Output Feedback Robust Model Predictive Control Research Articles

Sampled-data static output feedback robust MPC for LPV systems with bounded disturbances

This paper investigates a sampled-data static output feedback robust model predictive control (MPC) approach for continuous-time linear parameter varying (LPV) systems with unknown system states and bounded disturbances. Between two successive sampling time instants, it is assumed that the controlled LPV systems evolve in continuous-time, and the control inputs are piecewise constant. The robust stability conditions and control input constraints on the closed-loop system are considered in the formulated robust MPC optimization. The constraints in the formulated robust MPC optimizations are formulated as linear matrix inequalities (LMIs) and solved as convex optimization. The designed sampled-data static output feedback robust MPC optimization has a simple structure and directly optimizes output feedback controller. Furthermore, the system state constraint sets are on-line updated over the sampling interval. The designed sampled-data static output feedback robust MPC approach has the property of recursive feasibility, and can guarantee robust stability of the controlled continuous-time LPV systems. A simulation example is given to illustrate the effectiveness of the approach.

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.

Tube-Based Output Feedback Robust MPC for LPV Systems With Scaled Terminal Constraint Sets.

This article provides a solution to tube-based output feedback robust model predictive control (RMPC) for discrete-time linear parameter varying (LPV) systems with bounded disturbances and noises. The proposed approach synthesizes an offline optimization problem to design a look-up table and an online tube-based output feedback RMPC with tightened constraints and scaled terminal constraint sets. In the offline optimization problem, a sequence of nested robust positively invariant (RPI) sets and robust control invariant (RCI) sets, respectively, for estimation errors and control errors is optimized and stored in the look-up table. In the online optimization problem, real-time control parameters are searched based on the bounds of time-varying estimation error sets. Considering the characteristics of the uncertain scheduling parameter in LPV systems, the online tube-based output feedback RMPC scheme adopts one-step nominal system prediction with scaled terminal constraint sets. The formulated simple and efficient online optimization problem with fewer decision variables and constraints has a lower online computational burden. Recursive feasibility of the optimization problem and robust stability of the controlled LPV system are guaranteed by ensuring that the nominal system converges to the terminal constraint set, and uncertain state trajectories are constrained within robust tubes with the center of the nominal system. A numerical example is given to verify the approach.

Robust MPC for Systems With Model Uncertainties and Measurement Outliers

This paper considers the observer-based output feedback robust model predictive control (RMPC) problem for systems with model uncertainties and possible measurement outliers. For the sake of alleviating the effects from possible abnormal measurements, we design a set of observer-based output feedback RMPC controllers with the saturation constraint where the saturation level is adaptive according to the estimation errors. The purpose of the addressed problem is to design a set of desired RMPC controllers so as to guarantee the robustness and the asymptotical stability of the closed-loop system. Sufficient stability conditions are obtained by solving a time-varying terminal constraint set of an auxiliary optimization problem, and the corresponding control law and the upper bound of the quadratic cost function are derived. In addition, an algorithm including both off-line and on-line parts is provided to find a sub-optimal solution. Finally, two simulation examples are employed to illustrate the effectiveness of the proposed RMPC approach.

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.

Time-Varying Tube-Based Output Feedback Robust MPC for T–S Fuzzy Systems

For Takagi–Sugeno fuzzy systems subject to inexact membership functions, bounded disturbances, and noises, an output feedback robust model predictive control (RMPC) approach with time-varying robust tubes is investigated. The membership functions errors are bounded within convex sets via the properties of zonotopes and interval matrices. An offline table stores a series of structures that include nested robust positive invariant sets with the corresponding nominal feedback controller gains, ancillary controller gains, and observer gains. According to bounds of real-time estimation error sets, the time-varying structures in the offlined table are searched. Then, the output feedback RMPC problem with time-varying tightened constraints on inputs and states is optimized to stabilize the nominal system. The output feedback RMPC approach can not only update bounds of the estimation errors and uncertain terms resulting from inexact membership functions, but also reduce the computational burden. The proposed RMPC algorithm with recursive feasibility guarantees the robust stability of the controlled systems.

