Adolfo Anta

To Sample or not to Sample: Self-Triggered Control for Nonlinear Systems

Feedback control laws have been traditionally implemented in a periodic fashion on digital hardware. Although periodicity simplifies the analysis of the mismatch between the control design and its digital implementation, it also leads to conservative usage of resources such as CPU utilization in the case of embedded control. We present a novel technique that abandons the periodicity assumption by using the current state of the plant to decide the next time instant in which the state should be measured, the control law computed, and the actuators updated. This technique, termed self-triggered control, is developed for two classes of nonlinear control systems, namely, state-dependent homogeneous systems and polynomial systems. The wide applicability of the proposed results is illustrated in two well known physical examples: a jet engine compressor and the rigid body.

Brief paper: An ISS self-triggered implementation of linear controllers

Nowadays control systems are mostly implemented on digital platforms and, increasingly, over shared communication networks. Reducing resources (processor utilization, network bandwidth, etc.) in such implementations increases the potential to run more applications on the same hardware. We present a self-triggered implementation of linear controllers that reduces the amount of controller updates necessary to retain stability of the closed-loop system. Furthermore, we show that the proposed self-triggered implementation is robust against additive disturbances and provide explicit guarantees of performance. The proposed technique exhibits an inherent trade-off between computation and potential savings on actuation.

A Framework for the Event-Triggered Stabilization of Nonlinear Systems

Event-triggered control consists of closing the feedback loop whenever a predefined state-dependent criterion is satisfied. This paradigm is especially well suited for embedded systems and networked control systems since it is able to reduce the amount of communication and computation resources needed for control, compared to the traditional periodic implementation. In this paper, we propose a framework for the event-triggered stabilization of nonlinear systems using hybrid systems tools, that is general enough to encompass most of the existing event-triggered control techniques, which we revisit and generalize. We also derive two new event-triggering conditions which may further enlarge the inter-event times compared to the available policies in the literature as illustrated by two physical examples. These novel techniques exemplify the relevance of introducing additional variables for the design of the triggering law. The proposed approach as well as the new event-triggering strategies are flexible and we believe that they can be used to address other event-based control problems.

Self-triggered stabilization of homogeneous control systems

Digital implementations of feedback laws commonly consider periodic execution of control tasks. In this paper we go beyond the periodic model by developing self-triggered schedules for the execution of control tasks. These schedules guarantee asymptotic stability under sample-and-hold implementations while drastically reducing processor usage when compared with the more traditional periodic implementations. At the technical level the results rely on a homogeneity assumption on the continuous dynamics and extend to the self-triggered framework some of the advantages of event-triggered implementations recently studied by the authors. The results presented in this paper can be seen as an effort towards understanding the real-time scheduling requirements of control tasks.

System Architectures, Protocols and Algorithms for Aperiodic Wireless Control Systems

Wide deployment of wireless sensor and actuator networks in cyber-physical systems requires systematic design tools to enable dynamic tradeoff of network resources and control performance. In this paper, we consider three recently proposed aperiodic control algorithms which have the potential to address this problem. By showing how these controllers can be implemented over the IEEE 802.15.4 standard, a practical wireless control system architecture with guaranteed closed-loop performance is detailed. Event-based predictive and hybrid sensor and actuator communication schemes are compared with respect to their capabilities and implementation complexity. A two double-tank laboratory experimental setup, mimicking some typical industrial process control loops, is used to demonstrate the applicability of the proposed approach. Experimental results show how the sensor communication adapts to the changing demands of the control loops and the network resources, allowing for lower energy consumption and efficient bandwidth utilization.

On the Benefits of Relaxing the Periodicity Assumption for Networked Control Systems over CAN

A vast majority of control systems require the use of networks for the communication between the different agents: sensors, controllers, and actuators. The existing paradigm regards the messages, between sensors and controllers and between controllers and actuators, as periodic. Although this strategy facilitates the analysis and implementation, it leads to a conservative usage of the communication bandwidth. Based on previous work by the authors, an aperiodic strategy is proposed in this paper for the dynamic allocation of bandwidth according to the current state of the plants and the available resources. The case of control loops closed over Controller Area Networks (CANs) is discussed in detail and illustrated on a train car.

