Showing papers by "Paulo Tabuada published in 2012"

An introduction to event-triggered and self-triggered control

Abstract: 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.

Symbolic Models for Nonlinear Control Systems Without Stability Assumptions

Abstract: Finite-state models of control systems were proposed by several researchers as a convenient mechanism to synthesize controllers enforcing complex specifications. Most techniques for the construction of such symbolic models have two main drawbacks: either they can only be applied to restrictive classes of systems, or they require the exact computation of reachable sets. In this paper, we propose a new abstraction technique that is applicable to any nonlinear sampled-data control system as long as we are only interested in its behavior in a compact set. Moreover, the exact computation of reachable sets is not required. The effectiveness of the proposed results is illustrated by synthesizing a controller to steer a vehicle.

Security for control systems under sensor and actuator attacks

Abstract: We consider the problem of estimation and control of a linear system when some of the sensors or actuators are attacked by a malicious agent. In our previous work [1] we studied systems with no control inputs and we formulated the estimation problem as a dynamic error correction problem with sparse attack vectors. In this paper we extend our study and look at the role of inputs and control. We first show that it is possible to increase the resilience of the system to attacks by changing the dynamics of the system using state-feedback while having (almost) total freedom in placing the new poles of the system. We then look at the problem of stabilizing a plant using output-feedback despite attacks on sensors, and we show that a principle of separation of estimation and control holds. Finally we look at the effect of attacks on actuators in addition to attacks on sensors: we characterize the resilience of the system with respect to actuator and sensor attacks and we formulate an efficient optimization-based decoder to estimate the state of the system despite attacks on actuators and sensors.

Dynamic programming formulation of periodic event-triggered control: Performance Guarantees and co-design

Abstract: While potential benefits of choosing the transmissions times in a networked control system based on state or event information have been advocated in the literature, few general methods are available that guarantee closed-loop improvements over traditional periodic transmission strategies. In this paper, we propose event-triggered controllers that guarantee better quadratic discounted cost performance than periodic control strategies using the same average transmission rate. Moreover, we show that the performance of a method in the line of previous Lyapunov based approaches is within a multiplicative factor of periodic control performance, while using less transmissions. Our approach is based on a dynamic programming formulation for the co-design problem of choosing both transmission decisions and control inputs in the context of periodic event-triggered control for linear systems. A numerical example illustrates the advantages of the proposed method over traditional periodic control.

Exploiting Isochrony in Self-Triggered Control

Abstract: Event-triggered control and self-triggered control have been recently proposed as new implementation paradigms that reduce resource usage for control systems. In self-triggered control, the controller is augmented with the computation of the next time instant at which the feedback control law is to be recomputed. Since these execution instants are obtained as a function of the plant state, we effectively close the loop only when it is required to maintain the desired performance, thereby greatly reducing the resources required for control. In this paper we present a new technique for the computation of the execution instants by exploiting the concept of isochronous manifolds, also introduced in this paper. While our previous results showed how homogeneity can be used to compute the execution instants along some directions in the state space, the concept of isochrony allows us to compute the executions instants along every direction in the state space. Moreover, we also show in this paper how to homogenize smooth control systems thus making our results applicable to any smooth control system. The benefits of the proposed approach with respect to existing techniques are analyzed in two examples.

Kron reduction of power networks with lossy and dynamic transmission lines

Abstract: In this paper, we revisit the Kron reduction of electrical networks By drawing inspiration from the models of short transmissions lines, we introduce a class of electric networks that we call homogeneous RL networks We show how to perform Kron reduction for these networks in the time domain Our results can thus be applied to study both the steady state solutions as well as transients while avoiding the use of phasors altogether

Input-output robustness for discrete systems

Abstract: Robustness is the property that a system only exhibits small deviations from the nominal behavior upon the occurrence of small disturbances. While the importance of robustness in engineering design is well accepted, it is less clear how to verify and design discrete systems for robustness. We present a theory of input-output robustness for discrete systems inspired by existing notions of input-output stability (IO-stability) in continuous control theory. We show that IO-stability captures two intuitive goals of robustness: bounded disturbances lead to bounded deviations from nominal behavior, and the effect of a sporadic disturbance disappears in finitely many steps. We show that existing notions of robustness for discrete systems do not have these two properties. For systems modeled as finite-state transducers, we show that IO-stability can be verified and the synthesis problem can be solved in polynomial time. We illustrate our theory using a reference broadcast synchronization protocol for wireless networks.

Scaling up controller synthesis for linear systems and safety specifications

Abstract: In this paper we revisit the problem of automatically synthesizing control software enforcing formal specifications given in temporal logic. Existing approaches to solve this problem rely on the explicit or implicit construction of finite abstractions of control systems. Unfortunately, the existing abstraction techniques do not scale beyond a small number of state variables. The objective of this paper is to scale up the construction of such abstractions by focusing on linear control systems and safety specifications. In this more restricted scenario the controller synthesis problem can be reduced to the computation of control invariant subsets. Hence, we focus on the control invariance problem and propose a computational technique exploiting controllability. We illustrate the proposed methods on several synthetic examples illustrating the computational limits of our algorithm.

Kron Reduction of Generalized Electrical Networks

Abstract: Kron reduction is used to simplify the analysis of multi-machine power systems under certain steady state assumptions that underly the usage of phasors. In this paper we show how to perform Kron reduction for a class of electrical networks without steady state assumptions. The reduced models can thus be used to analyze the transient as well as the steady state behavior of these electrical networks.

Secure estimation and control for cyber-physical systems under adversarial attacks

Abstract: The vast majority of today's critical infrastructure is supported by numerous feedback control loops and an attack on these control loops can have disastrous consequences. This is a major concern since modern control systems are becoming large and decentralized and thus more vulnerable to attacks. This paper is concerned with the estimation and control of linear systems when some of the sensors or actuators are corrupted by an attacker. In the first part we look at the estimation problem where we characterize the resilience of a system to attacks and study the possibility of increasing its resilience by a change of parameters. We then propose an efficient algorithm to estimate the state despite the attacks and we characterize its performance. Our approach is inspired from the areas of error-correction over the reals and compressed sensing. In the second part we consider the problem of designing output-feedback controllers that stabilize the system despite attacks. We show that a principle of separation between estimation and control holds and that the design of resilient output feedback controllers can be reduced to the design of resilient state estimators.

A Behavioral Algorithm for State of Charge Estimation

Abstract: In Hybrid Electricle Vehicles (HEV), performing online energy management is an important task to be achieved to reduce emissions, fuel consumption and increase vehicle performance. For this task, estimating the State of Charge (SOC) is needed since it serves as a measure of energy that is left inside an electrochemical battery. A variety of methods to solve this estimation problem have been proposed in the literature. However, most of these methods either assume equivalent circuit models for the battery and thus lose their validity under some discharge conditions or depend heavily on the choice of parameters in the algorithm. In this paper, we use behavioral framework to avoid postulation of a specific model for a battery and develop a new and simple SOC estimation algorithm. Once the problem is formulated as the computation of a specific free response of the battery, algorithm computes this response using only terminal current and terminal voltage measurements. We demonstrate the effectiveness of the algorithm with different discharge profiles using both simulated and real data.