems, multi-agent systems, Boolean control networks, stochastic systems, and neural networks. Dr. Wu also serves as an Associate Editor/Editorial Board Member for some international journals, such as the IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS: SYSTEMS, the Journal of The Franklin Institute, Neurocomputing, the International Journal ofControl, Automation, and Systems, IEEE ACCESS, the International Journal of Sensors, Wireless Communications and Control, and IEEE Control Systems Society Conference Editorial Board. He was named a Highly Cited Researcher (Clarivate Analytics). He is also an Invited Reviewer of Mathematical Reviews of the American Mathematical Society. Victor Sreeram obtained Bachelor's degree in 1981 from Bangalore University, India, a Master's degree in 1983 from Madras University, India, and Ph.D. degree from the University of Victoria, British Columbia, Canada in 1990, all in Electrical Engineering. He worked as a Project Engineer in the Indian Space Research Organisation from 1983 to 1985. He joined the Department of Electrical, Electronic, and Computer Engineering, the University of Western Australia in 1990 as a lecturer and he is now a Professor and the Head of Department. He was a Graduate Research Coordinator from 2008 to 2017. He is an associated editor of IET Control Theory and Applications, and the Asian Journal of Control. He is currently the Vice President of the Asian Control Association for Technical Activities and the Chairman of the Australia New Zealand Control Conference Steering Committee Association Incorporated. He has authored over 250 publications including over 125 journal publications. He is a co-recipient of the 2012 Premium Award for Best Paper in IET Power Electronics, and the 2014 Premium Award for Best Paper in IET Generation, Transmission & Distribution. He is also a recipient of the 2013 Outstanding Reviewer for IEEE Transactions on Automatic Control Award. He is now a Fellow of the Institution of Engineers, Australia. He has successfully supervised over 25 PhD students and has examined over 50 PhD theses in his career. His teaching and research interests are Control Systems, Signal Processing, Communications, Power engineering and Smart Grid and Renewable Energy. Xiaofeng Wang is an associate professor in the Department of Electrical Engineering at the University of South Carolina, Columbia. He earned his B.S. degree in Applied Mathematics and M.S. in Operation Research and Control Theory from East China Normal University, China, in 2000 and2003, respectively, and obtained his PhD degree in Electrical Engineering from the University of Notre Dame in 2009. After that, he worked as postdoctoral research associate at the University of Illinois at Urbana and Champaign and then joined the University of South Carolina in 2012. His research interests include robotics and control, cyber-physical systems, networked control systems, robust adaptive control, and optimization. He is an associate editor of Journal of The Franklin Institute since 2015 and IEEE Transactions on Aerospace and Electronic Systems since 2021. He is also an associate editor of IEEE Control Systems Society Conference Editorial Board since 2018. He was the recipient of the best paper award in the Annual Conference of the Prognostics and Health Management Society in 2014. The authors declare no conflicts of interest.

Model Predictive Control for Linear Systems Under Relaxed Constraints

This article considers model predictive control (MPC) for linear systems under relaxed constraints. The main novelty of our proposal is the introduction, and an adequate use, of the terminal dynamics of the slack variable associated with relaxed constraints. The proposed MPC under relaxed constraints retains computational efficiency of the traditional MPC, while it guarantees positive invariance and exponential stability over an enlarged domain of attraction. The design method is also illustrated in a step-by-step manner by an academic example.

Data-Driven Safety-Certified Predictive Control for Linear Systems

Data-Driven Safety-Certified Predictive Control for Linear Systems

Moment based model predictive control for linear systems: Additive perturbations case

AbstractIn this article, we present a novel linear model predictive control (MPC) strategy for controlling uncertain dynamical systems. The moment based MPC strategy is based on the (centralized) moments of the stochastic cost and constraint functions. We show that moment based MPC formulations yield computationally tractable predictive control problems, due to the explicit analytic expressions of the moments and linearity in the dynamics. This article considers (i) the output regulation MPC configuration, where the output is steered towards a reference and state vector is not correctly accessible to the controller at the decision instants; (ii) the moment based MPC formulation with uncertainties that are non‐Gaussian random variables, and (iii) bound and polytopic constraints in the uncertain MPC problem subject to either Gaussian disturbances or uncertainties with symmetric distributions. We demonstrate the effectiveness of the proposed MPC technique on simulation examples such as a double integrator system and a quadruple tank system.

