Self-triggered Model Predictive Control Research Articles

Self-triggered model predictive control of discrete-time Markov jump linear systems

This paper proposes a self-triggered model predictive control algorithm for a class of discrete-time Markov jump linear systems with parametric uncertainties. A dual-mode design framework is employed to guarantee the optimality, feasibility and robust stability. The online control law is obtained by minimising the worst case of a novel cost function, which contains a self-triggered mechanism. Finally, a numerical example verifies the effectiveness and resource-saving capacity of the developed approach.

Self-triggered MPC for nonholonomic systems with multiple constraints by adaptive transmission intervals

In this paper, self-triggered model predictive control is proposed with adaptive transmission intervals for tracking a nonholonomic system with multiple constraints. The next triggering time and adaptive transmission intervals are obtained by the self-triggered mechanism to divide control sequence into several discrete portions. The control sequence with the adaptive transmission intervals reduces computation burden by a sample-and-hold way. On the premise of invariance constraints, the terminal tracking error converges to an adaptive terminal set for the nonlinear nonholonomic system with multiple constraints. Effectiveness of the proposed self-triggered model predictive control strategy is shown by simulation results via a leader–follower system.

Self-triggered model predictive control for nonlinear continuous-time networked system via ensured performance control samples selection

Self-triggered and event-triggered control have been widely implemented in various fields recently, especially in networked control systems. In order to save communication resources, trigger control conducts aperiodic control strategies instead of traditional time-driven scheme. Based on the self-triggered control mechanism, this paper investigates self-triggered strategy in model predictive control for nonlinear continuous-time networked system, selects aperiodic samples to ensure system performance while reducing computing energies and improving the resource usage efficiency. The usage of communication resources is quantified as a damping parameter that can characterize the communication effects in total cost function, such that the optimal sampling time and input trajectory can be obtained synchronously. In theoretical results, the feasibility of the proposed self-triggered strategy and the asymptotic stability of the nonlinear system are guaranteed. Furthermore, a simulation is given to illustrate the effectiveness of the proposed approach.

Self-Triggered Model Predictive Control for Perturbed Underwater Robot Systems

Aiming at solving the control problem of a constrained and perturbed underwater robot, a control method was proposed by combining the self-triggered mechanism and the nonlinear model predictive control (NMPC). The theoretical properties of the kinematic model of the underwater robot, as well as the corresponding MPC controller, are first studied. Then, a novel technique for determining the next update moment of both the optimal control problem and the system state is developed. It is further rigorously proved that the proposed algorithm can (1) stabilize the closed-loop underwater robot system, (2) reduce the time of solving the optimal control problem and (3) save the information transfer resources. Finally, a case study is provided to show the effectiveness of the developed researched scheme.

Fast Self-Triggered MPC for Constrained Linear Systems With Additive Disturbances

This article proposes a robust self-triggered model predictive control (MPC) algorithm for a class of constrained linear systems subject to bounded additive disturbances, in which the intersampling time is determined by a fast convergence self-triggered mechanism. The main idea of the self-triggered mechanism is to select a sampling interval so that a rapid decrease in the predicted costs associated with optimal predicted control inputs is guaranteed. This allows for a reduction in the required computation without compromising performance. By using a constraint tightening technique and exploring the nature of the open-loop control between sampling instants, a set of minimally conservative constraints is imposed on nominal states to ensure robust constraint satisfaction. A multistep open-loop MPC optimization problem is formulated, which ensures recursive feasibility for all possible realizations of the disturbance. The closed-loop system is guaranteed to satisfy a mean-square stability condition. To further reduce the computational load, when states reach a predetermined neighborhood of the origin, the control law of the robust self-triggered MPC algorithm switches to a self-triggered local controller. A compact set in the state space is shown to be robustly asymptotically stabilized. Numerical comparisons are provided to demonstrate the effectiveness of the proposed strategies.

