Self-triggered Model Predictive Control Research Articles

Self-triggered MPC with adaptive prediction horizon for nano-satellite attitude control system

Nano-satellites are essential tools for various applications, including scientific experiments, deep space exploration and astronomical observation. Achieving precise model predictions is crucial for their successful operation. To address the intricate constraints of nano-satellites and enhance control performance, the Model Predictive Control (MPC) algorithm is an effective solution. However, implementing an MPC-based attitude control system in actual engineering scenarios presents significant challenges, primarily due to the substantial computational burden, especially given the limited onboard computing resources of nano-satellites. In this paper, we introduce a modified adaptive self-triggered model predictive control (ST-MPC) algorithm designed to stabilize the attitude of nano-satellites, while simultaneously reducing communication and computational overhead compared to traditional MPC methods. The proposed self-triggered mechanism dynamically determines the next trigger time according to the system state. Moreover, we incorporate considerations for the efficiency of actuators to address the constraints imposed by the magnetic torque characteristics within the modified self-triggered mechanism. Additionally, a strategy for adaptive prediction horizon is proposed to balance computation load and control accuracy. The results of our simulations demonstrate the effectiveness of the modified ST-MPC algorithm in comparison to both traditional MPC and standard ST-MPC approaches. This algorithm may have the potential to significantly impact attitude control applications for nano-satellites.

Resilient Self-Triggered Model Predictive Control of Cyber-Physical Systems Under Two-Channel False Data Injection Attacks

Abstract This paper presents a novel resilient self-triggered model predictive control (ST-MPC) method to alleviate potential threats of false data injection (FDI) attacks on cyber-physical systems (CPSs). First, considering that the data transmitted via the sensor-to-controller (S–C) and controller-to-actuator (C–A) channels in CPS may be tampered with by FDI attacks, a novel input reconstruction strategy combined with the ST-MPC mechanism is proposed to alleviate the threats of FDI attacks while reducing the computational and communication resources, in which key optimal control signals are selected and protected based on systematic performance inequalities. Correspondingly, a resilient ST-MPC algorithm combined with the dual-mode strategy is further proposed. Moreover, the iterative feasibility and the closed-loop stability are strictly demonstrated. Finally, the effectiveness of the proposed strategy is verified via a simulation study.

Adaptive Transmission Interval-Based Self-Triggered Model Predictive Control for Autonomous Underwater Vehicles with Additional Disturbances

Most existing model predictive control (MPC) methods overlook the network resource limitations of autonomous underwater vehicles (AUVs), limiting their applicability in real systems. This article addresses this gap by introducing an adaptive transmission, interval-based, and self-triggered model predictive control for AUVs operating under ocean disturbances. This approach enhances system stability while reducing resource consumption by optimizing MPC update frequencies and communication resource usage. Firstly, the method evaluates the discrepancy between system states at sampling instants and their optimal predictions. This significantly reduces the conservatism in the state-tracking errors caused by ocean disturbances compared to traditional approaches. Secondly, a self-triggering mechanism was employed, limiting information exchange to specified triggering instants to conserve communication resources more effectively. Lastly, by designing a robust terminal region and optimizing parameters, the recursive feasibility of the optimization problem is ensured, thereby maintaining the stability of the closed-loop system. The simulation results illustrate the efficacy of the controller.

Resilient Self-Triggered Model Predictive Control of Discrete-Time Nonlinear Cyberphysical Systems Against False Data Injection Attacks

Resilient Self-Triggered Model Predictive Control of Discrete-Time Nonlinear Cyberphysical Systems Against False Data Injection Attacks

A Differential Error Based Self-Triggered MPC With Adaptive Prediction Horizon For Discrete Systems

Abstract For discrete time nonlinear networked control systems, a novel self-triggered adaptive model predictive control (MPC) strategy is developed. Different from the existing self-triggered MPC methods that determine the triggering instants based on the difference between the optimal and real states at one single instant, the proposed approach updates the MPC system according to the differential form of the state error of two consecutive sampling moments to effectively reduce the computation and communication burden while maintaining the ideal control performance. In addition, this paper introduces a new adaptive prediction horizon mechanism to the self-triggered MPC, so that the amplitude of prediction horizon contraction is sufficiently large to further reduce the computational burden of the MPC method. Finally, the recursive feasibility and robust stability of this proposed strategy are proved strictly by theoretical analysis, and the simulation comparison results are shown to verify the proposed framework.

