Output Feedback Model Predictive Control Research Articles

Networked Output-Feedback MPC: A Bounded Dynamic Variable and Time-Varying Threshold-Dependent Event-Based Approach.

The event-triggered model predictive control (MPC) problem is addressed for polytopic uncertain systems. A new dynamic event-triggered mechanism (DETM) with a bounded dynamic variable and a time-varying threshold is proposed to manage measurement data packet releases. The dynamic output-feedback MPC issue is detailed as a "min-max" optimization problem (OP) with an objective function over an infinite horizon, where the hard constraint on the predictive control is required. By applying a Lyapunov-like function containing the bounded dynamic variable, an auxiliary OP constrained by several matrix inequalities is proposed, and the design methods of the output-feedback gains are provided if this auxiliary OP is feasible. The designed MPC controller ensures that the closed-loop system is input-to-state practically stable. Two examples including an event-triggered DC motor are given to illustrate the validity of the developed MPC algorithm. Simulation results verify that the proposed DETM has advantages over some existing triggering mechanisms in decreasing the consumption of resources while meeting the required performance.

Output Feedback MPC for Nonlinear System in Large Operation Range

This paper studies the output feedback model predictive control (MPC) being suitable to a large operation range of the constrained system represented by a nonlinear model with a bounded disturbance. The model is further parameterized as a multiple linear parameter varying (LPV) state-space equation, each LPV representation being valid around an exclusive equilibrium. Off-line, for each equilibrium, a set of local control laws (in the dynamic output feedback), each having its region of attraction, are calculated. All the control laws for all the equilibriums constitute a lookup table, and all the corresponding regions of attraction take a union. On-line, the real-time control law is searched as one, as per its region of attraction, in the lookup table when the estimated system state moves inside of the union. Once the initial estimation error lies in a pre-specified set, the augmented state is guaranteed to converge to the neighborhood of the target equilibrium, and the constraints on input and output are consistently satisfied. An example is given to illustrate the effectiveness of the proposed algorithm.

Self-triggered robust output feedback model predictive control of discrete-time linear systems

In networked control systems, the communication load is a main concern for implementing model predictive control (MPC). This paper introduces a self-triggered MPC algorithm under network environments to reduce communication load, for discrete-time linear systems with bounded state and output disturbances, when only the system output can be measured at triggering instants. The proposed algorithm mainly based on a state estimator whose estimation error is bounded by an invariant set, and on the self-triggered model predictive control of a nominal system. Moreover, the new cost function explicitly adopts communication load is in consideration. The proposed algorithm is proved to drive the system to an invariant set with respect to the bounded disturbances. Finally, simulation results is provided to verify the effectiveness of the proposed robust output feedback MPC algorithm.

Adaptive event‐triggered efficient output feedback model predictive control for networked interval type‐2 T–S fuzzy system with data loss

AbstractThis article is concerned with the adaptive event‐triggered (AET) efficient output feedback model predictive control (EOFMPC) for a set of nonlinear networked interval type‐2 Takagi–Sugeno (IT2 T–S) fuzzy control systems with data loss. For the reduction in data transmission burden and required control performance, the AET scheme and a novel dynamic triggering law are introduced jointly in this article. The efficient model predictive control approach as in Kouvaritakis et al. (IEEE Trans Automat Contr. 2000;45(8):1545–1549.), which transfers the main part of online optimization work to offline stage by incorporating an extra perturbation into the fixed feedback law, is extended to networked control systems to reduce their online computational burden. This article proposes the following: (1) an unified closed‐loop model representation of data loss process and IT2 T–S fuzzy nonlinearities is established under the framework of EOFMPC, which explicitly considers the AET condition; (2) a new design method for the state observer gain is presented based on an ellipsoidal invariant set, so that a smaller bound of estimation error can be obtained through an extra optimization problem; (3) some optimization problems are formulated to design the proposed controllers, and the corresponding EOFMPC algorithm is summarized; (4) by means of the extra matrix partition technique, the online optimization problem subject to one ellipsoidal constraint is transformed into a novel convex form to solve the uncertainty of the estimation error. A simulation example and a few comparative simulation experiments illustrate the effectiveness and availability of the aforementioned approach.

