Maurice Heemels

Self-triggered linear quadratic control

a b s t r a c t Self-triggered control is a recently proposed paradigm that abandons the more traditional periodic time- triggered execution of control tasks with the objective of reducing the utilization of communication resources, while still guaranteeing desirable closed-loop behavior. In this paper, we introduce a self- triggered strategy based on performance levels described by a quadratic discounted cost. The classical LQR problem can be recovered as an important special case of the proposed self-triggered strategy. The self-triggered strategy proposed in this paper possesses three important features. Firstly, the control laws and triggering mechanisms are synthesized so that a priori chosen performance levels are guaranteed by design. Secondly, they realize significant reductions in the usage of communication resources. Thirdly, we address the co-design problem of jointly designing the feedback law and the triggering condition. By means of a numerical example, we show the effectiveness of the presented strategy. In particular, for the self-triggered LQR strategy, we show quantitatively that the proposed scheme can outperform conventional periodic time-triggered solutions.

A hybrid MPC approach to the design of a Smart adaptive cruise controller

In this paper we investigate the possibility of applying the hybrid Model Predictive Control (MPC) framework to solve a control problem regarding tracking of a moving vehicle. The study originates from the design of an adaptive cruise controller (ACC) of a Smart car, that aims to closely follow a reference trajectory transmitted by a leading vehicle. The physical behavior of the Smart and the constraints arising from the specifications related to safety and security issues make the hybrid MPC framework suitable for this task. An adaptation of the terminal cost and constraint set MPC approach, which is commonly used for fixed set-point regulation, is employed in order to achieve good tracking of a time-varying reference trajectory. The simulation results indicate the effectiveness of the developed hybrid MPC algorithm and the industrial feasibility with respect to on-line computation restrictions.

Robust self-triggered MPC for constrained linear systems

We propose a robust self-triggered control algorithm for constrained linear discrete-time systems subject to additive disturbances based on MPC. At every sampling instant, the controller provides both the next sampling instant, as well as the inputs that are applied to the system until the next sampling instant. By maximizing the inter-sampling time subject to bounds on the MPC value function, the average sampling frequency in the closed-loop system is decreased while guaranteeing an upper bound on the performance loss when compared with an MPC scheme sampling at every point in time. Robust constraint satisfaction is achieved by tightening input and state constraints based on a Tube MPC approach. Moreover, a compact set in the state space, which is a parameter in the MPC scheme, is shown to be robustly asymptotically stabilized.

Stability analysis of large-scale networked control systems with local networks: a hybrid small-gain approach

In this paper we consider large-scale networked control systems (NCSs) with multiple communication networks connecting sensors, controllers and actuators. Using a recently developed small-gain theorem for general interconnections of hybrid systems, we are able to find to find a maximum allowable transmission interval (MATI) and a maximum allowable delay (MAD) for each individual network, such that input-to-state stability of the complete NCS is guaranteed.

Positive feedback stabilization of compressor surge

Stable operation of axial and centrifugal compressors is limited towards low mass flows due to the onset of surge. The stable operating region can be enlarged by active control. In this study, we use a control valve which is nominally closed and only opens to stabilize the system around the desired operating point. Hence, only non-negative control values are allowed which complicates the controller design considerably. A novel positive feedback controller is proposed with clear design parameters to obtain a desirable closed loop behavior. The technique has successfully been applied to a compression system model. For arbitrarily large control valve capacities, the system can be stabilized in the entire operating region. Simulations show that the surge point mass flow can be reduced up to 15% for the relatively small control valve to be implemented on the actual installation. Using this efficient control strategy, the stabilized operating point is reached with zero control valve mass flow.