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.

Self-triggered Control with Energy Harvesting Sensor Nodes

Distributed embedded systems are pervasive components jointly operating in a wide range of applications. Moving toward energy harvesting powered systems enables their long-term, sustainable, scalable, and maintenance-free operation. When these systems are used as components of an automatic control system to sense a control plant, energy availability limits when and how often sensed data are obtainable and therefore when and how often control updates can be performed. The time-varying and non-deterministic availability of harvested energy and the necessity to plan the energy usage of the energy harvesting sensor nodes ahead of time, on the one hand, have to be balanced with the dynamically changing and complex demand for control updates from the automatic control plant and thus energy usage, on the other hand. We propose a hierarchical approach with which the resources of the energy harvesting sensor nodes are managed on a long time horizon and on a faster timescale, self-triggered model predictive control controls the plant. The controller of the harvesting-based nodes’ resources schedules the future energy usage ahead of time and the self-triggered model predictive control incorporates these time-varying energy constraints. For this novel combination of energy harvesting and automatic control systems, we derive provable properties in terms of correctness, feasibility, and performance. We evaluate the approach on a double integrator and demonstrate its usability and performance in a room temperature and air quality control case study.

Self-Triggered Model Predictive Control With Sample-and-Hold Fashion for Constrained Continuous-Time Linear Systems

Abstract A novel self-triggered model predictive control (STMPC) strategy for linear constrained systems with additive disturbance is presented in this paper. The actuator adopts the control input from the controller by sample-and-hold fashion. At the same time, the triggering threshold is designed to ensure the feasibility of the algorithms and the stability of the closed-loop system. Furthermore, two different ways to generate the event triggered input signal, namely, using single sample and multiple samples, are proposed and it is shown that better triggering performance can be obtained as the number of samples increases. In the last, the effectiveness and applicability of the proposed methods are verified by simulation.

Finite-time control of discrete-time semi-Markov jump linear systems: A self-triggered MPC approach

In this paper, a self-triggered model predictive control (MPC) strategy is developed for discrete-time semi-Markov jump linear systems to achieve a desired finite-time performance. To obtain the multi-step predictive states when system mode jumping is subject to the semi-Markov chain, the concept of multi-step semi-Markov kernel is addressed. Meanwhile, a self-triggered scheme is formulated to predict sampling instants automatically and to reduce the computational burden of the on-line solving of MPC. Furthermore, the co-design of the self-triggered scheme and the MPC approach is adjusted to design the control input when keeping the state trajectories within a pre-specified bound over a given time interval. Finally, a numerical example and a population ecological system are introduced to evaluate the effectiveness of the proposed control.

Self-triggered adaptive model predictive control of constrained nonlinear systems: A min–max approach

In this paper, a self-triggered adaptive model predictive control (MPC) method is proposed for constrained discrete-time nonlinear systems subject to parametric uncertainties and additive disturbances. Firstly, a real-time zonotope-based set-membership parameter estimator is developed to refine a set-valued description of the time-varying parametric uncertainty based on the available measurements. By approximating the reachable sets for the states between two successive triggering time instants, the proposed estimator can be used for dynamic systems sampled in an aperiodic manner, including the self-triggered scheduling. We leverage this estimation scheme to design a novel self-triggered adaptive MPC (ST-AMPC) approach for uncertain nonlinear systems. Compared with the existing self-triggered robust MPC methods, the proposed ST-AMPC method can further reduce the average sampling frequency while preserving comparable closed-loop performance. We theoretically show that, under some reasonable assumptions, the proposed ST-AMPC algorithm is recursively feasible, and the closed-loop system is input-to-state practical stable (ISpS) at triggering time instants. Numerical experiments and comparisons are conducted to demonstrate the efficacy of the proposed method.