A unifying Lyapunov-based framework for the event-triggered control of nonlinear systems

We present a prescriptive framework for the event-triggered control of nonlinear systems. Rather than closing the loop periodically, as traditionally done in digital control, in event-triggered implementations the loop is closed according to a state-dependent criterion. Event-triggered control is especially well suited for embedded systems and networked control systems since it reduces the amount of resources needed for control such as communication bandwidth. By modeling the event-triggered implementations as hybrid systems, we provide Lyapunov-based conditions to guarantee the stability of the resulting closed-loop system and explain how they can be utilized to synthesize event-triggering rules. We illustrate the generality of the approach by showing how it encompasses several existing event-triggering policies and by developing new strategies which further reduce the resources needed for control.

Event-triggered and self-triggered stabilization of distributed networked control systems

Event-triggered and self-triggered control have recently been proposed as implementation strategies that considerably reduce the resources required for control. Although most of the work so far has focused on closing a single control loop, some researchers have started to investigate how these new implementation strategies can be applied when closing multiple-feedback loops in the presence of physically distributed sensors and actuators. In this paper, we consider a scenario where the distributed sensors, actuators, and controllers communicate via a shared wired channel. We use our recent prescriptive framework for the event-triggered control of nonlinear systems to develop novel policies suitable for the considered distributed scenario. Afterwards, we explain how self-triggering rules can be deduced from the developed event-triggered strategies.

Automatic verification of control system implementations

Software implementations of controllers for physical subsystems form the core of many modern safety-critical systems such as aircraft flight control and automotive engine control. A fundamental property of such implementations is stability, the guarantee that the physical plant converges to a desired behavior under the actions of the controller. We present a methodology and a tool to perform automated static analysis of embedded controller code for stability of the controlled physical system. The design of controllers for physical systems provides not only the controllers but also mathematical proofs of their stability under idealized mathematical models. Unfortunately, since these models do not capture most of the implementation details, it is not always clear if the stability properties are retained by the software implementation, either because of software bugs, or because of imprecisions arising from fixed-precision arithmetic or timing. Our methodology is based on the following separation of concerns. First, we analyze the controller mathematical models to derive bounds on the implementation errors that can be tolerated while still guaranteeing stability. Second, we automatically analyze the controller software to check if the maximal implementation error is within the tolerance bound computed in the first step. We have implemented this methodology in Costan, a tool to check stability for controller implementations. Using Costan, we analyzed a set of control examples whose mathematical models are given in Matlab/Simulink and whose C implementation is generated using Real-Time Workshop. Unlike previous static analysis research, which has focused on proving low-level runtime properties such as absence of buffer overruns or arithmetic overflows, our technique combines analysis of the mathematical controller models and automated analysis of source code to guarantee application-level stability properties.

Self-triggered control over wireless sensor and actuator networks

Energy and communication bandwidth are scarce resources in wireless sensor and actuator networks. Recent research efforts considered the control of physical processes over such resource limited networks. Most of the existing literature addressing this topic is dedicated to periodically sampled control loops and scheduled communication, because it simplifies the analysis and the implementation. We propose instead an aperiodic network transmission scheme that reduces the number of transmission instances for the sensor and control nodes, thereby reducing energy consumption and increasing network lifetime, without sacrificing control performance. As an added benefit, we show the possibility of dynamically allocating the network bandwidth based on the physical system state and the available resources. In order to allow timely, reliable, and energy efficient communication, we propose a new co-design framework for the wireless medium access control, compatible with the IEEE 802.15.4 standard. Furthermore, we validate our approach in a real wireless networked control implementation.