Sven Reimann

Suboptimal Event-Triggered Control for Time-Delayed Linear Systems

This technical note considers event-triggering conditions and controller synthesis approaches for delayed linear systems. Optimization problems for minimizing the upper bound of quadratic cost functions are formulated in the form of linear matrix inequalities (LMIs). By solving the optimization problems a unique control gain can be obtained. The performance considered in this technical note includes a linear quadratic cost function for quantifying the control performance and average event times at which the control input must be updated for quantifying the transmission reductions. Comparisons with other approaches in the literature are given to demonstrate the advantages with respect to the two performance indices. Furthermore, an experimental implementation of the proposed methods in an inverted pendulum system shows the applicability and effectiveness in real world.

Event-Triggered Control for Linear Systems Subject to Actuator Saturation

Abstract Event-triggered control is developed to reduce the communication load in networked control systems. This means that output or actuator signals are only transmitted over the network when an event-triggering condition is violated which is designed such that a certain control performance can be guaranteed. This paper considers event-triggered control subject to actuator saturation for linear systems. Therefore we present a method to estimate the domain of attraction which represents a contractive invariant set. The contractive invariant set is estimated by an ellipsoid which is determined by solving a linear matrix inequality (LMI) optimization problem. Further a controller synthesis design considering the event-triggering condition in our criterion is given to maximize the contractive ellipsoid. Simulations are given to illustrate the results.

Event-based control and scheduling codesign of networked embedded control systems

For networked embedded control systems (NECSs) besides control performance an efficient usage of computation and communication resources is crucial. This paper presents a novel event-based codesign concept for NECSs. The codesign concept involves a joint design of a control law, a scheduler, and an event generator. The control law serves for improving control performance, the scheduler and the event generator for an efficient usage of the limited resources. The codesign problem is formulated as a linear matrix inequality (LMI) problem which can be solved efficiently. The developed theory is evaluated through a simulation for networked embedded control of a set of inverted pendulums. Noteworthy, the codesign concept is generally applicable to discrete-time switched linear systems.

A novel control-schedule codesign method for embedded control systems

This paper addresses the control and scheduling of embedded control systems with shared computation resources. The holistic system consisting of several linear plants, which are controlled by one single processor, is modeled as a switched control system. Based on quadratic Lyapunov function a method is introduced to design jointly schedule and control, which guarantees stability of all plants controlled by the processor. The proposed strategy is formulated as a constrained optimization problem, which firstly allows checking the feasibility of the stabilization of all plants by controlling them by one processor. Moreover, the solution of the constrained optimization problem contains the control gain and the necessary parameters for an appropriate online scheduling. The method is illustrated by an example.

Output-based control and scheduling codesign for control systems sharing a limited resource

This paper addresses the output-based control and scheduling codesign problem for control systems sharing a limited resource, especially embedded control systems (ECSs). The joint design (codesign) of a controller and a scheduler is for the purpose of improving the resulting control performance. ECSs with a set of independent linear time-invariant plants and considerable computation time delays are modeled as discrete-time switched linear systems. Based on the resulting model, the codesign problem is introduced and decomposed into a state-based control and scheduling codesign subproblem and an observer design subproblem using the separation principle. Both subproblems are eventually formulated as LMI subproblems which can be solved efficiently. Two types of observers are introduced to cope with the lack of all states: Prediction observer and current-state observer. The effectiveness of the proposed output-based codesign method is illustrated for simultaneous stabilization of three inverted pendulums.

Real-Time Scheduling of PI Control Tasks

Modern control systems are increasingly realized on embedded systems, where the computation resources are limited. This brief addresses the scheduling of a set of control tasks that are implemented on one single processor. For improving the control performance and achieving an efficient utilization of the limited computation resources, an intelligent scheduling algorithm is essential. Therefore, a novel scheduling algorithm with output feedback resource allocation is proposed for scheduling a set of proportional-integral (PI) control tasks. Thereby, an extended PI controller is introduced that can handle time-varying sampling intervals. For deriving an a posteriori stability criterion, each plant with the scheduled PI controller is modeled as a discrete-time switched linear system. The stability criterion is eventually formulated as a linear matrix inequality feasibility problem. The effectiveness of the proposed online scheduling approach is illustrated by simulation and practical implementation.

Stability analysis and PI control synthesis under event-triggered communication

Although setpoint tracking problems are common in practice, they are still widely unexplored in the event-triggered control framework. Therefore, an event-triggered PI control design strategy with guaranteed performance for networked control systems is proposed in this paper. The integral state of the proposed PI controller is updated at every sampling instant. The update is done by the proposed event generator and sent with new measurements to the PI controller when necessary. Based on a discretized system model and a quadratic cost function, the event-triggered PI control design problem is introduced and formulated as an LMI optimization problem. The effectiveness of the proposed strategy is then experimentally evaluated and compared with other existing strategies in the literature for a case study.

PI Control and Scheduling Design for Embedded Control Systems

Abstract This paper addresses the control and scheduling design for control systems sharing a limited computation resource, especially embedded control systems (ECSs). The complementary design of controller and scheduler is for improving the control performance and achieving an efficient utilization of the limited computation resources. A novel PI control design method as well as a novel output-based scheduling approach are introduced to achieve setpoint-tracking for multiple plants. For verifying stability the whole system, namely all plants with the scheduled controllers, is modeled as a discrete-time switched linear system. The stability criteria is eventually formulated as a linear matrix inequality (LMI) feasibility problem. The effectivenes of the proposed control and scheduling approach is illustrated by a practical implementation where two DC motors are controlled by one processor.

PI control synthesis for event-triggered control systems

Abstract Event-triggered control aims at reducing the resource utilization, especially the communication over the feedback link, while guaranteeing a certain control performance. Although setpoint tracking problems are common in practice, the majority of the proposed approaches in literature focus on regulation problems. Therefore, an event-triggered PI control design strategy with guaranteed performance is proposed in this paper, where both the event-triggering condition and the PI controller are implemented periodically. Based on a quadratic cost function, the PI control design problem is introduced and formulated as an LMI optimization problem. Comparisons with other approaches in the literature are made by simulation and by experimental studies to demonstrate the effectiveness of the proposed strategy.