A self-triggered stochastic model predictive control for uncertain networked control system

This paper is concerned with the stochastic model predictive control problem (SMPC) for a class of networked control systems with exogenous disturbances and restrictions on communication frequency. A self-triggered SMPC algorithm with an improved triggering condition is designed which integrates the co-design of both the current control inputs and the maximum sampling interval, with the aim of reducing the amounts of communication transmission while guaranteeing the specific performance. To give consideration to both probabilistic guarantee and computability, chance constraints on both states and inputs are transformed into deterministic ones by leveraging Cantelli's inequality and linearisation techniques, so as to be solvable for the optimisation problem. Meanwhile, the nonconvex terms in dynamics of covariance propagation are averted through introducing the covariance upper bound control approach. The formulated online optimisation problem is convex to all decision variables. The theoretical analysis on recursive feasibility and closed-loop stability is addressed for the proposed self-triggered SMPC scheme. Finally, the efficacy and achievable performance of the proposed algorithm are showcased through numerical simulations.

Dual Self-Triggered Model-Predictive Control for Nonlinear Cyber-Physical Systems

This article is concerned with the event-based model-predictive control (MPC) problem of nonlinear cyber-physical systems with control constraints. A novel dual self-triggered MPC strategy is proposed to significantly reduce communication loads. In particular, two triggering mechanisms with two different optimal control problems are appropriately designed by considering whether the system state belongs to the terminal set. We prove that the strategy guarantees the algorithm feasibility and the closed-loop stability if the controller parameters satisfy the proposed conditions. Simulation and comparison studies verify effectiveness and advantages over the existing results.

Wide-area damping power system control based on robust self-triggered model predictive control

Unavoidable random disturbances during the operation of large-scale interconnected power systems may undermine their stability. To prevent this problem, we propose a damping control method based on robust self-triggered model predictive control. First, we linearize the power system model and determine the controller installation location and feedback signal through geometric measurements. Subsequently, the model order is reduced by applying Schur method for balanced truncation. According to the assumed distribution and boundary range of random disturbance, the multi-cell robust predictive control minimax optimization problem described by the vertex is established. By deriving the upper bound of the maximum problem, the minimax problem is transformed into minimizing the upper bound problem to deal with the uncertain problem, which is transformed into linear matrix inequality for controller design. Finally, we introduce a self-triggered control strategy that avoids solving a constrained optimization problem at every time step. This strategy reduces the number of controller responses and resource requirements for sampling and communication, thereby improving computational efficiency. Selecting the two zone four-machine system as the test system, the simulation results demonstrate that the proposed control strategy can effectively eliminate the effect of random disturbances on the stable operation of power systems, improve the damping characteristics of power systems, and suppress low-frequency oscillations.

Resilient predictive control strategy of cyber–physical systems against FDI attack

Self-triggered control strategy has been widely applied in cyber–physical systems, which are unavoidable to suffer various malicious cyber-attacks. This paper is aimed at solving the cyber security problem of self-triggered model predictive control in cyber–physical systems under false data injection attack, and a resilient control strategy is proposed based on control signal reconstruction. Firstly, the continuous control signal is discretely sampled at the controller side, and the key data samples are determined and protected. Then, the discretised control samples are transmitted through the network channel, based on which the control signal is reconstructed at the controlled system side according to a preset mode. It is further theoretically proved that the control signals reconstructed from the critical control samples can guarantee the feasibility and stability of the control system against the FDI attacks. Finally, a simulation verification on a robot system is conducted to verify the effectiveness of the proposed algorithm.

