Control of discrete time nonlinear systems with a time-varying structure

In this paper, we present a control methodology for a class of discrete time nonlinear systems that depend on a possibly exogenous scheduling variable. This class of systems consists of an interpolation of nonlinear dynamic equations in strict feedback form, and it may represent systems with a time-varying nonlinear structure. Moreover, this class of systems is able to represent some cases of gain scheduling control, Takagi-Sugeno fuzzy systems, as well as input-output realizations of nonlinear systems which are approximated via localized linearizations. We present two control theorems, one using what we call a “global” approach (akin to traditional backstepping), and a “local” approach, our main result, where backstepping is again used but the control law is an interpolation of local control terms. An aircraft wing rock regulation problem with varying angle of attack is used to illustrate and compare the two approaches.     

Stability robustness of networked control systems with respect to packet loss

This paper is concerned with stability analysis of discrete-time networked control systems over a communication channel subject to packet loss whose behavior is modeled by an i.i.d Bernoulli process with a packet dropping probability bounded by a constant. A necessary and sufficient condition for stability is obtained. A packet dropping margin is introduced as a measure of stability robustness of a system against packet dropping, and a formula for it is derived. A design method is proposed for achieving a large margin subject to a constraint that the system has a set of prescribed nominal closed-loop poles.     

Decentralized adaptive coordinated control of multiple robot arms without using a force sensor

This paper presents a distributed adaptive coordinated control method for multiple robot arms grasping a common object. The cases of rigid contact and rolling contact are analyzed. In the proposed controller, the dynamic parameters of both object and robot arms are estimated adaptively. The desired motions of the robot arms are generated by an estimated object reference model. The control method requires only the measurements of the positions and velocities of the object and robot arms, but not the measurements of forces and moments at contact points. The asymptotic convergence of trajectory is proven by the Lyapunov-like Lemma. Experiments involving two robot arms handling a common object are shown.     

Controlled linear system with delayed relay output under impulse random disturbances

The paper is devoted to the first order delayed linear system with relay output controlled by the proportional-integral (PI) regulator. The deterministic system exhibits stable oscillations, and, since the system itself is stable, it can be suitable to switch off the controller if there are no disturbances during a long time interval. In the present work, the random disturbances are modelled by a Poisson stream of impulses, and the goal is to determine the instants of switching on (off) of the PI controller. After several assumptions and quantization of the time axis, we construct the new optimal control problem which is successfully solved with the help of the dynamic programming approach.     

Solving the small sample size problem in face recognition using generalized discriminant analysis

The goal of face recognition is to distinguish persons via their facial images. Each person's images form a cluster, and a new image is recognized by assigning it to the correct cluster. Since the images are very high-dimensional, it is necessary to reduce their dimension. Linear discriminant analysis (LDA) has been shown to be effective at dimension reduction while preserving the cluster structure of the data. It is classically defined as an optimization problem involving covariance matrices that represent the scatter within and between clusters. The requirement that one of these matrices be nonsingular restricts its application to datasets in which the dimension of the data does not exceed the sample size. For face recognition, however, the dimension typically exceeds the number of images in the database, resulting in what is referred to as the small sample size problem. Recently, the applicability of LDA has been extended by using the generalized singular value decomposition (GSVD) to circumvent the nonsingularity requirement, thus making LDA directly applicable to face recognition data. Our experiments confirm that LDA/GSVD solves the small sample size problem very effectively as compared with other current methods.     

A stochastic realization algorithm via block LQ decomposition in Hilbert space

A stochastic realization problem of a stationary stochastic process is re-visited, and a new stochastically balanced realization algorithm is derived in a Hilbert space generated by second-order stationary processes. The present algorithm computes a stochastically balanced realization by means of the singular value decomposition of a weighted block Hankel matrix derived by a “block LQ decomposition”. Extension to a stochastic subspace identification method explains how the proposed abstract algorithm is implemented in system identification.     

Fundamental properties of reset control systems

Reset controllers are linear controllers that reset some of their states to zero when their input is zero. We are interested in their feedback connection with linear plants, and in this paper we establish fundamental closed-loop properties including stability and asymptotic tracking. This paper considers more general reset structures than previously considered, allowing for higher-order controllers and partial-state resetting. It gives a testable necessary and sufficient condition for quadratic stability and links it to both uniform bounded-input bounded-state stability and steady-state performance. Unlike previous related research, which includes the study of impulsive differential equations, our stability results require no assumptions on the evolution of reset times.