A Novel Self-Triggered MPC Scheme for Constrained Input-Affine Nonlinear Systems

This brief develops a novel self-triggered model predictive control algorithm based on time delay estimation for input-affine nonlinear systems. At each triggering instant, the algorithm determines simultaneously the predictive control sequence to feedforward compensate for the disturbance and the next triggering instant. As a result, the unnecessary samplings and transmissions are suppressed, and the frequency of solving the optimal control problem is reduced. The feasibility as well as the associated stability are verified, with a numerical example illustrating the effectiveness of the proposed scheme.

Co-design of Sampling Pattern and Control in Self-triggered Model Predictive Control for Sampled-data Systems

Abstract This paper studies the event-triggered model predictive control (MPC) problem for networked control systems with input constraints, where the control is of the sampled-data form. A novel self-triggered MPC (STMPC) method which enables the optimal design of sampling pattern and control law is proposed to reduce the conservatism of separate design of trigger and control law in existing approaches. The conditions on ensuring the algorithm feasibility and the closed-loop system stability are developed. In addition, an upper bound of the closed-loop system performance is derived which provides performance guarantee for the designed STMPC. Finally, simulation results are presented to verify the effectiveness of the proposed STMPC method.

A Resource-Aware Approach to Self-Triggered Model Predictive Control

In this paper, we consider a self-triggered formulation of model predictive control. In this variant, the controller decides at the current sampling instant itself when the next sample should be taken and the optimization problem be solved anew. We incorporate a pointwise-in-time resource constraint into the optimization problem, whose exact form can be chosen by the user. Thereby, the proposed scheme is made resource-aware with respect to a universal resource, which may pertain in practice for instance to communication, computation, energy or financial resources. We show that by virtue of the pointwise-in-time constraints, also a transient and an asymptotic average constraint on the resource usage are guaranteed. Furthermore, we derive conditions on the resource under which the proposed scheme achieves recursive feasibility and convergence. Finally, we demonstrate our theoretical results in a numerical example.

Robust self-triggered control for time-varying and uncertain constrained systems via reachability analysis

This paper develops a robust self-triggered control algorithm for time-varying and uncertain systems with constraints based on reachability analysis. The resulting piecewise constant control inputs achieve communication reduction and guarantee constraint satisfactions. In the particular case when there is no uncertainty, we propose a control design with minimum number of samplings over finite time horizon. Furthermore, when the plant is linear and the constraints are polyhedral, we prove that the previous algorithms can be reformulated as computationally tractable mixed integer linear programs. The method is compared with the robust self-triggered model predictive control in a numerical example and applied to a robot motion planning problem with temporal constraints.

Self‐triggered robust model predictive control for nonlinear systems with bounded disturbances

A self-triggered model predictive control (MPC) scheme for continuous-time perturbed nonlinear systems subject to bounded disturbances is investigated in this study. A self-triggered strategy is designed to obtain the inter-execution time before the next trigger using the current sampled state. An optimisation problem is addressed to obtain the optimal control trajectory at each triggered instant. The so-called dual-mode approach is used to stabilise the perturbed closed-loop system. Furthermore, sufficient conditions are derived to ensure the feasibility and stability, respectively. It is shown that with a properly designed prediction horizon, the feasibility of the proposed self-triggered MPC algorithm can be guaranteed if the disturbance is bounded in a small enough area. Meanwhile, the stability is proved under the self-triggered condition. Finally, a numerical example is given to illustrate the efficacy of the authors proposed scheme.

Cooperative control of high-speed trains for headway regulation: A self-triggered model predictive control based approach

The advanced train-to-train and train-to-ground communication technologies equipped in high-speed railways have the potential to allow trains to follow each with a steady headway and improve the safety and performance of the railway systems. A key enabler is a train control system that is able to respond to unforeseen disturbances in the system (e.g., incidents, train delays), and to adjust and coordinate the train headways and speeds. This paper proposes a multi-train cooperative control model based on the dynamic features during train longitude movement to adjust train following headway. In particular, our model simultaneously considers several practical constraints, e.g., train controller output constraints, safe train following distance, as well as communication delays and resources. Then, this control problem is solved through a rolling horizon approach by calculating the Riccati equation with Lagrangian multipliers. Due to the practical communication resource constraints and riding comfort requirement, we also improved the rolling horizon approach into a novel self-triggered model predictive control scheme to overcome these issues. Finally, two case studies are given through simulation experiments. The simulation results are analyzed which demonstrate the effectiveness of the proposed approach.

