Consistency analysis of some closed-loop subspace identification methods

We study statistical consistency of two recently proposed subspace identification algorithms for closed-loop systems. These algorithms may be seen as implementations of an abstract state-space construction procedure described by the authors in previous work on stochastic realization of closed-loop systems. A detailed error analysis is undertaken which shows that both algorithms are biased due to an unavoidable mishandling of initial conditions which occurs in closed-loop identification. Instability of the open loop system may also be a cause of trouble.     

Discrete-time certainty equivalence output feedback: allowing discontinuous control laws including those from model predictive control

We present certainty equivalence output feedback results for discrete-time nonlinear systems that employ possibly discontinuous control laws in the feedback loop. Coupling assumptions of nominal robustness with uniform observability or detectability assumptions, we assert nominally robust stability for output feedback closed loops. We further show that model predictive control (MPC) can be used to generate a feedback control law that is robustly globally asymptotically stabilizing when used in a certainty equivalence output feedback closed loop. Allowing for discontinuous feedback control laws is important for systems employing MPC, since the method can, and sometimes necessarily does, result in discontinuous control laws.     

Nonlinear system identification via direct weight optimization

A general framework for estimating nonlinear functions and systems is described and analyzed in this paper. Identification of a system is seen as estimation of a predictor function. The considered predictor function estimate at a particular point is defined to be affine in the observed outputs and the estimate is defined by the weights in this expression. For each given point, the maximal mean-square error (or an upper bound) of the function estimate over a class of possible true functions is minimized with respect to the weights, which is a convex optimization problem. This gives different types of algorithms depending on the chosen function class. It is shown how the classical linear least squares is obtained as a special case and how unknown-but-bounded disturbances can be handled.Most of the paper deals with the method applied to locally smooth predictor functions. It is shown how this leads to local estimators with a finite bandwidth, meaning that only observations in a neighborhood of the target point will be used in the estimate. The size of this neighborhood (the bandwidth) is automatically computed and reflects the noise level in the data and the smoothness priors.The approach is applied to a number of dynamical systems to illustrate its potential.     

On controllability and trajectory tracking of a kinematic vehicle model

This paper presents some further results concerning the issues of controllability and trajectory tracking regarding a front-wheel drive vehicle kinematic model. A simple procedure for computing an open-loop control strategy that transfers the system between given initial and final states, is presented. In particular, the input function is computed by means of a set of linear algebraic equations. The resulting motion planning procedure allows us to present a control scheme for solving the trajectory (a time-parameterized reference signal) tracking problem. Various applications of the approach in forward and backward motions are considered, and simulation results are presented.     

Identification of piecewise affine systems based on statistical clustering technique

This paper is concerned with the identification of a class of piecewise affine systems called a piecewise affine autoregressive exogenous (PWARX) model. The PWARX model is composed of ARX sub-models each of which corresponds to a polyhedral region of the regression space. Under the temporary assumption that the number of sub-models is known a priori, the input-output data are collected into several clusters by using a statistical clustering algorithm. We utilize support vector classifiers to estimate the boundary hyperplane between two adjacent regions in the regression space. In each cluster, the parameter vector of the sub-model is obtained by the least squares method. It turns out that the present statistical clustering approach enables us to estimate the number of sub-models based on the information criteria such as CAIC and MDL. The estimate of the number of sub-models is performed by applying the identification procedure several times to the same data set, after having fixed the number of sub-models to different values. Finally, we verify the applicability of the present identification method through a numerical example of a Hammerstein model.     

Safe diagnosability for fault-tolerant supervision of discrete-event systems

The problem of achieving fault-tolerant supervision of discrete-event systems is considered from the viewpoint of safe and timely diagnosis of unobservable faults. To this end, the new property of safe diagnosability is introduced and studied. Standard definitions of diagnosability of discrete-event systems deal with the problem of detecting the occurrence of unobservable fault events using model-based inferencing from observed sequences of events. In safe diagnosability, it is required in addition that fault detection occur prior to the execution of a given set of forbidden strings in the failed mode of operation of the system. For instance, this constraint could be required to prevent local faults from developing into failures that could cause safety hazards. If the system is safe diagnosable, reconfiguration actions could be forced upon the detection of faults prior to the execution of unsafe behaviour, thus achieving the objective of fault-tolerant supervision. Necessary and sufficient conditions for safe diagnosability are derived. In addition, the problem of explicitly considering safe diagnosability in controller design, termed “active safe diagnosis problem”, is formulated and solved. A brief discussion of safe diagnosability for timed models of discrete-event systems is also provided.     

Kalman filtering for multiple time-delay systems

This paper is to study the linear minimum variance estimation for discrete-time systems with instantaneous and l-time delayed measurements by using re-organized innovation analysis. A simple approach to the problem is presented in this paper. It is shown that the derived estimator involves solving l+1 different standard Kalman filtering with the same dimension as the original system.     

Clean system inversion learning control law

In this paper, an iterative learning control approach, clean system inversion, is proposed for multi-input multi-output (MIMO) time-invariant systems, as a remedy to the system inversion law. The analysis and design are carried out in the frequency domain. This model based scheme relies on non-causal filtering and need no high order derivatives of error signals and no numerical differentiation. Experimental results on an industrial robot system show that the scheme is effective.