Adaptive dual model predictive control for linear systems with parametric uncertainties

Adaptive dual model predictive control (DMPC) for linear systems with constant parametric uncertainties is investigated in this paper. In particular, chance constraints on output and input are considered. The online set-membership identification and recursive least squares are utilized for shrinking the uncertain parameter set and getting the estimation point of the parameters. The dual effect represented by the parameters' prediction error is considered in the receding horizon optimization problem for easing the impact of the uncertainties and improving the performance simultaneously. Chance constraints on output are tackled by converting into convex alternatives. The output tracking problem is transformed into a quadratically constrained quadratic-programming (QCQP) problem, which is computationally tractable. A numerical example is provided to illustrate the effectiveness of the proposed method.

Stochastic model predictive control for linear systems with unbounded additive uncertainties

This paper presents two stochastic model predictive control methods for linear time-invariant systems subject to unbounded additive uncertainties. The new methods are developed by formulating the chance constraints into deterministic form, which are treated in analogy with robust constraints, by using the probabilistic reachable set. The first one is the time-varying tube-based stochastic model predictive control algorithm, which is designed by employing the time-varying probabilistic reachable sets as tubes. The second one is the constant tube-based stochastic model predictive control algorithm, which is developed by enforcing a constant tightened constraint in the entire prediction horizon. In addition, the soft constraints are proposed to associate with the state initialization in the algorithms to enhance the feasibility. The algorithm feasibility and closed-loop stability results are provided. The efficacy of the approaches is demonstrated by means of numerical simulations.

Robust distributed model predictive control of linear systems: Analysis and synthesis

To provide robustness of distributed model predictive control (DMPC), this work proposes a robust DMPC formulation for discrete-time linear systems subject to unknown-but-bounded disturbances. Taking advantage of the structure of certain classes of distributed systems seen in applications with inter-agent coupling, a novel robust DMPC is formulated. The proposed approach is characterised by separable terminal costs and locally robust terminal sets, with the latter sets adaptively estimated in the online optimisation problem. A constraint tightening approach based on a set-membership approach is used to guarantee constraint satisfaction for coupled subsystems in the presence of disturbances. Under this formulation, the closed-loop system is shown to be recursively feasible and input-to-state stable. To aid in the deployment of the proposed robust DMPC, a possible synthesis method and design conditions for practical implementation are presented. Finally, simulation results with a mass–spring–damper system are provided to demonstrate the proposed robust DMPC.

Stochastic model predictive control for linear systems affected by correlated disturbances

In this paper, the problem of stability, recursive feasibility and convergence conditions of stochastic model predictive control for linear discrete-time systems affected by a large class of correlated disturbances is addressed. A stochastic model predictive control that guarantees convergence, average cost bound and chance constraint satisfaction is developed. The results rely on the computation of probabilistic reachable and invariant sets using the notion of correlation bound. This control algorithm results from a tractable deterministic optimal control problem with a cost function that upper-bounds the expected quadratic cost of the predicted state trajectory and control sequence. The proposed methodology only relies on the assumption of the existence of bounds on the mean and the covariance matrices of the disturbance sequence.

Data-driven MPC of descriptor systems: A case study for power networks

Recently, data-driven predictive control of linear systems has received wide-spread research attention. It hinges on the fundamental lemma by Willems et al. In a previous paper, we have shown how this framework can be applied to predictive control of linear time-invariant descriptor systems. In the present paper, we present a case study wherein we apply data-driven predictive control to a discrete-time descriptor model obtained by discretization of the power-swing equations for a nine-bus system. Our results show the efficacy of the proposed control scheme and they underpin the prospect of the data-driven framework for control of descriptor systems.

Constrained stochastic predictive control of linear systems with uncertain communication

Abstract This paper proposes a scheme of model predictive control for single-loop networked control system (NCS) with probabilistically modeled communication channel and disturbances. Uncertainties of the communication network are projected onto a tailored probability for the satisfaction of state and input constraints. The proposed receding horizon control scheme uses a probabilistic terminal state and set to establish a balance between control performance and state probability distribution, while satisfying the given constraints. In addition to describing the control approach, its properties are discussed, and it is illustrated by an example.

A Distributed Active Set Method for Model Predictive Control

Abstract This paper presents a novel distributed active set method for model predictive control of linear systems. The method combines a primal active set strategy with a decentralized conjugate gradient method to solve convex quadratic programs. An advantage of the proposed method compared to existing distributed model predictive algorithms is the primal feasibility of the iterates. Numerical results show that the proposed method can compete with the alternating direction method of multipliers in terms of communication requirements for a chain of masses example.

