An energy-balancing perspective of interconnection and damping assignment control of nonlinear systems

Stabilization of nonlinear feedback passive systems is achieved assigning a storage function with a minimum at the desired equilibrium. For physical systems a natural candidate storage function is the difference between the stored and the supplied energies—leading to the so-called energy-balancing control, whose underlying stabilization mechanism is particularly appealing. Unfortunately, energy-balancing stabilization is stymied by the existence of pervasive dissipation, that appears in many engineering applications. To overcome the dissipation obstacle the method of Interconnection and Damping Assignment, that endows the closed-loop system with a special—port-controlled Hamiltonian—structure, has been proposed. If, as in most practical examples, the open-loop system already has this structure, and the damping is not pervasive, both methods are equivalent. In this brief note we show that the methods are also equivalent, with an alternative definition of the supplied energy, when the damping is pervasive. Instrumental for our developments is the observation that, swapping the damping terms in the classical dissipation inequality, we can establish passivity of port-controlled Hamiltonian systems with respect to some new external variables—but with the same storage function.     

Manipulator motion control in operational space using joint velocity inner loops

This paper addresses the operational space motion control—trajectory tracking—of robot manipulators endowed with joint velocity feedback inner loops. A general structure for model-based joint velocity controllers is proposed for the inner loop. The required joint velocity reference is provided by an outer loop inspired from the robot kinematic control approach. It is shown that above two-loops control schemes lead to a nice cascade structure for the corresponding closed-loop systems. A stability result adapted for analysis of this particular kind of systems is developed in the paper; sufficient conditions for global exponential stability of this class of cascade systems are obtained. The effectiveness of the proposed control approach is evaluated on a direct-drive mechanical arm, and compared with a typical control strategy based on inverse kinematics resolution for computation of the desired motion in joint space, and the use of the computed-torque technique. The experimental evidences show better performance of the proposed two-loops controller.     

Self-tuning regulators for a class of multivariable systems

Control of a class of multivariable systems described by linear vector difference equations with constant but unknown parameters is discussed. A multivariable minimum variance strategy is first presented. This gives a generalization of the minimum variance strategy for single-input single-output systems. A multivariable self-tuning regulator based on the minimum variance strategy is then proposed. It uses a recursive least squares estimator and a linear controller obtained directly from the current estimates. The asymptotic properties of the algorithm are discussed. If the estimated parameters converge, the resulting controller will under certain conditions give the minimum variance strategy. The analysis also gives insight into the case when several single-input single-output self-tuning regulators are operating in cascade mode.     

Approximating the buffer allocation problem using epochs

The correctness of applications that perform asynchronous message passing typically relies on the underlying hardware having a sufficient amount of memory (message buffers) to hold all undelivered messages—such applications may deadlock when executed on a system with an insufficient number of message buffers. Thus, determining the minimum number of buffers that an application needs to prevent deadlock is an important task when writing portable parallel applications. Unfortunately, both this problem (called the Buffer Allocation Problem) and the simpler problem of determining whether an application may deadlock for a given number of available message buffers are intractable [A. Brodsky, J. Pedersen, A. Wagner, On the complexity of buffer allocation in message passing systems, Journal of Parallel and Distributed Computing 65 (2005) 692–713].     

Asymptotic stabilization of passive systems without damping injection: A sampled integral technique

Passivity in physical systems is a restatement of energy balancing, and therefore is a ubiquitous property in engineering applications. Under some weak conditions, the unique equilibrium state of passive systems is stable. However, to ensure asymptotic stability, strict output passivity and a detectability property are required. Although strict output passivity may be enforced via a damping injection that feeds back the passive output, this signal may be noisy or unmeasurable — the paradigmatic example being velocity in mechanical systems. In this paper a sampled integral stabilization (SIS) technique for the asymptotic regulation of passive systems, that requires only the knowledge of the time integral of the passive output — i.e. position in mechanical systems — is proposed. As a generalization of the previous result, it is shown that SIS is applicable to cascade connections of passive systems measuring only the storage function of the second one. Several examples, including a planar elbow manipulator and the rigid body dynamics are shown to satisfy the assumptions for the application of SIS.     

一种直接多变量自适应解耦控制算法

本文将广义最小方差控制策略和前馈控制策略结合进来,提出了解耦控制器并讨论了如何采用修改最小二乘辨识算法和直接方案对具有任意延时结构的一般随机多变量系统实现自适应解耦控制,本文还证明了所提出的自适应算法即使用于开环不稳定或非最小相位系统也具有整体稳定性和收敛性。     

A linear process-algebraic format with data for probabilistic automata

This paper presents a novel linear process-algebraic format for probabilistic automata. The key ingredient is a symbolic transformation of probabilistic process algebra terms that incorporate data into this linear format while preserving strong probabilistic bisimulation. This generalises similar techniques for traditional process algebras with data, and — more importantly — treats data and data-dependent probabilistic choice in a fully symbolic manner, leading to the symbolic analysis of parameterised probabilistic systems. We discuss several reduction techniques that can easily be applied to our models. A validation of our approach on two benchmark leader election protocols shows reductions of more than an order of magnitude.     

Note on covering monotone orthogonal polygons with star-shaped polygons

In 1986, Keil provided an O(n²) time algorithm for the problem of covering monotone orthogonal polygons with the minimum number of r-star-shaped orthogonal polygons. This was later improved to O(n) time and space by Gewali et al. in [L. Gewali, M. Keil, S.C. Ntafos, On covering orthogonal polygons with star-shaped polygons, Information Sciences 65 (1992) 45-63]. In this paper we simplify the latter algorithm—we show that with a little modification, the first step Sweep1 of the discussed algorithm—which computes the top ceilings of horizontal grid segments—can be omitted.In addition, for the minimum orthogonal guard problem in the considered class of polygons, our approach provides a linear time algorithm which uses O(k) additional space, where k is the size of the optimal solution—the algorithm in [L. Gewali, M. Keil, S.C. Ntafos, On covering orthogonal polygons with star-shaped polygons, Information Sciences 65 (1992) 45-63] uses both O(n) time and O(n) additional space.     

Hybrid parallel computing of minimum action method

In this work, we report a hybrid (MPI/OpenMP) parallelization strategy for the minimum action method recently proposed in [17]. For nonlinear dynamical systems, the minimum action method is a useful numerical tool to study the transition behavior induced by small noise and the structure of the phase space. The crucial part of the minimum action method is to minimize the Freidlin–Wentzell action functional. Due to the fact that the corresponding Euler–Lagrange equation is, in general, highly nonlinear and of high order, we solve the optimization problem directly instead of discretizing the Euler–Lagrange equation to provide a general but equivalent numerical framework. To enhance the efficiency of the minimum action method for general dynamical systems we consider parallel computing. In particular, we present a hybrid parallelization strategy based on MPI and OpenMP. Numerical results are presented to demonstrate the efficiency of the proposed parallelization strategy.