Robust self-triggered MPC with fast convergence for constrained linear systems

In this paper, a robust self-triggered model predictive control (MPC) scheme is proposed for linear discrete-time systems subject to additive disturbances, state and control constraints. To reduce the amount of computation on controller sides, MPC optimization problems are only solved at certain sampling instants which are determined by a novel self-triggering mechanism. The main idea of the self-triggering mechanism is to choose inter-sampling times by guaranteeing a fast decrease in optimal costs. It implies a fast convergence of system states to a compact set where it is ultimately bounded and a reduction of computation times to stabilize the system. Once the state enters a terminal region, the system can be stabilized to a robust invariant set by a state feedback controller. Robust constraint satisfaction is ensured by utilizing the worst-case set-valued predictions of future states in such a way that recursive feasibility is guaranteed for all possible realisations of disturbances. In the case where a priority is given to reducing communication costs rather than improvement in control performance in a neighborhood of the origin, a feedback control law based on nominal state predictions is designed in the terminal region to avoid frequent feedback. Performances of the closed-loop system are demonstrated by a simulation example.

Self-Triggered Model Predictive Control for Linear Systems With Switched Cost Functions

This paper investigates the self-triggered model predictive control for networked linear systems. The self-triggered mechanism is designed based on switched cost functions, which can be used to enhance systems performance and are more appropriate for complex industrial requirements in contrast with a single cost function approach. The model predictive controller is designed by solving an optimization problem and the self-triggered condition is designed. With the proposed self-triggered mechanism, much network computation and communication burden are reduced and Zeno behavior can be excluded. Moreover, asymptotic stability of the networked systems with model predictive control strategy is shown via average dwell-time technique. Finally, the numerical simulation example is given to illustrate the effectiveness of the proposed methods.

Robust Self-Triggered MPC With Adaptive Prediction Horizon for Perturbed Nonlinear Systems

This paper proposes a robust self-triggered model predictive control (MPC) with an adaptive prediction horizon scheme for constrained nonlinear discrete-time systems subject to additive disturbances. At each triggering instant, the controller provides an optimal control sequence by solving an optimal control problem (OCP), and at the same time, determines the next triggering time and prediction horizon. By implementing the algorithm, the average sampling frequency is reduced and the prediction horizon is adaptively decreased as the system state approaches a terminal region. Meanwhile, an upper bound of performance loss is guaranteed when compared with a nominal periodic sampling MPC. Feasibility of the OCP and stability of the closed-loop system are established. Simulation results verify the effectiveness of the scheme.

Triggering and Control Codesign in Self-Triggered Model Predictive Control of Constrained Systems: With Guaranteed Performance

This note studies the self-triggered MPC problem for constrained discrete-time nonlinear systems. A novel self-triggered MPC algorithm enabling the codesign of triggering and control is proposed, in which the communication cost is explicitly considered in the total cost function, and both the control and triggering intervals can be optimally designed. For constrained nonlinear systems, the theoretical conditions on ensuring feasibility and closed-loop stability are developed, and the achieved control and communication performance is proved to be guaranteed. In particular, the parameter design approaches for satisfying feasibility and stability conditions are further presented in the case of quadratic cost functions. Furthermore, stronger results are provided for linear case. Finally, the effectiveness and advantages are verified via simulation and comparison studies.

