Karl Henrik Johansson

The quadruple-tank process: a multivariable laboratory process with an adjustable zero

A multivariable laboratory process that consists of four interconnected water tanks is presented. The linearized dynamics of the system have a multivariable zero that is possible to move along the real axis by changing a valve. The zero can be placed in both the left and the right half-plane. In this way the quadruple-tank process is ideal for illustrating many concepts in multivariable control, particularly performance limitations due to multivariable right half-plane zeros. The location and the direction of the zero have an appealing physical interpretation. Accurate models are derived from both physical and experimental data and decentralized control is demonstrated on the process.

Event-based broadcasting for multi-agent average consensus

A novel control strategy for multi-agent coordination with event-based broadcasting is presented. In particular, each agent decides itself when to transmit its current state to its neighbors and the local control laws are based on these sampled state measurements. Three scenarios are analyzed: Networks of single-integrator agents with and without communication delays, and networks of double-integrator agents. The novel event-based scheduling strategy bounds each agents measurement error by a time-dependent threshold. For each scenario it is shown that the proposed control strategy guarantees either asymptotic convergence to average consensus or convergence to a ball centered at the average consensus. Moreover, it is shown that the inter-event intervals are lower-bounded by a positive constant. Numerical simulations show the effectiveness of the novel event-based control strategy and how it compares to time-scheduled control.

An introduction to event-triggered and self-triggered control

Recent developments in computer and communication technologies have led to a new type of large-scale resource-constrained wireless embedded control systems. It is desirable in these systems to limit the sensor and control computation and/or communication to instances when the system needs attention. However, classical sampled-data control is based on performing sensing and actuation periodically rather than when the system needs attention. This paper provides an introduction to event- and self-triggered control systems where sensing and actuation is performed when needed. Event-triggered control is reactive and generates sensor sampling and control actuation when, for instance, the plant state deviates more than a certain threshold from a desired value. Self-triggered control, on the other hand, is proactive and computes the next sampling or actuation instance ahead of time. The basics of these control strategies are introduced together with a discussion on the differences between state feedback and output feedback for event-triggered control. It is also shown how event- and self-triggered control can be implemented using existing wireless communication technology. Some applications to wireless control in process industry are discussed as well.

On the regularization of Zeno hybrid automata

Fundamental properties of hybrid automata, such as existence and uniqueness of executions, are studied. Particular attention is devoted to Zeno hybrid automata, which are hybrid automata that take infinitely many discrete transitions in finite time. It is shown that regularization techniques can be used to extend the Zeno executions of these automata to times beyond the Zeno time. Different types of regularization may, however, lead to different extensions. A water tank control problem and a bouncing ball system are used to illustrate the results.

Cyber security analysis of state estimators in electric power systems

In this paper, we analyze the cyber security of state estimators in Supervisory Control and Data Acquisition (SCADA) systems operating in power grids. Safe and reliable operation of these critical infrastructure systems is a major concern in our society. In current state estimation algorithms there are bad data detection (BDD) schemes to detect random outliers in the measurement data. Such schemes are based on high measurement redundancy. Although such methods may detect a set of very basic cyber attacks, they may fail in the presence of a more intelligent attacker. We explore the latter by considering scenarios where deception attacks are performed, sending false information to the control center. Similar attacks have been studied before for linear state estimators, assuming the attacker has perfect model knowledge. Here we instead assume the attacker only possesses a perturbed model. Such a model may correspond to a partial model of the true system, or even an out-dated model. We characterize the attacker by a set of objectives, and propose policies to synthesize stealthy deceptions attacks, both in the case of linear and nonlinear estimators. We show that the more accurate model the attacker has access to, the larger deception attack he can perform undetected. Specifically, we quantify trade-offs between model accuracy and possible attack impact for different BDD schemes. The developed tools can be used to further strengthen and protect the critical state-estimation component in SCADA systems.

Subgradient methods and consensus algorithms for solving convex optimization problems

In this paper we propose a subgradient method for solving coupled optimization problems in a distributed way given restrictions on the communication topology. The iterative procedure maintains local variables at each node and relies on local subgradient updates in combination with a consensus process. The local subgradient steps are applied simultaneously as opposed to the standard sequential or cyclic procedure. We study convergence properties of the proposed scheme using results from consensus theory and approximate subgradient methods. The framework is illustrated on an optimal distributed finite-time rendezvous problem.

Event-triggered control for multi-agent systems

Event-driven strategies for multi-agent systems are motivated by the future use of embedded microprocessors with limited resources that will gather information and actuate the individual agent controller updates. The control actuation updates considered in this paper are event-driven, depending on the ratio of a certain measurement error with respect to the norm of a function of the state, and are applied to a first order agreement problem. A centralized formulation of the problem is considered first and then the results are extended to the decentralized counterpart, in which agents require knowledge only of the states of their neighbors for the controller implementation.

Event-Based Sensor Data Scheduling: Trade-Off Between Communication Rate and Estimation Quality

We consider sensor data scheduling for remote state estimation. Due to constrained communication energy and bandwidth, a sensor needs to decide whether it should send the measurement to a remote estimator for further processing. We propose an event-based sensor data scheduler for linear systems and derive the corresponding minimum squared error estimator. By selecting an appropriate event-triggering threshold, we illustrate how to achieve a desired balance between the sensor-to-estimator communication rate and the estimation quality. Simulation examples are provided to demonstrate the theory.

A secure control framework for resource-limited adversaries

Cyber-secure networked control is modeled, analyzed, and experimentally illustrated in this paper. An attack space defined by the adversarys model knowledge, disclosure, and disruption resources is introduced. Adversaries constrained by these resources are modeled for a networked control system architecture. It is shown that attack scenarios corresponding to denial-of-service, replay, zero-dynamics, and bias injection attacks on linear time-invariant systems can be analyzed using this framework. Furthermore, the attack policy for each scenario is described and the attacks impact is characterized using the concept of safe sets. An experimental setup based on a quadruple-tank process controlled over a wireless network is used to illustrate the attack scenarios, their consequences, and potential counter-measures.

Brief paper: Distributed fault detection for interconnected second-order systems

In this paper, the existence of unknown input observers for networks of interconnected second-order linear time invariant systems is studied. Two classes of distributed control systems of large practical relevance are considered. It is proved that for these systems, one can construct a bank of unknown input observers, and use them to detect and isolate faults in the network. The result presents a distributed implementation. In particular, by exploiting the system structure, this work provides further insight into the design of UIO for networked systems. Moreover, the importance of certain network measurements is shown. Infeasibility results with respect to available measurements and faults are also provided, as well as methods to remove faulty agents from the network. Applications to power networks and robotic formations are presented. It is shown how the developed methodology apply to a power network described by the swing equation with a faulty bus. For a multi-robot system, it is illustrated how a faulty robot can be detected and removed.