Dynamic model predictive control for constrained cyber-physical systems subject to actuator attacks

Modern networked control systems are cyber-physical systems (CPSs), in which the cyber space is tightly integrated with the physical world and human intervention. Forming the basis of future smart services, CPSs are expected to significantly promote our life. However, CPSs also suffer from cyber-attacks due to their increasing connections to the Internet. This paper investigates secure model predictive control (MPC) for constrained CPSs subject to actuator attacks, which intentionally manipulate control commands from a controller to actuators. In our study, the theory of invariant set is used to construct a Luenberger observer for error-bounded state estimation in the presence of actuator attacks. Then, a robust output feedback MPC controller is designed for constrained and attacked systems based on a set-membership state estimator. After that, stability conditions are theoretically established for the proposed MPC controller. A numerical example is also given to demonstrate the effectiveness of the proposed secure MPC approach.

Security Control for LPV System With Deception Attacks via Model Predictive Control: A Dynamic Output Feedback Approach

This article considers security control under the network environment for a system with deception attacks, polytopic uncertainty, and persistent bounded disturbance. Since the state is immeasurable and the physical constraint is considered, the output feedback robust model predictive control (MPC) is utilized. The previous results on the output feedback robust MPC are extended to address the deception attacks. The mean-square quadratic boundedness is defined in order to characterize the closed-loop stability. An optimization problem is proposed, which can be solved by linear matrix inequality techniques. By a simple refreshment of the state estimation error set, the optimization problem is shown to be recursively feasible, and the augmented state converges to the neighborhood of equilibrium point. The effectiveness of the proposed theoretical approach is demonstrated by a numerical simulation example.

A Summary of Dynamic Output Feedback Robust MPC for Linear Polytopic Uncertainty Model with Bounded Disturbance

This paper is the summary and enhancement of the previous studies on dynamic output feedback robust model predictive control (MPC) for the linear parameter varying model (described in a polytope) with additive bounded disturbance. When the state is measurable and there is no bounded disturbance, the robust MPC has been developed with several paradigms and seems becoming mature. For the output feedback case for the LPV model with bounded disturbance, we have published a series of works. Anyway, it lacks a unification of these publications. This paper summarizes the existing results and exposes the ideas in a unified framework. Indeed there is a long way to go for the output feedback case for the LPV model with bounded disturbance. This paper can pave the way for further research on output feedback MPC.

Output feedback robust MPC of uncertain norm-bounded linear systems with disturbance

The output feedback robust model predictive control (MPC) for the linear systems with norm-bounded uncertainty and disturbance is studied. A new state estimator is formulated where both estimator dynamic matrix and estimator gain are decision variables being optimised on-line. The infinite horizon control moves are parameterised as a feedback control law, and the resultant non-convex optimisation problem is solved through a linearisation method. The recursive feasibility and closed-loop stability are guaranteed. The proposed approach can achieve better performance and include previous approaches as special cases. Two numerical examples are given to illustrate the effectiveness of the proposed approach.

A Synthesis Approach to Output Feedback MPC for LPV Model With Bounded Disturbance

The model with polytopic parametric uncertainty and bounded disturbance is controlled by the approach named dynamic OFRMPC (Output Feedback Robust Model Predictive Control). A key knob for control performance and region of attraction for this approach is the selection of Lyapunov matrix. A Lyapunov matrix, which does not have structural restriction, is proposed. In the ICCA (Iterative Cone Complementary Approach), which is invoked in optimizing the control law parameters, the starting up steps are designed as a variant CCA (Cone Complementary Approach). ICCA designs an outer loop, over CCA, for searching the minimum cost bound, while the variant CCA omits the outer loop by adding the cost bound in CCA objective function. This starting up can reduce the computational burden. The suboptimal dynamic OFRMPC (where CCA is avoided) is discussed, and a previous approach is re-formulated. A numerical example is given to show the advantages of the proposed approach.

