Benjamin Kern

Event-based model predictive control for Networked Control Systems

Thanks to their cheap startup costs, flexibility, and standard infrastructure re-usability, Networked Control Systems have gained the attention of both the control community and the industry. Unfortunately, the presence of communication networks might introduce nondeterminism due to (random) delays and/or (unpredictable) information losses. In this paper, an event-based model predictive control approach for nonlinear continuous time systems under state and input constraints is presented. This method is able to counteract bounded delays, information losses, as well as deal with event triggering due to sensors and actuators. Under standard weak assumptions, closed loop stability, in the sense of asymptotic convergence, is achieved. Simulation results for a planar vertical takeoff and landing aircraft are provided.

Model predictive path-following for constrained nonlinear systems

We propose a model predictive control approach to path-following problems of constrained nonlinear systems. We directly consider input and state constraints. Furthermore, we introduce an extended corridor path-following problem, which allows to add spatial degrees of freedom to the path formulation.We give sufficient stability conditions for predictive solutions to 1d and corridor path-following problems. To illustrate the performance of our approach we discuss the example of an autonomous vehicle subject to input constraints.

Practical set invariance for decentralized discrete time systems

This paper discusses set invariance notions for decentralized discrete time systems which are physically inter-connected. We employ independent set-dynamics induced by the underlying subsystems subject to the available information in the decentralized setting. The main novelty of the approach lies within the fact that the concept of set invariance for independent set-dynamics is formalized by employing appropriate families of sets. The complexity of the exact notion is alleviated by introducing a practical set invariance notion which is then complemented with the corresponding relaxed stability analysis. Under mild assumptions, the introduced notion allows for safe, stable and independent operation of the subsystems forming the overall decentralized system.

Receding horizon control for linear periodic time-varying systems subject to input constraints

In this paper, a receding horizon control scheme able to stabilize linear periodic time-varying systems, in the sense of asymptotic convergence, is proposed. The presented approach guarantees that input constraints are always satisfied if the optimization problem is feasible at the initial time.

Event-based reduced-attention predictive control for nonlinear uncertain systems

Event-based control is an alternative to traditional control where new measurements are sampled only if critical events occur. This not only allows to reduce the control effort but it satisfies nowadays application requirements, such for example reduction of information exchange, computational power, or energy consumption. The work in this field is, however, still sparse and only a few results are available. Properly choosing an event-detection logic can considerably improve the overall systems performance. We propose a control algorithm which makes use of a model-based triggering strategy to reduce the control effort (reduced-attention control), while guaranteeing robustness against bounded additive perturbations for nonlinear continuous time systems. In particular, we derive conditions which guarantee that asymptotic stability of the nominal system implies practical stability of the real one in a neighborhood of the origin. A continuous stirred tank reactor is used as a benchmark problem to show the effectiveness of the presented algorithm.

Practical Robust Positive Invariance for Large{Scale Discrete Time Systems

Abstract This note introduces practical set invariance notions for physically interconnected, discrete–time systems, subject to additive but bounded disturbances. The developed approach provides a decentralized, non–conservative and computationally tractable way to study desirable robust positive invariance and stability notions for the overall system as well as to guarantee safe and independent operation of the constituting subsystems. These desirable properties are inherited, under mild assumptions, from the classical stability and invariance properties of the associated vector–valued dynamics which capture in a simple but appropriate and non–conservative way the dynamical behavior induced by the underlying set–dynamics of interest.

Dissipativity-based Distributed Nonlinear Predictive Control for Cascaded Systems

Abstract Developing centralized controllers for large-scale systems, e.g. complex chemical processes, electrical power networks, is an important, yet challenging problem. Typically, it would be of advantage if one could divide the problem into smaller parts (or subproblems), and to opt for a decentralized or distributed alternative. On the other hand, due to physical interconnections between subsystems, it is often complicated to find such a solution. Additionally, performance loss or even instability of the overall system can arise if the decentralization is not done properly. It is, therefore, fundamental to develop suitable distributed/decentralized techniques in order to avoid these issues. In this paper, we propose a decentralized dissipativity-based nonlinear model predictive control strategy for cascades of physically interconnected systems, e.g cascades of hydroelectric power plants, multi-cell batteries. Under mild assumptions, we prove that the control method guarantees overall stability by independently enforcing stability of the local subsystems. This allows for efficient decentralized solutions. Furthermore, the local controllers only exchange limited information and no model of the neighbor systems is required, facilitating decoupled local controller design. Two interconnected water tanks are used to demonstrate the effectiveness of our approach.

Distributed and Networked Model Predictive Control

In this chapter, we consider the problem of controlling networked and distributed systems by means of model predictive control (MPC). The basic idea behind MPC is to repeatedly solve an optimal control problem based on a model of the system to be controlled. Every time a new measurement is available, the optimization problem is solved and the corresponding input sequence is applied until a new measurement arrives. As explained in the sequel, the advantages of MPC over other control strategies for networked systems are due to the fact that a model of the system is available at the controller side, which can be used to compensate for random bounded delays. At the same time, for each iteration of the optimization problem an optimal input sequence is calculated. In case of packet dropouts, one can reuse this information to maintain closed-loop stability and performance.

Nonlinear Predictive Control based on Asynchronous Measurement and Control Signals

Zusammenfassung In vielen Regelungsproblemen stehen die notwendigen Messgrößen nicht zu äquidistanten Zeitpunkten zur Verfügung und es kann auf die zu regelnde Strecke nicht zu äquidistanten Zeitpunkten eingewirkt werden. Daneben treten auf Grund von notwendigen Auswertungszeiten im Sensor, etwaigen Kalibrierungsvorgängen des Stellglieds oder Sensors oder auch Rechenverzögerungen im Regler oft unvermeidliche Verzögerungen auf. Sowohl die variablen Abtastzeiten als auch die Verzögerungen müssen im Reglerentwurf berücksichtigt werden, um Instabilität oder Einschränkungen der Regelgüte zu vermeiden. Im Rahmen dieser Arbeit wird aufgezeigt, dass prädiktive Regelungsverfahren basierend auf kontinuierlichen Streckenmodellen in der Lage sind, Systeme unter nicht äquidistanter Abtastung und Verzögerungen zu stabilisieren. Zusätzlich werden neue Konzepte umrissen, die aufzeigen, wie durch aktive Sensoren Messungen ausgelöst werden können, sodass Stelleingriffe nur erfolgen, wenn dies notwendig ist.

Analysis and constrained control of nonlinear interconnected systems exploiting positively invariant family of sets

The design of decentralized controllers for physically coupled interconnected systems is a challenging task, especially if constraints on the states and inputs must be satisfied. In this work we focus on the design of decentralized controllers for interconnected linear systems subject to nonlinear, homogeneous physical couplings. For the design and the characterization of controlled invariant regions we exploit the concept of positively invariant family of sets. Basically we utilize in the analysis and design a dynamically varying upper bound for the interconnections between the subsystems. This allows to overcome some conservatism related to existing design approaches. As shown, the controller synthesis can be formulated as loosely coupled LMI feasibility problems. This conceptually allows us to decompose the design into as series of smaller subproblems, which are computationally attractive. We obtain for the coupled nonlinear systems suitable decentralized linear control laws, as well as a family of ellipsoidal sets for which satisfaction of the state and input constraints, as well as positive invariance can be guaranteed. The application of the approach is validated considering the decentralized control of two systems that are interconnected with nonlinear functions.