Output consensus of heterogeneous linear MASs by self-triggered MPC scheme

Abstract In this paper, a self-triggered Model Predictive Control (MPC) scheme is proposed to solve the output consensus problem of heterogeneous linear Multi-agent Systems (MASs). First, a self-triggered condition is designed to determine the time for solving optimization problem of each agent. Then, a self-triggered MPC scheme is built. The scheme not only formulates the aperiodic control form, but also avoids the design of observers for each agent compared with conventional method. On the whole, the communication load and actuator burden can be reduced. Zeno behavior is excluded by detailed analysis. Moreover, parameters selection of the cost function is introduced and analysis of the scheme feasibility is conducted. Sufficient conditions are developed to guarantee the scheme feasibility. Finally, some simulation examples are given to demonstrate the effectiveness of the scheme.

Stochastic self-triggered MPC for linear constrained systems under additive uncertainty and chance constraints

This paper presents a stochastic self-triggered model predictive control (MPC) scheme for linear systems with additive uncertainty, and with the states and inputs being subject to chance constraints. In the proposed control scheme, the succeeding sampling time instant and current control inputs are computed online by solving a formulated optimization problem. The chance constraints are reformulated into a deterministic fashion by leveraging the Cantelli’s inequality. Under few mild assumptions, the online computational complexity of the proposed control scheme is similar to that of a nominal self-triggered MPC. Furthermore, initial constraints are incorporated into the MPC problem to guarantee the recursive feasibility of the scheme, and the stability conditions of the system have been developed. Finally, numerical examples are provided to illustrate the achievable performance of the proposed control strategy.

Stochastic self-triggered model predictive control for linear systems with probabilistic constraints

A stochastic self-triggered model predictive control (SSMPC) algorithm is proposed for linear systems subject to exogenous disturbances and probabilistic constraints. The main idea behind the self-triggered framework is that at each sampling instant, an optimization problem is solved to determine both the next sampling instant and the control inputs to be applied between the two sampling instants. Although the self-triggered implementation achieves communication reduction, the control commands are necessarily applied in open-loop between sampling instants. To guarantee probabilistic constraint satisfaction, necessary and sufficient conditions are derived on the nominal systems by using the information on the distribution of the disturbances explicitly. Moreover, based on a tailored terminal set, a multi-step open-loop MPC optimization problem with infinite prediction horizon is transformed into a tractable quadratic programming problem with guaranteed recursive feasibility. The closed-loop system is shown to be stable. Numerical examples illustrate the efficacy of the proposed scheme in terms of performance, constraint satisfaction, and reduction of both control updates and communications with a conventional time-triggered scheme.

Robust self-triggered min–max model predictive control for discrete-time nonlinear systems

In this paper, we propose a robust self-triggered model predictive control (MPC) algorithm for constrained discrete-time nonlinear systems subject to parametric uncertainties and disturbances. To fulfill robust constraint satisfaction, we take advantage of the min–max MPC framework to consider the worst case of all possible uncertainty realizations. In this framework, a novel cost function is designed based on which a self-triggered strategy is introduced via optimization. The conditions on ensuring algorithm feasibility and closed-loop stability are developed. In particular, we show that the closed-loop system is input-to-state practical stable (ISpS) in the attraction region at triggering time instants. In addition, we show that the main feasibility and stability conditions reduce to a linear matrix inequality for linear case. Finally, numerical simulations and comparison studies are performed to verify the proposed control strategy.

Self‐triggered model predictive control for networked control systems based on first‐order hold

SummaryIn this work, a new self‐triggered model predictive control (STMPC) algorithm is proposed for continuous‐time networked control systems. Compared with existing STMPC algorithms, the proposed STMPC is implemented based on linear interpolation (first‐order hold) rather than the standard zero‐order hold, which helps further reduce the difference between the self‐triggered control signal and the original time‐triggered counterpart and thus reduce the rate of triggering. Based on the first‐order hold implementation, a self‐triggering condition is derived and the corresponding theoretical properties of the closed‐loop system are analyzed. Finally, the comparison between the proposed algorithm and the zero‐order hold–based STMPC is carried out through both theoretical analysis and a simulation example to illustrate the effectiveness of the proposed method.