A Convexity Approach to Dynamic Output Feedback Robust MPC for LPV Systems with Bounded Disturbances

A convexity approach to dynamic output feedback robust model predictive control (OFRMPC) is proposed for linear parameter varying (LPV) systems with bounded disturbances. At each sampling time, the model parameters and disturbances are assumed to be unknown but bounded within pre-specified convex sets. Robust stability conditions on the augmented closed-loop system are derived using the techniques of robust positively invariant (RPI) set and the S-procedure. A convexity method reformulates the non-convex bilinear matrix inequalities (BMIs) problem as a convex optimization one such that the on-line computational burden is significantly reduced. The on-line optimized dynamic output feedback controller parameters steer the augmented states to converge within RPI sets and recursive feasibility of the optimization problem is guaranteed. Furthermore, bounds of the estimation error set are refreshed by updating the shape matrix of the future ellipsoidal estimation error set. The dynamic OFRMPC approach guarantees that the disturbance-free augmented closed-loop system (without consideration of disturbances) converges to the origin. In addition, when the system is subject to bounded disturbances, the augmented closed-loop system converges to a neighborhood of the origin. Two simulation examples are given to verify the effectiveness of the approach.

Dynamic output-feedback RMPC for systems with polytopic uncertainties under Round-Robin protocol

This paper is concerned with the dynamic output-feedback robust model predictive control (RMPC) problem for systems with polytopic uncertainties under the Round-Robin (RR) protocol. In the backward channel, i.e., from the sensors to the controller, several sensors share a communication network to transmit the data to the remote controller, and thus data collision might happen if these sensors start transmissions together. In order to prevent data from collisions, a so-called RR protocol is utilized to orchestrate the data transmission order, where only one node with token is allowed to send data at each transmission instant. The aim of the problem addressed is to design a set of controllers in the framework of dynamic output-feedback RMPC (OFRMPC) so as to guarantee the asymptotical stability of the closed-loop system in terms of the token-dependent Lyapunov-like approach. By taking the influence of the underlying RR protocol into consideration, sufficient conditions with less conservatism are obtained by solving a time-varying terminal constraint set of an auxiliary optimization problem. Furthermore, an algorithm including both off-line and online parts is provided to find a sub-optimal solution. Finally, a numerical simulation result is exploited to illustrate the usefulness and effectiveness of the proposed RMPC strategy.

Output feedback robust MPC using general polyhedral and ellipsoidal true state bounds for LPV model with bounded disturbance

ABSTRACTThis paper considers the dynamic output feedback robust model predictive control (MPC) for a system with both polytopic model parametric uncertainty and bounded disturbance. For this topic, the techniques for handling the unknown true state are crucial, and the strict guarantee of the input/output/state constraints requires replacing the true state by its bounds in the optimisation problems. Previously, in the separate works, we (i) gave the general polyhedral bound; (ii) proposed the general ellipsoidal bound; (iii) applied some special polyhedral bounds to tighten the ellipsoidal bound since the latter is crucial for guaranteeing recursive feasibility. In this paper, (i)–(iii) are unified, and the up-to-date least conservative treatment of the true state bound is given, so the control performance can be greatly improved. The contribution mainly lies in overcoming the difficulties in developing technical details for the unification. A numerical example is given to illustrate the effectiveness of the new method.

Effective Recursive Set-membership State Estimation for Robust Linear MPC

Abstract In this paper the problem of robust output-feedback Model Predictive Control (MPC) is considered. Uncertainty in the state estimates obtained from noisy measurements is bounded using set-membership techniques as we consider the noise to be bounded. Robustness of the MPC controller is achieved in a min-max sense. We use parallelotopic bounding for the state estimates. We propose enhancements to a well-known Recursive Optimal Parallelotopic Outbounding (ROPO) algorithm such that the resulting closed-loop cost is improved. All methodologies are tested using a simple linear case study. The results obtained show the benefits of the developed methods.

