Showing papers by "Paulo Tabuada published in 2010"

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

Abstract: 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.

Approximately Bisimilar Symbolic Models for Incrementally Stable Switched Systems

Abstract: Switched systems constitute an important modeling paradigm faithfully describing many engineering systems in which software interacts with the physical world. Despite considerable progress on stability and stabilization of switched systems, the constant evolution of technology demands that we make similar progress with respect to different, and perhaps more complex, objectives. This paper describes one particular approach to address these different objectives based on the construction of approximately equivalent (bisimilar) symbolic models for switched systems. The main contribution of this paper consists in showing that under standard assumptions ensuring incremental stability of a switched system (i.e., existence of a common Lyapunov function, or multiple Lyapunov functions with dwell time), it is possible to construct a finite symbolic model that is approximately bisimilar to the original switched system with a precision that can be chosen a priori. To support the computational merits of the proposed approach, we use symbolic models to synthesize controllers for two examples of switched systems, including the boost dc-dc converter.

PESSOA: a tool for embedded controller synthesis

Abstract: In this paper we present Pessoa, a tool for the synthesis of correct-by-design embedded control software Pessoa relies on recent results on approximate abstractions of control systems to reduce the synthesis of control software to the synthesis of reactive controllers for finite-state models We describe the capabilities of Pessoa and illustrate them through an example.

Automatic verification of control system implementations

Abstract: 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.

Decentralized event-triggered control over wireless sensor/actuator networks

Abstract: In recent years we have witnessed a move of the major industrial automation providers into the wireless domain. While most of these companies already offer wireless products for measurement and monitoring purposes, the ultimate goal is to be able to close feedback loops over wireless networks interconnecting sensors, computation devices, and actuators. In this paper we present a decentralized event-triggered implementation, over sensor/actuator networks, of centralized nonlinear controllers. Event-triggered control has been recently proposed as an alternative to the more traditional periodic execution of control tasks. In a typical event-triggered implementation, the control signals are kept constant until the violation of a condition on the state of the plant triggers the re-computation of the control signals. The possibility of reducing the number of re-computations, and thus of transmissions, while guaranteeing desired levels of performance makes event-triggered control very appealing in the context of sensor/actuator networks. In these systems the communication network is a shared resource and event-triggered implementations of control laws offer a flexible way to reduce network utilization. Moreover reducing the number of times that a feedback control law is executed implies a reduction in transmissions and thus a reduction in energy expenditures of battery powered wireless sensor nodes.

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.

Symbolic Approximate Time-Optimal Control

Abstract: There is an increasing demand for controller design techniques capable of addressing the complex requirements of todays embedded applications. This demand has sparked the interest in symbolic control where lower complexity models of control systems are used to cater for complex specifications given by temporal logics, regular languages, or automata. These specification mechanisms can be regarded as qualitative since they divide the trajectories of the plant into bad trajectories (those that need to be avoided) and good trajectories. However, many applications require also the optimization of quantitative measures of the trajectories retained by the controller, as specified by a cost or utility function. As a first step towards the synthesis of controllers reconciling both qualitative and quantitative specifications, we investigate in this paper the use of symbolic models for time-optimal controller synthesis. We consider systems related by approximate (alternating) simulation relations and show how such relations enable the transfer of time-optimality information between the systems. We then use this insight to synthesize approximately time-optimal controllers for a control system by working with a lower complexity symbolic model. The resulting approximately time-optimal controllers are equipped with upper and lower bounds for the time to reach a target, describing the quality of the controller. The results described in this paper were implemented in the Matlab Toolbox Pessoa which we used to workout several illustrative examples reported in this paper.

Dynamic Scheduling and Control-Quality Optimization of Self-Triggered Control Applications

Abstract: Time-triggered periodic control implementations are over provisioned for many execution scenarios in which the states of the controlled plants are close to equilibrium. To address this inefficient use of computation resources, researchers have proposed self-triggered control approaches in which the control task computes its execution deadline at runtime based on the state and dynamical properties of the controlled plant. The potential advantages of this control approach cannot, however, be achieved without adequate online resource-management policies. This paper addresses scheduling of multiple self-triggered control tasks that execute on a uniprocessor platform, where the optimization objective is to find trade-offs between the control performance and CPU usage of all control tasks. Our experimental results show that efficiency in terms of control performance and reduced CPU usage can be achieved with the heuristic proposed in this paper.