Finite-frequency self-triggered model predictive control for Markov jump systems subject to actuator saturation

In this paper, a self-triggered saturated model predictive control (SMPC) for Markov jump system (MJS) is studied in finite-frequency domain. First, the MJS with multi-modes is transformed into a single mode system with embedded transition probability to prepare for the use of generalized Kalman–Yakubovich–Popov (GKYP) lemma. Second, a dynamic self-triggered mechanism with time-varying threshold is developed to predict the next triggering time according to the current time, states, and jumping mode. Third, for disturbances that only possess finite-frequency band, a co-design of triggering condition and SMPC is realized by properly employing GKYP lemma. Compared with existing works, the main motivation of this paper is to improve the anti-interference ability within a specified frequency range. Moreover, we also aim to shorten the gap between the finite band control theory and its applications to practical engineering problems. Finally, the effectiveness of the proposed approach is demonstrated by both the numerical and practical simulations.

Toward Optimal False Data Injection Attack against Self‐Triggered Model Predictive Controllers

AbstractThis paper is aimed at exploring the optimal false data injection (FDI) attack against continuous time self‐triggered model predictive control (STMPC) systems with sample‐and‐hold input signals to address the potential security defects. First, the mathematical model of FDI attack against the considered STMPC system is established. Then, the difference between the states of the nominal system and the attacked system is explicitly calculated such that the impact of FDI attacks on the STMPC systems can be quantitatively analyzed. And finally, an efficient and effective algorithm to realize the desired FDI attack is proposed, and in order to maintain the flexibility of the attacker, the designed FDI attack algorithm is developed under different attacking scenarios, including attacking a single control node at each sampling time and attacking multiple control nodes each time. Finally, two simulation experiments are carried out based on a robot system and a cart–damper–spring system to verify the efficacy and optimality of the designed FDI attack strategy.

Self-Triggered Model Predictive Control of AC Microgrids with Physical and Communication State Constraints

In this paper, we investigate the secondary control problems of AC microgrids with physical states (i.e., voltage, frequency and power, etc.) constrained in the process of actual control, namely, under the condition of state constraint. On the basis of the primary control (i.e., droop control), the control signals generated by distributed secondary control algorithm are used to solve the problems of voltage and frequency recovery and power allocation for each distributed generators (DGs). Therefore, the model predictive control (MPC) with the mechanism of rolling optimization is adopted in the second control layer to achieve the above control objectives and solve the physical state constraint problem at the same time. Meanwhile, in order to reduce the communication cost, we designed the self-triggered control based on the prediction mechanism of MPC. In addition, the proposed algorithm of self-triggered MPC does not need sampling and detection at any time, thus avoiding the design of observer and reducing the control complexity. In addition, the Zeno behavior is excluded through detailed analysis. Furthermore, the stability of the algorithm is verified by theoretical derivation of Lyapunov. Finally, the effectiveness of the algorithm is proved by simulation.

Scheduling Delays and Curtailment for Household Appliances With Deterministic Load Profiles Using MPC

Smart home appliances can time-shift and curtail their power demand to assist demand side management or allow operation with limited power, as in an off-grid application. This paper proposes a scheduling process to start appliances with time-varying deterministic load profiles. Self-triggered model predictive control is used to limit the household net power demand below a given threshold. Meanwhile, deterministic load profiles are more difficult to schedule compared to variable charging or thermal loads because system failure will occur once power demand is not satisfied. The proposed scheme formulates the decision of the load shifting time as a continuous optimization problem, and an inhomogeneous time grid system is introduced to handle the optimization of different appliances and their consensus at this resolution. The efficacy of the proposed scheme is studied by numerical comparison with a mixed-integer MPC controller and by a case study of three home appliances and an interruptible washing machine.

Robust Resource-Aware Self-Triggered Model Predictive Control

The wide adoption of wireless devices in the Internet of Things requires controllers that are able to operate with limited resources, such as battery life. Operating these devices robustly in an uncertain environment, while managing available resources, increases the difficultly of controller design. This paper proposes a robust self-triggered model predictive control approach to optimize a control objective while managing resource consumption. In particular, a novel zero-order-hold aperiodic discrete-time feedback control law is developed to ensure robust constraint satisfaction for continuous-time linear systems.

Self-triggered Model Predictive Control for Trajectory Tracking of Mobile Robot

Self-triggered Model Predictive Control for Trajectory Tracking of Mobile Robot