Distributed model predictive control for linear systems under communication noise: Algorithm, theory and implementation

We study the distributed model predictive control (DMPC) problem for a network of linear discrete-time subsystems in the presence of stochastic noise among communication channels, where the system dynamics are decoupled and the system constraints are coupled. The DMPC is cast as a stochastic distributed consensus optimization problem by modeling the exchanged variables as stochastic ones and a novel noisy alternating direction multiplier method (NADMM) is proposed to solve it in a fully distributed way. We prove that the sequences of the primal and dual variables converge to their optimal values almost surely (a.s.) with communication noise. Furthermore, a new stopping criterion and a DMPC scheme termed as current–previous DMPC (cpDMPC) are proposed, which guarantees deterministic termination even when the NADMM algorithm may not converge in a practical realization. Next, the strict analysis on the feasibility of the cpDMPC strategy and the closed-loop stability is carried out, and it is shown that the cpDMPC strategy is feasible at each time step and the closed-loop system is asymptotically stable. Finally, the effectiveness of the proposed NADMM algorithm is verified via an example.

Adaptive stochastic model predictive control of linear systems using Gaussian process regression

This paper presents a stochastic model predictive control method for linear time-invariant systems subject to state-dependent additive uncertainties modelled by Gaussian process (GP). The new method is developed by re-building the tube-based model predictive control framework with chance constraints via adaptive constraint tightening. In particular, the tightened constraint set is constructed by forecasting the confidence region of uncertainty. Utilising this adaptive strategy, the Gaussian process based stochastic model predictive control (GP-SMPC) algorithm is designed by applying the adaptive tightened constraints in all prediction horizons. To reduce the computation load, the one-step GP-SMPC algorithm is further developed by imposing the tightened constraints only to the first-step nominal state and the worst-case constraints to the remaining steps. Under the assumption that the state-dependent uncertainties are bounded, the recursive feasibility of the designed optimisation problem is ensured, and the closed-loop system stability is guaranteed. The effectiveness and advantage over existing methods are verified via simulation and comparison studies.

A Comparative Study of Stochastic Model Predictive Controllers

A comparative study of two state-of-the-art stochastic model predictive controllers for linear systems with parametric and additive uncertainties is presented. On the one hand, Stochastic Model Predictive Control (SMPC) is based on analytical methods and solves an optimal control problem (OCP) similar to a classic Model Predictive Control (MPC) with constraints. SMPC defines probabilistic constraints on the states, which are transformed into equivalent deterministic ones. On the other hand, Scenario-based Model Predictive Control (SCMPC) solves an OCP for a specified number of random realizations of uncertainties, also called scenarios. In this paper, Classic MPC, SMPC and SCMPC are compared through two numerical examples. Thanks to several Monte-Carlo simulations, performances of classic MPC, SMPC and SCMPC are compared using several criteria, such as number of successful runs, number of times the constraints are violated, integral absolute error and computational cost. Moreover, a Stochastic Model Predictive Control Toolbox was developed by the authors, available on MATLAB Central, in which it is possible to simulate a SMPC or a SCMPC to control multivariable linear systems with additive disturbances. This software was used to carry out part of the simulations of the numerical examples in this article and it can be used for results reproduction.

Predictive Control of Linear Systems with Switched Actuators Subject to Dwell-Time Constraints

This paper is concerned with the control of linear systems with switched actuators subject to lower bounds on dwell times. The problem addressed herein consists of driving the system state to a desired periodic trajectory through suitable perturbations in the switching times. For this purpose, a linearization procedure is derived to describe the relationship between the switching-time perturbations and the resulting state trajectory. This procedure allows the constrained predictive control problem to be cast in the form of a convex quadratic program, which is a key contribution of the present work. Simulation examples with single-input and two-input models are presented for illustration. In all cases, the system state is driven to the desired trajectory with satisfaction of the dwell-time constraints on the switched input signal.

Event‐triggered estimation and model predictive control for linear systems with actuator fault

This study is concerned with the design of an event-triggered fault estimation and fault tolerant model predictive control scheme for linear systems subject to disturbances and actuator faults by using the method of delta operator. First, an observer is established to estimate the state and the fault simultaneously. An H 2 / H ∞ model predictive controller with fault compensation signals is then proposed through solving a constrained optimisation problem. An event-triggered scheme is employed to conserve the network bandwidth. The new design techniques are shown to be effective via simulation results.