Adaptive Event-Triggered Model Predictive Load Frequency Control for Power Systems

This paper investigates the adaptive event-triggered (AET) output feedback model predictive control (MPC) method for the load frequency control (LFC) problem of hybrid power system involving the thermal power and the photovoltaic power. First, an AET communication mechanism, which possesses the ability to dynamically adjust the trigger threshold parameter according to an adaptive law, is addressed to reducing the communication overhead, while keeping the required control performance; Second, the output feedback model predictive controller which is composed of an off-line designed state observer and an on-line solved optimization problem, is proposed using the techniques of quadratic boundedness and S-procedure. The state observer gain is obtained by off-line maximizing the trace of a matrix which is closely related to minimal positively invariant set; While the output feedback MPC strategy is acquired by expressing the infinite horizon control moves as a free control move and a linear feedback law based on the estimated state; Third, the recursive feasibility of the on-line optimization problem and the stability of the closed-loop system are analyzed by the fact that the estimated state and estimation error will converge to the presented minimal positively invariant set. Finally, MATLAB and its linear matrix inequality (LMI) toolbox are used to solve the optimization problem, and the LFC system with load disturbance is simulated and analyzed. The simulation results show that the proposed method is feasible and effective.

Dynamic output-feedback model predictive control for polytopic uncertain systems with amplify-and-forward relays

In this paper, the dynamic output-feedback model predictive control (MPC) problem is investigated for systems with polytopic uncertainties and amplify-and-forward (AF) relays, where the signal transmission with random power is adopted to facilitate the remote transmission with the limited transmission capacity of sensors. With respect to the parameter uncertainties of the system and the randomness of AF relays, a new objective function is constructed, which is defined by the mathematical expectation of the conventional quadratic function over the infinite time horizon. Then, the singular value decomposition technique is applied to handle the inherent couplings of variables to formulate a solvable optimization problem. Furthermore, sufficient conditions are provided to guarantee the recursive feasibility of the proposed MPC algorithm, meanwhile the underlying system can be stabilized in the mean-square sense by the designed controllers. Finally, two simulation examples are used to show the effectiveness of the proposed MPC strategy.

Adaptive event‐triggering mechanism‐based N‐step predictive load frequency control for power systems with cyber attack

AbstractAlthough there have already been many works on the model predictive control (MPC) for load frequency control (LFC) of modern power systems, limited works can be found in the literature related to the output feedback MPC. This article studies an N‐step synthesis approach of output feedback MPC for LFC systems considering the problems of communication efficiency and network security. First, to improve the communication efficiency, an adaptive event‐triggering (AET) scheme involving two adaptive laws is designed to reduce the number of transmitted data packages which offers more flexible compared with existing event‐triggering schemes; Second, to handle the network security, a new model of LFC power system combining the AET scheme and random deception attack under an unified framework is established; Moreover, a synthesis approach of output feedback MPC with N‐step strategy is addressed for LFC of power system by parameterizing the infinite control moves into a series of output feedback laws. Compared with the existing predictive load frequency control methods, the present technique is shown as an useful way to improve the control performance since more degrees freedom is introduced by the N‐step strategy. Finally, the simulation experiment is carried out to verify our technique.

Event-triggered robust distributed output feedback model predictive control for nonlinear MASs against false data injection attacks

In this paper, an event-triggered distributed output feedback model predictive control scheme for the nonlinear disturbed multiagent systems with sensor–controller channel false data injection attacks is proposed. To provide valid system states to the controller in the event of cyber attacks, a robust multivariate observer is designed to realize the estimation and separation of uncompromised system states, false data injection attacks, and measurement disturbances, simultaneously. Based on these reconstructed signals and a newly-designed linear robustness constraint, the distributed predictive controller is established to achieve smooth cooperative stabilization among agents. Meanwhile, an event-triggered mechanism is applied to save computing resources, and it restricts the error of predictive states and estimated states to guarantee the feasibility of the optimization control problem. Theoretical analyses on robustness and security for the nonlinear multiagent systems under event-triggered distributed output feedback model predictive control are presented. Finally, a simulation on two pairs of one-link flexible joint manipulator systems verifies the theoretical results.

Codesign of Quantized Dynamic Output Feedback MPC for the Takagi–Sugeno Model

We present a co-design of measurement quantized dynamic output feedback model predictive control (DOFMPC) for Takagi-Sugeno model with bounded disturbance. The system output is quantized by a dynamic quantizer before it is transmitted to the DOFMPC controller. Hence, we utilize the dynamic output feedback control law with quantized output signal and consider the mixed input and quantized output constraint for the controller design. By optimizing the quantizer and controller paramters on-line, the control performance is enhanced. Moreover, we formulate a 2-leveled optimizations, with the upper level optimizing the performance index and the lower level optimizing the soft constraint in a lexicographic order, for the co-design of the DOFMPC controller and dynamic quantizer. Thus, there are more degrees of freedom for tighting the soft constraints. The recursive feasibility and stability of the proposed approaches are guaranteed. The applicability of the proposed approach is illustrated by a simulation example.

