Passivity-based control of implicit port-Hamiltonian systems with holonomic constraints

Implicit port-Hamiltonian representations of mechanical systems are considered from a control perspective. Energy shaping is used for the purpose of stabilizing a desired equilibrium. When using implicit models, the problem turns out to be a simple quadratic programming problem (as opposed to the partial differential equations that need to be solved when using explicit representations). The described approach is generalized to address the problem of stabilization of homoclinic orbits thus leading to the formulation of swing-up strategies for underactuated systems.     

Asymptotic stabilization via control by interconnection of port-Hamiltonian systems

We study the asymptotic properties of control by interconnection, a passivity-based controller design methodology for stabilization of port-Hamiltonian systems. It is well-known that the method, in its basic form, imposes some unnatural controller initialization to yield asymptotic stability of the desired equilibrium. We propose two different ways to overcome this restriction, one based on adaptation ideas, and the other one adding an extra damping injection to the controller. The analysis and design principles are illustrated through an academic example.     

Dirac structures on Hilbert spaces and boundary control of distributed port-Hamiltonian systems

Aim of this paper is to show how the Dirac structure properties can be exploited in the development of energy-based boundary control laws for distributed port-Hamiltonian systems. Usually, stabilization of non-zero equilibria has been achieved by looking at, or generating, a set of structural invariants, namely Casimir functions, in closed-loop. Since this approach fails when an infinite amount of energy is required at the equilibrium (dissipation obstacle), this paper illustrates a novel approach that enlarges the class of stabilizing controllers. The starting point is the parametrization of the dynamics provided by the image representation of the Dirac structure, that is able to show the effects of the boundary inputs on the state evolution. In this way, energy-balancing and control by state-modulated source methodologies are extended to the distributed parameter scenario, and a geometric interpretation of these control techniques is provided. The theoretical results are discussed with the help of a simple but illustrative example, i.e. a transmission line with an RLC load in both serial and parallel configurations. In the latter case, energy-balancing controllers are not able to stabilize non-zero equilibria because of the dissipation obstacle. The problem is solved thanks to a (boundary) state-modulated source.     

Explicit simplicial discretization of distributed-parameter port-Hamiltonian systems

Simplicial Dirac structures as finite analogues of the canonical Stokes–Dirac structure, capturing the topological laws of the system, are defined on simplicial manifolds in terms of primal and dual cochains related by the coboundary operators. These finite-dimensional Dirac structures offer a framework for the formulation of standard input–output finite-dimensional port-Hamiltonian systems that emulate the behavior of distributed-parameter port-Hamiltonian systems. This paper elaborates on the matrix representations of simplicial Dirac structures and the resulting port-Hamiltonian systems on simplicial manifolds. Employing these representations, we consider the existence of structural invariants and demonstrate how they pertain to the energy shaping of port-Hamiltonian systems on simplicial manifolds.     

Asymptotic stability of port-Hamiltonian systems with constant inputs

In this paper,the asymptotic stability of Port-Hamiltonian (PH) systems with constant inputs is studied.Constant inputs are useful for stabilizing systems at th...     

Achievable behavior of general systems

A basic question in systems and control theory concerns the characterization of the set of all achievable closed-loop systems for a given plant system and a controller system to be designed. This problem is addressed in a general behavioral context. Sufficient, and often necessary, conditions for a behavior to be achievable are given, and for any achievable behavior a canonical controller is defined. The results generalize previously obtained results obtained for finite-dimensional linear systems. The application to nonlinear differential systems is outlined.     

Full-order observer design for a class of port-Hamiltonian systems

We consider a special class of port-Hamiltonian systems for which we propose a design methodology for constructing globally exponentially stable full-order observers using a passivity based approach. The essential idea is to make the augmented system consisting of the plant and the observer dynamics to become strictly passive with respect to an invariant manifold defined on the extended state-space, on which the state estimation error is zero. We first introduce the concept of passivity of a system with respect to a manifold by defining a new input and output on the extended state-space and then perform a partial state feedback passivation which leads to the construction of the observer. We then illustrate this observer design procedure on two physical examples, the magnetic levitation system and the inverted pendulum on the cart system.     

Robust integral control of port-Hamiltonian systems: The case of non-passive outputs with unmatched disturbances

Regulation of passive outputs of nonlinear systems can be easily achieved with an integral control (IC). In many applications, however, the signal of interest is not a passive output and ensuring its regulation remains an open problem. Also, IC of passive systems rejects constant input disturbances, but no similar property can be ensured if the disturbance is not matched. In this paper we address the aforementioned problems and propose a procedure to design robust ICs for port-Hamiltonian models, that characterize the behavior of a large class of physical systems. Necessary and sufficient conditions for the solvability of the problem, in terms of some rank and controllability properties of the linearized system, are provided. For a class of fully actuated mechanical systems, a globally asymptotically stabilizing solution is given. Simulations of the classical pendulum system illustrate the good performance of the scheme.     

Achievable sensitivity bounds for MIMO control systems via an information theoretic approach

This paper deals with an MIMO feedback control system that has two channels with additive noises and studies the effects of the noises on the input and output signals of the plant. We derive achievable bounds of integral type for sensitivity-like properties of the system based on an information theoretic approach. These bounds are generalizations of Bode’s integral formula for the case that the feedback system includes nonlinear elements.     

