Showing papers by "Paulo Tabuada published in 2009"

Verification and Control of Hybrid Systems: A Symbolic Approach

Abstract: Hybrid systems describe the interaction of software, described by finite models such as finite-state machines, with the physical world, described by infinite models such as differential equations. This book addresses problems of verification and controller synthesis for hybrid systems. Although these problems are very difficult to solve for general hybrid systems, several authors have identified classes of hybrid systems that admit symbolic or finite models. The novelty of the book lies on the systematic presentation of these classes of hybrid systems along with the relationships between the hybrid systems and the corresponding symbolic models. To show how the existence of symbolic models can be used for verification and controller synthesis, the book also outlines several key results for the verification and controller design of finite systems. Several examples illustrate the different methods and techniques discussed in the book.

Verification and Control of Hybrid Systems

Abstract: In what case do you like reading so much? What about the type of the verification and control of hybrid systems book? The needs to read? Well, everybody has their own reason why should read some books. Mostly, it will relate to their necessity to get knowledge from the book and want to read just to get entertainment. Novels, story book, and other entertaining books become so popular this day. Besides, the scientific books will also be the best reason to choose, especially for the students, teachers, doctors, businessman, and other professions who are fond of reading.

Symbolic Models for Nonlinear Control Systems: Alternating Approximate Bisimulations

Abstract: Symbolic models are abstract descriptions of continuous systems in which symbols represent aggregates of continuous states In the last few years there has been a growing interest in the use of symbolic models as a tool for mitigating complexity in control design In fact, symbolic models enable the use of well-known algorithms in the context of supervisory control and algorithmic game theory for controller synthesis Since the 1990s many researchers faced the problem of identifying classes of dynamical and control systems that admit symbolic models In this paper we make further progress along this research line by focusing on control systems affected by disturbances Our main contribution is to show that incrementally globally asymptotically stable nonlinear control systems with disturbances admit symbolic models

On self-triggered control for linear systems: Guarantees and complexity

Abstract: Typical digital implementations of feedback controllers periodically measure the state, compute the control law, and update the actuators. Although periodicity simplifies the analysis and implementation, it results in a conservative usage of resources. In this paper we drop the periodicity assumption in favor of self-trigger strategies that decide when to measure the state, execute the controller, and update the actuators according to the current state of the system. In particular, we develop a general procedure leading to self-triggered implementations of feedback controllers, that highly reduces the number of controller executions while guaranteeing a desired level of performance. We also analyze the inherent trade-off between the computational resources required for the self-triggered implementation and the resulting performance. The theoretical results are applied to a physical example to show the benefits of the approach.

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

Abstract: 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.

Symbolic models for nonlinear time-delay systems using approximate bisimulations

Abstract: Time-delay systems are an important class of dynamical systems which provide a solid mathematical framework to deal with many application domains of interest ranging from biology, chemical, electrical, and mechanical engineering, to economics. However, the inherent complexity of such systems poses serious difficulties to control design, when control objectives depart from the standard ones investigated in the current literature, e.g. stabilization, regulation, and etc. In this paper we propose one approach to control design, which is based on the construction of symbolic models, where each symbolic state and each symbolic label correspond to an aggregate of continuous states and to an aggregate of input signals in the original system. The use of symbolic models offers a systematic methodology for control design in which constraints coming from software and hardware, interacting with the physical world, can be integrated. The main contribution of this paper is in showing that incrementally input-to-state stable time-delay systems do admit symbolic models that are approximately bisimilar to the original system, with a precision that can be rendered as small as desired. An algorithm is also presented which computes the proposed symbolic models. When the state and input spaces of time-delay systems are bounded, which is the case in many realistic situations, the proposed algorithm is shown to terminate in a finite number of steps.

