Virtual Reference Feedback Tuning for non-minimum phase plants

Model reference control design methods fail when the plant has one or more non-minimum phase zeros that are not included in the reference model, leading possibly to an unstable closed loop. This is a very serious problem for data-based control design methods, where the plant is typically unknown. In this paper, we extend the Virtual Reference Feedback Tuning method to non-minimum phase plants. This extension is based on the idea proposed in Lecchini and Gevers (2002) for Iterative Feedback Tuning. We present a simple two-step procedure that can cope with the situation where the unknown plant may or may not have non-minimum phase zeros.     

Vision-based control for rigid body stabilization

This paper addresses the problem of stabilizing to a desired equilibrium point an eye-in-hand system, which consists of a single camera mounted on a rigid body free to move on . It is assumed that there is a collection of landmarks fixed in the environment and that the image coordinates of those landmarks are provided to the system by an on-board CCD camera. The proposed method addresses not only the problem of stabilization but also that of maintaining feature visibility along the system’s trajectory. The resulting solution consists of a feedback control law based on the current and desired image coordinates and reconstructed attitude and depth ratio information, which guarantees that (i) the desired equilibrium point is an almost global attractor; (ii) a set of necessary conditions for feature visibility holds throughout the system’s trajectories; and (iii) the image of a predefined feature point is kept inside the camera’s field of view.     

Feedback stabilization for high order feedforward nonlinear time-delay systems

This paper investigates the problem of global strong stabilization by state feedback, for a family of high order feedforward nonlinear time-delay systems. The uncertain nonlinearities are assumed to satisfy a polynomial growth assumption with an input or delayed input dependent rate. With the help of the appropriate Lyapunov–Krasovskii functionals, and a rescaling transformation with a gain to be tuned online by a dynamic equation, we propose a dynamic low gain state feedback control scheme. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.     

Identification and data-driven model reduction of state-space representations of lossless and dissipative systems from noise-free data

We illustrate procedures to identify a state-space representation of a lossless or dissipative system from a given noise-free trajectory; important special cases are passive systems and bounded-real systems. Computing a rank-revealing factorization of a Gramian-like matrix constructed from the data, a state sequence can be obtained; the state-space equations are then computed by solving a system of linear equations. This idea is also applied to perform model reduction by obtaining a balanced realization directly from data and truncating it to obtain a reduced-order model.     

Active fault tolerant control of discrete event systems using online diagnostics

The aim of this paper is to deal with the problem of fault tolerant control in the framework of discrete event systems modeled as automata. A fault tolerant controller is a controller able to satisfy control specifications both in nominal operation and after the occurrence of a fault. This task is solved by means of a parameterized controller that is suitably updated on the basis of the information provided by online diagnostics: the supervisor actively reacts to the detection of a malfunctioning component in order to eventually meet degraded control specifications. Starting from an appropriate model of the system, we recall the notion of safe diagnosability as a necessary step in order to achieve fault tolerant control. We then introduce two new notions: (i) “safe controllability”, which represents the capability, after the occurrence of a fault, of steering the system away from forbidden zones and (ii) “active fault tolerant system”, which is the property of safely continuing operation after faults. Finally, we show how the problem can be solved using a general control architecture based on the use of special kind of diagnoser, called “diagnosing controller”, which is used to safely detect faults and to switch between the nominal control policy and a bank of reconfigured control policies. A simple example is used to illustrate the new notions and the control architecture introduced in the paper.     

Certifying spatially uniform behavior in reaction–diffusion PDE and compartmental ODE systems

We present a condition that guarantees spatial uniformity for the asymptotic behavior of the solutions of a reaction–diffusion PDE with Neumann boundary conditions. This condition makes use of the Jacobian matrix of the reaction terms and the second Neumann eigenvalue of the Laplacian operator on the given spatial domain, and eliminates the global Lipschitz assumptions commonly used in mathematical biology literature. We then derive numerical procedures that employ linear matrix inequalities to certify this condition, and illustrate these procedures on models of several biochemical reaction networks. Finally, we present an analog of this PDE result for the synchronization of a network of identical ODE models coupled by diffusion terms. From a systems biology perspective, the main contribution of the paper is to blend analytical and numerical tools from nonlinear systems and control theory to derive a relaxed and verifiable condition for spatial uniformity of biological processes.     

An adaptive learning regulator for uncertain minimum phase systems with undermodeled unknown exosystems

The design of an adaptive learning regulator is addressed for uncertain minimum phase linear systems (with known bounds, known upper bound on system order, known relative degree, known high frequency gain sign) and for unknown exosystems (with unknown order, uncertain frequencies). On the basis of a known bound on system uncertainties and a known bound on the modeled exosystem frequencies, a new adaptive output error feedback control algorithm is proposed which guarantees exponential convergence of both the output and the control input errors into residual bounds which decrease as the exosystem modeling error decreases. Exponential convergence of both errors to zero is obtained when the regulator exactly models all exosystem excited frequencies, while asymptotic convergence of both errors to zero is achieved when the actual exosystem is overmodeled by the regulator. The new algorithm generalizes existing learning controllers since, in the case of periodic references and/or disturbances, the knowledge of the period is not required.     

Sensorless supervision of linear dynamical systems: The Feed-Forward Command Governor approach

This paper proposes a novel class of Command Governor (CG) strategies for input and state-related constrained discrete-time LTI systems subject to bounded disturbances in the absence of explicit state or output measurements. While in traditional CG schemes the set-point manipulation is undertaken on the basis of either the actual measure of the state or its suitable estimation, it is shown here that the CG design problem can be solved, with limited performance degradation and with similar properties, also in the case that such an explicit measure is not available. This approach, which will be referred to as the Feed-Forward CG (FF-CG) approach, may be a convenient alternative CG solution in all situations whereby the cost of measuring the state may be a severe limitation, e.g. in distributed or decentralized applications. In order to evaluate the method proposed here, numerical simulations on a physical example have been undertaken and comparisons with the standard state-based CG solution reported.     

Partial-realization theory for linear switched systems —A formal power series approach

The paper presents partial-realization theory and a realization algorithm for linear switched systems. The results are similar to partial-realization theory of linear and bilinear systems. Our main tool is the theory of rational formal power series.     

Feedback control of nonlinear stochastic systems for targeting a specified stationary probability density

In the present paper, an innovative procedure for designing the feedback control of multi-degree-of-freedom (MDOF) nonlinear stochastic systems to target a specified stationary probability density function (SPDF) is proposed based on the technique for obtaining the exact stationary solutions of the dissipated Hamiltonian systems. First, the control problem is formulated as a controlled, dissipated Hamiltonian system together with a target SPDF. Then the controlled forces are split into a conservative part and a dissipative part. The conservative control forces are designed to make the controlled system and the target SPDF have the same Hamiltonian structure (mainly the integrability and resonance). The dissipative control forces are determined so that the target SPDF is the exact stationary solution of the controlled system. Five cases, i.e., non-integrable Hamiltonian systems, integrable and non-resonant Hamiltonian systems, integrable and resonant Hamiltonian systems, partially integrable and non-resonant Hamiltonian systems, and partially integrable and resonant Hamiltonian systems, are treated respectively. A method for proving that the transient solution of the controlled system approaches the target SPDF as t→∞ is introduced. Finally, an example is given to illustrate the efficacy of the proposed design procedure.