Robust Output Feedback Model Predictive Control for Systems With Norm-Bounded Uncertainty: An LMI Approach

This paper investigates the robust output feedback model predictive control (ROFMPC) for the discrete-time linear system with norm-bound uncertainty and disturbance. An LMI approach is proposed in this paper, and its computational burden is much less than the approach of previous work. Besides, in previous work, the estimation error set is updated online at each sampling time by the set-membership state estimation algorithm, which may lose recursive feasibility. This paper overcomes the drawback by imposing a new updating condition. The closed-loop system is asymptotically stable by the recursive feasibility of the optimization problem. A numerical example demonstrates the advantage of the proposed approach.

A Multi-step Output Feedback Robust MPC Approach for LPV Systems with Bounded Parameter Changes and Disturbance

This paper considers a multi-step output feedback robust model predictive control (OFRMPC) approach for the linear parameter varying (LPV) systems with bounded changes of scheduling parameters and bounded disturbance. Less conservative bounds of future estimation error sets and system parametric uncertain sets are predicted by considering bounded changes of scheduling parameters in LPV systems. In the multi-step OFRMPC approach, an optimization problem is solved to obtain a sequence of controller gains, which considers predictions of future bounds of estimation error sets and system parametric uncertain sets. The optimized sequence of controller gains corresponding to a sequence of Lyaponov matrices have less constraint conditions and also introduce more degree of freedom for the optimization. The proposed multi-step OFRMPC guarantees robust uniform ultimately bounded of the estimation error and robust stability of the observer system. A numerical example is given to demonstrate the effectiveness of the approach.

Tube-based robust output feedback MPC for constrained LTV systems with applications in chemical processes

Robust output feedback model predictive control (MPC) of linear time-varying (LTV) systems subject to bounded state and output disturbances is considered in this paper. The output feedback controller is designed in such a way that the observer is time-varying so the unknown state and the observer state are bounded by the tubes whose center is the state of the nominal LTV system that is steered to the origin. The on-line computational complexity is similar to that required for nominal MPC for LTV systems. Robust stability is ensured by using the notion of Lyapunov functions. The controller design is illustrated via two examples in chemical processes. The results show that the proposed output feedback controller can guarantee robust stability and constraint satisfaction of the LTV systems in the presence of bounded state and output disturbances.

Effective recursive parallelotopic bounding for robust output-feedback control

In this paper an approach is studied to guaranteed (set-membership) state estimation for robust output-feedback model predictive control (MPC) with hard input and state constraints. Uncertainties are assumed to arise in a dynamic system from unknown initial conditions of state variables and due to unknown-but-bounded measurement noise. The uncertainty in the state variables is represented as a parallelotopic set. The employed state-estimation algorithm recursively outbounds the feasible set that is given by an intersection of model predictions with obtained measurement information. Along with the well-known minimum-volume criterion for parallelotopic outbounding, three alternative criteria are proposed and studied. The aim is to identify the best outbounding approach for improving performance of the robust MPC.

Synchronization for chaotic systems via mixed-objective dynamic output feedback robust model predictive control

This paper focuses on mixed-objective dynamic output feedback robust model predictive control (OFRMPC) for the synchronization of two identical discrete-time chaotic systems with polytopic uncertainties, energy bounded disturbances, and input constraint. Using active control strategy, the chaos synchronization is transformed into standard dynamic OFRMPC scenarios tractable through receding horizon min–max optimization. Utilizing the notion of quadratic boundedness, the augmented closed-loop stability is further characterized. Then, the concepts of mixed performance criteria are firstly incorporated into the dynamic OFRMPC scheme to guarantee both the robust stability and the disturbance attenuation ability while preserving better dynamical behaviors. Necessary and/or sufficient conditions for desired mixed-objective dynamic OFRMPC are formulated involving linear matrix inequalities (LMIs). Finally, two numerical examples are given to demonstrate the theoretical results.