Input-to-state stability of self-triggered control systems

Abstract: Event-triggered and self-triggered control have recently been proposed as an alternative to periodic implementations of feedback control laws over sensor/actuator networks. In event-triggered control, each sensing node continuously monitors the plant in order to determine if fresh information should be transmitted and if the feedback control law should be recomputed. In general, event-triggered control substantially reduces the number of exchanged messages when compared with periodic implementations. However, such energy savings must be contrasted with the energy required to perform local computations. In self-triggered control, computation of the feedback control law is followed by the computation of the next time instant at which fresh information should be sensed and transmitted. Since this time instant is computed as a function of the current state and plant dynamics, it is still much larger than the sampling period used in periodic implementations. Moreover, no energy is spent in local computations at the sensors. However, the plant operates in open-loop between updates of the feedback control law and robustness is a natural concern. We analyze the robustness to disturbances of a self-triggered implementation recently introduced by the authors for linear control systems. We show that such implementation is exponentially input-to-state stable with respect to disturbances.

Isochronous manifolds in self-triggered control

Abstract: Feedback control laws are predominantly implemented on digital platforms as periodic tasks. Although periodicity simplifies the analysis and design of the implementation, new applications call for more efficient utilization of available resources such as processor utilization. To address this issue, new implementation paradigms, such as event-triggered and self-triggered control, have recently been proposed. These policies allow for a dynamic allocation of resources, since the execution times of the control task are defined according to the current state of the system. In this paper we continue our exploratory journey in the field of self-triggered control for nonlinear systems. In our previous work, we exploited the geometry of homogeneous and polynomial control systems to identify one dimensional manifolds along which the execution times scaled in a predictable manner. In this paper we complement our previous work by focusing on manifolds where the times remain constant. By merging both ideas new self-trigger conditions are derived, outperforming existing techniques.

A symbolic model approach to the digital control of nonlinear time-delay systems

Abstract: In this paper we propose an approach to control design of nonlinear time-delay systems, which is based on the construction of symbolic models, where each symbolic state and each symbolic label correspond to an aggregate of continuous states and to an aggregate of input signals in the original system. The use of symbolic models offers a systematic methodology for control design in which constraints coming from software and hardware, interacting with the physical world, can be integrated. The main contribution of this paper is in showing that incrementally input-to-state stable time-delay systems do admit symbolic models that are approximately bisimilar to the original system, with a precision that can be rendered as small as desired. An algorithm is also presented which computes the proposed symbolic models. When the state and input spaces of time-delay systems are bounded the proposed algorithm is shown to terminate in a finite number of steps.

Self-Triggered Control: trading actuation for computation

Abstract: 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 over the same hardware. We present a self-triggered implementation of linear controllers for control systems 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.

Exact symbolic models for verification

Abstract: The evolution of physical quantities such as position, temperature, humidity, etc, is usually described by differential equations with solutions evolving on \({\mathbb R}^n\) or appropriate subsets. The infinite cardinality of \({\mathbb R}^n\) prevents a direct application of the verification methods described in Chapter 5. However, verification algorithms are still applicable whenever suitable finite-state abstractions of these infinite-state systems can be constructed. In recent years, several methods have been proposed for the construction of these abstractions based on a very interesting blend of different mathematical techniques. We present several of these methods starting with timed automata to illustrate the general principles of the abstraction process. Most of the abstraction techniques described in this chapter require linear differential equations. For this reason, we discuss as a special topic how to transform a class of nonlinear differential equations into linear di_erential equations in larger state spaces.

Approximate symbolic models for verification

Abstract: The abstraction techniques presented in Chapter 7 and Chapter 8 were based on the construction of quotient systems In generalizing exact to approximate similarity relationships, we abandon quotient based abstractions to focus on a different abstraction technique introduced in this chapter for affine dynamical systems Similar results for nonlinear dynamical systems are presented as special topics The results in Chapter 11 further enlarge the class of approximate symbolic models for verification by considering the effect of adversarial inputs

A symbolic model approach to the digital control of nonlinear time-delay systems

Abstract: In this paper we propose an approach to control design of nonlinear time-delay systems, which is based on the construction of symbolic models, where each symbolic state and each symbolic label correspond to an aggregate of continuous states and to an aggregate of input signals in the original system. The use of symbolic models offers a systematic methodology for control design in which constraints coming from software and hardware, interacting with the physical world, can be integrated. The main contribution of this paper is in showing that incrementally input-to-state stable time-delay systems do admit symbolic models that are approximately bisimilar to the original system, with a precision that can be rendered as small as desired. An algorithm is also presented which computes the proposed symbolic models. When the state and input spaces of time-delay systems are bounded the proposed algorithm is shown to terminate in a finite number of steps.