Energy shaping of distributed parameter port-Hamiltonian systems based on finite element approximation

The main contribution of this paper is a procedure for the control by energy shaping via Casimir generation of infinite dimensional port-Hamiltonian systems based on a particular finite element approximation. The proposed approach is justified by the fact that the adopted spatial discretization technique is able to preserve Casimir functions in the closed-loop system when going from the distributed to the (approximated) lumped parameter system. Besides the intrinsic difficulties related to the large number of state variables, the finite element model is generally given in terms of a Dirac structure and is completely a-causal, which implies that the plant dynamics is not given in standard input-state-output form, but as a set of DAEs. Consequently, the classical energy Casimir method has to be extended in order to deal with dynamical systems with constraints, usually appearing in the form of Lagrangian multipliers. The general methodology is illustrated with the help of an example in which the distributed parameter system is a lossless transmission line.     

A port-Hamiltonian formulation of physical switching systems with varying constraints

This paper extends a generic method to design a port-Hamiltonian formulation modeling all geometric interconnection structures of a physical switching system with varying constraints. A non-minimal kernel representation of this family of structures (named Dirac structures) is presented. It is derived from the parameterized incidence matrices which are a mathematical representation of the primal and dual dynamic network graphs associated with the system. This representation has the advantage of making it possible to model complex physical switching systems with varying constraints and to fall within the framework of passivity-based control.     

Jet bundle formulation of infinite-dimensional port-Hamiltonian systems using differential operators

We consider infinite-dimensional port-Hamiltonian systems described on jet bundles. Based on a power balance relation we introduce the port-Hamiltonian system representation using differential operators regarding the structural mapping, the dissipation mapping and the input mapping. In contrast to the well-known representation on the basis of the underlying Stokes–Dirac structure our approach is not necessarily based on using energy-variables which leads to a different port-Hamiltonian representation of the analyzed partial differential equations. The presented constructions will be specialized to mechanical systems to which class also the presented examples belong.     

Achievable performance of multivariable systems with unstable zeros and poles

This paper examines the fundamental limitations imposed by unstable (right half plane; RHP) zeros and poles in multivariable feedback systems. We generalize previously known controller-independent lower bounds on the H     

Structure preserving model reduction of port-Hamiltonian systems by moment matching at infinity

Model reduction of port-Hamiltonian systems by means of the Krylov methods is considered, aiming at port-Hamiltonian structure preservation. It is shown how to employ the Arnoldi method for model reduction in a particular coordinate system in order to preserve not only a specific number of the Markov parameters but also the port-Hamiltonian structure for the reduced order model. Furthermore it is shown how the Lanczos method can be applied in a structure preserving manner to a subclass of port-Hamiltonian systems which is characterized by an algebraic condition. In fact, for the same subclass of port-Hamiltonian systems the Arnoldi method and the Lanczos method turn out to be equivalent in the sense of producing reduced order port-Hamiltonian models with the same transfer function.     

A dual relation between port-Hamiltonian systems and the Brayton-Moser equations for nonlinear switched RLC circuits

In the last decades, several researchers have concentrated on the dynamic modeling of nonlinear electrical circuits from an energy-based perspective. A recent perspective is based on the concept of port-Hamiltonian (PH) systems. In this paper, we discuss the relations between the classical Brayton-Moser (BM) equations—stemming from the early sixties—and PH models for topologically complete nonlinear RLC circuits, with and without controllable switches. It will be shown that PH systems precisely dualize the BM equations, leading to possible advantages at the level of controller design. Consequently, useful and important properties of the one framework can be translated to the other. Control designs for the PH model cannot be directly implemented since they require observation of flux and charges, which are not directly available through standard sensors, while the BM models require only observation of currents and voltages. The introduced duality allows to pull back PH designs to the space of currents and voltages. This offers the possibility to exchange several different techniques, available in the literature, for modeling, analysis and controller design for RLC circuits. Illustrative examples are provided to emphasize the duality between both frameworks.     

Case-based reasoning and its implications for legal expert systems

Reasoners compare problems to prior cases to draw conclusions about a problem and guide decision making. All Case-Based Reasoning (CBR) employs some methods for generalizing from cases to support indexing and relevance assessment and evidences two basic inference methods: constraining search by tracing a solution from a past case or evaluating a case by comparing it to past cases. Across domains and tasks, however, humans reason with cases in subtly different ways evidencing different mixes of and mechanisms for these components.In recent CBR research in Artificial Intelligence (AI), five paradigmatic approaches have emerged: statistically-oriented, model-based, planning/design-oriented, exemplar-based, and adversarial or precedent-based. The paradigms differ in the assumptions they make about domain models, the extent to which they support symbolic case comparison, and the kinds of inferences for which they employ cases.Reasoning with cases is important in legal practice of all kinds, and legal practice involves a wide variety of case-based tasks and methods. The paradigms' respective benefits and costs suggest different approaches for different legal tasks.CBR research and development in the field of AI and Law should be pursued vigoriously for several reasons. CBR can supplement rule-based expert systems, improving their abilities to reason about statutory predicates, solve problems efficiently, and explain their results. CBR can also contribute to the design of intelligent legal data retrieval systems and improve legal document assembly programs. Finally, in cognitive studies of various fields, it can model methods of transforming ill-structured problems into better structured ones through the use of case comparisons.     

可重构技术及其在网络控制系统中的应用综述

可重构技术在对系统的维护、优化、扩展以及自适应、自组织、自恢复上有其独特的优势．对此,介绍了可重构技术的基本原理、实现方法和应用领域;阐述了其在网络控制系统中分别对系统、节点和协议的应用．并对其发展趋势进行了展望．