On the minimum attention and anytime attention problems for nonlinear systems

Abstract: The current convergence of control, communication and computation opens the door to new avenues for the applicability of control systems, but it also leads to new constraints and requirements. The traditional quadratic cost function has become too plain to represent the diverse performance indices of today's complex applications. For instance, the implementation cost of a control law has become a major factor, since resources are frequently shared among different tasks. Implementation costs of control laws depend on a wide range of factors: computation complexity, sensor accuracy, required bandwidth, actuation speed, or sampling rates, to name a few. In this paper we focus on the notion of attention, that is, how often the loop needs to be closed in order to achieve a desired performance. We propose two attention-aware control laws: first, a technique to construct minimum attention control laws that maximizes the open loop operation of a nonlinear control system; and second, a control algorithm that permits the system run in open loop for a pre-scheduled amount of time.

Approximate time-optimal control via approximate alternating simulations

Abstract: Symbolic models of control systems have recently been used to synthesize controllers enforcing specifications given by temporal logics, regular languages, or automata. These specification mechanisms can be regarded as qualitative since they divide the set of trajectories into bad trajectories (those that should be eliminated by control) and good trajectories (those that need not be eliminated). In many situations, however, a quantitative specification, where each trajectory is assigned a cost, is more appropriate. As a first step towards the synthesis of controllers enforcing qualitative and quantitative specifications we investigate in this paper the use of symbolic models for timeoptimal controller synthesis. Our results show that it is possible to obtain upper and lower bounds for the time to reach a desired target by an algorithmic analysis of the symbolic model. Moreover, we can also algorithmically synthesize a feedback controller enforcing the upper bound. All the algorithms have been implemented using Binary Decision Diagrams and are illustrated by some examples.

Towards backstepping design for incremental stability

Abstract: The notion of incremental stability has been successfully used as a tool for the analysis and design of intrinsic observers, output regulation of nonlinear systems, frequency estimators, synchronization of coupled identical dynamical systems, symbolic models for nonlinear control systems, and bio-molecular systems. However, most of the existing controller design techniques provide controllers enforcing stability rather than incremental stability. Hence, there is a growing need for design methods for incremental stability. In this paper, we take a step in this direction by developing a backstepping design approach to incremental stability. The effectiveness of the proposed method is illustrated by synthesizing a controller rendering a magnetic levitator incrementally stable.

Symbolic models for unstable nonlinear control systems

Abstract: In this paper we take an important step in our quest to synthesize correct-by-design embedded control software for nonlinear systems. We have shown in previous work that by relying on diverse stability and stabilizability assumptions it is possible to construct finite-state models describing the dynamics of nonlinear control systems. Such finite-state models enable the use of algorithmic techniques to automatically synthesize controllers enforcing control and software requirements. In the present paper, we show that similar results can still be obtained by replacing the stability or stabilizability assumptions by the much weaker assumption of incremental forward completeness. We illustrate the new results by synthesizing a controller for an inverted pendulum subject to a schedulability constraint.

Safety-Guarantee Controller Synthesis for Cyber-Physical Systems

Abstract: The verification and validation of cyber-physical systems is known to be a difficult problem due to the different modeling abstractions used for control components and for software components A recent trend to address this difficulty is to reduce the need for verification by adopting correct-by-design methodologies According to the correct-by-design paradigm, one seeks to automatically synthesize a controller that can be refined into code and that enforces temporal specifications on the cyber-physical system In this paper we consider an instance of this problem where the specifications are given by a fragment of Linear Temporal Logic (LTL) and the physical environment is described by a smooth differential equation The contribution of this paper is to show that synthesis for cyber-physical systems is viable by considering a fragment of LTL that is expressive enough to describe interesting properties but simple enough to avoid Safra's construction We report on two examples illustrating a preliminary implementation of these techniques on the tool PESSOALTL

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 smooth 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.

Backstepping design for incremental stability

Abstract: Stability is arguably one of the core concepts upon which our understanding of dynamical and control systems has been built. The related notion of incremental stability, however, has received much less attention until recently, when it was successfully used as a tool for the analysis and design of intrinsic observers, output regulation of nonlinear systems, frequency estimators, synchronization of coupled identical dynamical systems, symbolic models for nonlinear control systems, and bio-molecular systems. However, most of the existing controller design techniques provide controllers enforcing stability rather than incremental stability. Hence, there is a growing need to extend existing methods or develop new ones for the purpose of designing incrementally stabilizing controllers. In this paper, we develop a backstepping design approach for incremental stability. The effectiveness of the proposed method is illustrated by synthesizing a controller rendering a synchronous generator incrementally stable.