Event-triggered control systems under packet losses

Networked control systems (NCSs) offer many benefits in terms of increased flexibility and maintainability but might also suffer from inevitable imperfections such as packet dropouts and limited communications resources. In this paper, (static and dynamic) event-triggered control (ETC) strategies are proposed that aim at reducing the utilization of communication resources while guaranteeing desired stability and performance criteria and a strictly positive lower bound on the inter-event times despite the presence of packet losses. For the packet losses, we consider both configurations with an acknowledgement scheme (as, e.g., in the transmission control protocol (TCP)) and without an acknowledgement scheme (as, e.g., in the user diagram protocol (UDP)). The proposed design methodology will be illustrated by means of a numerical example which reveals tradeoffs between the maximum allowable number of successive packet dropouts, (minimum and average) inter-event times and Lp-gains of the closed-loop NCS.

MOBY-DIC : a Matlab toolbox for circuit-oriented design of explicit MPC

This paper describes a MATLAB Toolbox for the integrated design of Model Predictive Control (MPC) state-feedback control laws and the digital circuits implementing them. Explicit MPC laws can be designed using optimal and sub-optimal formulations, directly taking into account the specifications of the digital circuit implementing the control law (such as latency and size), together with the usual control specifications (stability, performance, constraint satisfaction). Tools for a-posteriori stability analysis of the closed-loop system, and for the simulation of the circuit in Simulink, are also included in the toolbox.

Co-design of output feedback laws and event-triggering conditions for the L2 -stabilization of linear systems

We investigate the L2-stabilization of linear systems using output feedback event-triggered controllers. In particular, we are interested in the scenario where the plant output and the control input are transmitted to the controller and to the actuators, respectively, over two different digital channels, which have their own sampling rule. The plant dynamics is affected by external disturbances and the output measurement and the control input are corrupted by noises. We present a co-design procedure to simultaneously synthesize dynamic output feedback laws and event-triggering conditions such that the closed-loop system is L2-stable with a given upper-bound on the L2-gain. The required conditions are formulated in terms of the feasibility of linear matrix inequalities (LMIs). Then, we exploit these LMIs to maximize the guaranteed minimum time between two transmissions of the plant output and/or of the control input. We also present a heuristic method to reduce the amount of transmissions for each channel. The developed technique encompasses time-driven (and so periodic) sampling as a particular case and the result is also new in this context. The effectiveness of the proposed methods is illustrated on a numerical example.

Dynamic Periodic Event-Triggered Control for Linear Systems

In event-triggered control systems, events are typically generated when a static function of the output (or state) of the system exceeds a given threshold. Recently, event-generators have been proposed that generate events based on an additional dynamic variable, with dynamics that depend on the output of the system. It is shown that these dynamic event-generators are able to guarantee the same performance as their static counterparts, while typically generating significantly fewer events. However, all dynamic event-generators available in literature require continuous measuring of the output of the plant, which is difficult to realize on digital platforms. In this paper, we propose new dynamic event-generators for linear systems, which require only periodic sampling of the output, and are therefore easy to implement on digital platforms. Based on hybrid modelling techniques combined with constructive designs of Lyapunov/storage functions for the resulting hybrid models, it is shown that these (dynamic periodic) event-generators lead to closed-loop systems which are globally exponentially stable (GES) with a guaranteed decay rate and MC L2-stable with a guaranteed L2-gain. The benefits of these new event-generators are also demonstrated via a numerical example.

Hybrid control lyapunov functions for the stabilization of hybridsystems

The design of stabilizing controllers for hybrid systems is particularly challenging due to the heterogeneity present within the system itself. In this paper we propose a constructive procedure to design stabilizing dynamic controllers for a fairly general class of hybrid systems. The proposed technique is based on the concept of a hybrid control Lyapunov function (hybrid CLF) that was previously introduced by the authors. In this paper we generalize the concept of hybrid control Lyapunov function, and we show that the existence of a hybrid CLF guarantees the existence of a standard control Lyapunov function (CLF) for the hybrid system. We provide a constructive procedure to design a hybrid CLF and the corresponding dynamic control law, which is stabilizing because of the established connection to a standard CLF that becomes a Lyapunov function for the closed-loop system. The obtained control law can be conveniently implemented by constrained predictive control in the form of a receding horizon control strategy. A numerical example highlighting the features of the proposed approach is presented.