Learning-Enabled Output-Feedback-MPC-Based Synchronization Tracking Control of Multiaxis Motion Systems

The unknown and time-varying model parameters and measurement noises impose great influence on the highprecision synchronization tracking control performance of multiaxis motion systems (MAMSs). To deal with the influence of the factors on the high-precision synchronization tracking control performance in MAMSs, a learning-enabled output feedback model predictive control (MPC) strategy for MAMSs is proposed. Firstly, an efficient learning mechanism is introduced to capture the unknown and slow time-varying behavior of the system parameters. Then, considering both the existence of the measurement noises and the unavailability of the velocity signals in system and synchronization coupling errors, the learning-enabled output feedback MPC based synchronization tracking controller is designed to achieve the high-precision synchronization tracking control of the MAMSs. The stability of overall synchronization tracking system with proposed learning procedure is analyzed. Finally, simulations and experiments are performed on fourmotor motion system to demonstrate the practicability and effectiveness of the proposed control strategy.

Security-based dynamic output-feedback model predictive control for nonlinear systems in T-S fuzzy form subject to deception attacks

This paper is concerned with the security-based fuzzy model predictive control (FMPC) problem for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems with deception attacks on the measured outputs. With respect to the unmeasurable system states, the nonlinearity of the system and the destructiveness of deception attacks, the dynamic output-feedback control in the framework of FMPC is adopted, meanwhile, the worst-case optimization problem over the infinite moving horizon is formulated for the performance analysis and control synthesis. By means of the quadratic function approach and the singular value decomposition technique, the non-convexity caused by couplings between decisive variables is coped with and conditions are derived to suffice the terminal constraint set. In addition, to mitigate the destruction of attacks to the recursive feasibility, the inequality analysis technique is applied with the aid of the introduction of special scalars. Based on the establishments, a certain auxiliary optimization problem with solvability is put forward to find the desired controllers, and sufficient conditions are obtained to guarantee that the underlying system subject to deception attacks under the proposed FMPC-based controllers is mean square secure in H2-sense. Finally, an illustrative example is used to demonstrate the validity of the proposed methods.

Constrained linear output regulation via measurement output feedback model predictive control

Recently, the output regulation problem with input constraints for incrementally stable plants was solved by an error feedback model predictive control (MPC) algorithm. This paper further considers the case with both state and input constraints for linear systems and uses a measurement output feedback MPC algorithm to solve the problem. By relaxing two restrictions, the result of this paper can handle a larger class of linear systems than the existing result. Due to the uncontrollability of the augmented system composed of the plant and the exosystem, a key assumption in the literature fails, we manage to overcome this difficulty by introducing novel tightened constraints and the terminal constraint. As a result, the proposed algorithm solves the linear output regulation problem in the presence of both state and input constraints. The effectiveness of our design is illustrated by a numerical example.

Finite‐frequency output feedback MPC for Markov jump systems

AbstractThis 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.

Event‐triggered output feedback predictive control for Takagi‐Sugeno model with bounded disturbance and redundant channels

AbstractIn this paper, the problem of dynamic output feedback model predictive control (MPC) for the Takagi‐Sugeno (T‐S) model with bounded disturbance and redundant channels is investigated based on an event‐triggered scheme. The redundant channels, described by a set of mutually independent Bernoulli processes, are applied to improve the reliability of data transmission. The state immeasurable is considered, and an event‐triggered state estimator with a time‐varying threshold is designed to estimate the true system state. The estimator and controller gains are parameterized as a non‐convex optimization problem. In order to online solve the resulting optimization problem, the cone complementarity approach (CCA) with iteration optimization is adopted. The mean‐square quadratic boundedness (MSQB) is utilized to characterize the invariance of the system state and guarantee the closed‐loop stability, while the recursive feasibility is ensured via online refreshing the estimation error set. Finally, a numerical simulation example is presented to illustrate the effectiveness of the proposed theoretical method.

Adaptive Output Feedback Model Predictive Control

Model predictive control (MPC) for uncertain systems in the presence of hard constraints on state and input is a non-trivial problem, and the challenge is increased manyfold in the absence of state measurements. In this paper, we propose an adaptive output feedback MPC technique, based on a novel combination of an adaptive observer and robust MPC, for single-input single-output discrete-time linear time-invariant systems. At each time instant, the adaptive observer provides estimates of the states and the system parameters that are then leveraged in the MPC optimization routine while robustly accounting for the estimation errors. The solution to the optimization problem results in a homothetic tube where the state estimate trajectory lies. The true state evolves inside a larger outer tube obtained by augmenting a set, invariant to the state estimation error, around the homothetic tube sections. The proof for recursive feasibility for the proposed `homothetic and invariant' two-tube approach is provided, along with simulation results on an academic system.

Robust Output Feedback MPC for LPV Systems Using Interval Observers

This article addresses the problem of robust output feedback model predictive control for discrete-time, constrained, linear parameter-varying systems subject to (bounded) state and measurement disturbances. The vector of scheduling parameters is assumed to be an unmeasurable signal taking values in a given compact set. The proposed controller incorporates an interval observer, that uses the available measurement to update the set-membership estimation of the states, and an interval predictor, used in the prediction step of the model predictive control (MPC) algorithm. The resulting MPC scheme offers guarantees on recursive feasibility, constraint satisfaction, and input-to-state stability in the terminal set. Furthermore, this novel algorithm shows low computation complexity and ease of implementation (similar to conventional MPC schemes).

Output Feedback Model Predictive Control for NCSs with Input Quantization

This paper addresses the robust output feedback model predictive control (MPC) schemes for networked control systems (NCSs) with input quantization. The logarithmic quantizer is considered in this paper, and the sector bound approach is applied, which appropriately treats the quantization error as a sector-bounded uncertainty. The presented method involves an offline designed state observer using linear matrix inequality (LMI) and online robust output feedback MPC algorithms which optimize one free control move followed by the output feedback using the estimated state. Moreover, due to the uncertainty of estimation error, a technique of refreshing the bound of estimation error which involves the quantization error is provided so as to guarantee the recursive feasibility of the optimization problem. The proposed MPC schemes inherit the characteristics of the synthesis approach of MPC, guaranteeing the recursive feasibility of the optimization problem and the stability of a closed-loop system, and explicitly account for quantization error. Two simulation examples are given to illustrate the effectiveness of the proposed methods.

Output feedback model predictive control for Hammerstein model with bounded disturbance

This paper proposes two model predictive control (MPC) methods for a Hammerstein model with both unmeasurable state and bounded disturbance. First, a dynamic output feedback MPC is designed such that the dynamics of the state estimation error is decoupled from that of the estimated state. Hence, the separation principle holds and a part of the controller parameters can be designed off-line. Second, a case is considered where Hammerstein nonlinearity is not exactly inverted, that is, a reserved static nonlinearity exists in the closed-loop system. This reserved nonlinearity is merged into a polytopic description in combination with the linear dynamic part. The control move is then parameterized as a feedback law followed by the approximate inverse of Hammerstein nonlinearity. The recursive feasibility and closed-loop stability of both approaches are guaranteed. Numerical examples are given in order to show effectiveness of the proposed approaches.

Output feedback model predictive control of spacecrafts based on proportional-integral observer

A novel attitude control algorithm is developed for spacecrafts based on the model predictive control and proportional-integral observer (PIO) in the presence of constraints. The high dimensional nonlinear dynamics are firstly transformed into three single-input single-output linear structural subsystems with coupled actions. Then these actions are viewed as disturbances estimated by the PIOs, and their values are embedded into the models to improve the accuracy of prediction. The predictive controller is composed of the analytical solution and the heuristic constraint handling. In addition, the angular position information is only needed for implementation. Finally, several simulations are used to verify the effectiveness of the developed algorithm. The results show that the designed system compensates the coupled actions well and makes the attitude control performance good.

Stagewise Newton Method for Dynamic Game Control With Imperfect State Observation

In this letter, we study dynamic game optimal control with imperfect state observations and introduce an iterative method to find a local Nash equilibrium. The algorithm consists of an iterative procedure combining a backward recursion similar to minimax differential dynamic programming and a forward recursion resembling a risksensitive Kalman smoother. A coupling equation renders the resulting control dependent on the estimation. In the end, the algorithm is equivalent to a Newton step but has linear complexity in the time horizon length. Furthermore, a merit function and a line search procedure are introduced to guarantee convergence of the iterative scheme. The resulting controller reasons about uncertainty by planning for the worst case disturbances. Lastly, the low computational cost of the proposed algorithm makes it a promising method to do output-feedback model predictive control on complex systems at high frequency. Numerical simulations on realistic robotic problems illustrate the risk-sensitive behavior of the resulting controller.