An algorithm for the improvement of linear separation†

A method is presented for the improvement of linear separation. The characteristic vector is modified using the required distance of the boundary from the nearest pattern. Using this modified characteristic vector the weight vector is adjusted.     

A recursive least-squares approach to the on-line adaptive control problem†

A practical study of the application of recursive least squares methods to the adaptive control of a multivariable process is described. The process has a number of inputs and an equal number of state variables are required to be controlled. Investigations are carried out both off-line and in real-time using a hybrid computer. Results show the techniques to be ideally suited for on-line application.     

An approach for improved modal control of multi-input multi-output discrete time systems†

It is shown that the state feedback gains for a given multi-input multi-output discrete time system can be computed by matching a finite model output sequence members to prespecified ones. Relationship of the pole positioning control schemes to such matching is first examined and it is shown that better control is possible by adopting the method proposed in this paper. The results are illustrated through a numerical example.     

An approach for incomplete state feedback control systems design†

An alternative method for designing linear regulators with incomplete state feedback is presented. This approach is based on approximation of the impulse response of the closed-loop system with incomplete state feedback to the optimal closod-loop system with complete state feedback.     

An iterative procedure for the training of a two-layered machine†

An iterative method is presented for the training of a two-layered machine used for pattern dichotomization. It is assumed that there is only one TLU in the second layer and a number of TLU's in the first layer. The central idea of the method is getting the desired responses of the first-layer TLU's, knowing the desired response of the output TLU. Using these desired responses the TLU's are adjusted. A method is given for testing the non-linear separability of R category case.     

An alternative approach to non-linear filtering†

The following non-linear filtering problem is discussed. Consider a process {X_t, t≥0}, determined by the stochastic differential equation

with the noisy observations of this process given by dy = h(x) dt + y(x) dB, t> 0, y?R^r, where W and B are R^m valued and R^r valued Wiener processes respectively and q is a zero-mean Poisson random measure on [0, ∞) × R^m. An observer is required of the form dz = j(z) dt + G(z) (dy — h(z) dt), t>0, z?R^m, where the ‘ gain matrix ” G has yet to be determined. Let DeRIm be a given centrally symmetric open and bounded domain with the origin at its centre, and let t be the first time that (X_t; Z_i)D given that (X₀, Z₀)?D (Zt is the state of the observer). The approach adopted here is to choose a matrix G*, of a bang-bang type, in such a manner that tho expected value of A{t:0≤tt- Z_t≤?} is maximized on a class of admissible gain matrices. Here A is the Lebesgue measure on the real line and ?>0 is given. Sufficient conditions on the maximizing gain matrix are derived. These conditions can be applied off-line and can be used in the design of the observers. Several examples are solved numerically.     

An adaptive FEM with ITP approach for steady Schrödinger equation

ABSTRACT

In this paper, an adaptive numerical method is proposed for solving a 2D Schrödinger equation with an imaginary time propagation approach. The differential equation is first transferred via a Wick rotation to a real time-dependent equation, whose solution corresponds to the ground state of a given system when time approaches infinity. The temporal equation is then discretized spatially via a finite element method, and temporally utilizing a Crank–Nicolson scheme. A moving mesh strategy based on harmonic maps is considered to eliminate possible singular behaviour of the solution. Several linear and nonlinear examples are tested by using our method. The experiments demonstrate clearly that our method provides an effective way to locate the ground state of the equations through underlying eigenvalue problems.     

On the speed of response of a model-reference adaptive control system†

An analytical evaluation of the adaptive loop response of a model-reference adaptive control system is presented using sinusoids as a test signal. A schematic diagram of the feedback system containing a primary control loop and an adaptive control loop are given.     

Direct adaptive control for linear multivariable systems†

The aim of this paper is to survey direct adaptive control for linear multivariable systems. The discrete-time case is emphasized because of the increasing use of digital computers. Some adaptive control structures are given, as well as the different assumptions made on the process in order to achieve some specified objectives. Trends, new solutions and open problems are also discussed.     

Decentralized adaptive control of robotic manipulators†

We develop a self-tuning-type adaptive control for robotic manipulators with six joints, and analyse the stability of the control system. In order to reduce the computational effort for obtaining the control input in real time, a decentralized adaptive control system is designed in which each joint of the manipulator is regarded as a subsystem and controlled independently in parallel. In this control system we regard the interaction among the multiple joints as an unknown input in each subsystem. The influence of the interaction on the stability of the overall control system is analysed using a Lyapunov function. The theoretical result obtained is that the control system is always stable in the sense that the error between the output of the adaptive predictor and the real output (angular velocity of each joint) will not exceed the amount of interaction. This result is verified by some simulation studies.     

An input‐output approach to achieve adaptive tracking for saturating stable systems

The problem of controlling time-invariant linear systems subject to parametric uncertainty and input saturation constraint, is dealt with using a pole placement adaptive controller. It is shown that the resulting adaptive control system can be described by a non-linear feedback scheme. Then, the l 2 -stability condition for the control system turns out to be the positive-realness of a transfer function involving the plant (estimated) model and the specified closed-loop poles. This makes it necessary to adapt on-line the desired closed-loop poles to the time-varying (estimated) model. The proposed adaptive controller keeps bounded all the closed loop sequences, whatever the initial conditions. Furthermore, it ensures a quite interesting output-reference tracking behaviour. More precisely, the quality of the tracking depends on the reference sequence rate: the slower the reference the better the tracking.     

Convergence rate of least-squares identification and adaptive control for stochastic systems†

The strong consistency and the convergence rate of least-squares identification for the multidimensional ARMAX model are established under some decaying excitation conditions which are satisfied if both input and output do not grow too fast and the attenuating excitation technique is applied. The parameter-identification results are applied to adaptive-control systems with a quadratic loss function. The rate of convergence of the loss function to its minimum is also obtained.     

Distributional approach to the analysis of linear time-varying systems†

This paper is devoted to the analysis of linear time-varying systems using distribution theory. The technique is developed to obtain the output given the input as well as to obtain the impulse response from the knowledge of the output and input. All quantities are considered time varying. The basic approach used converts the integral equation into a distributional differential equation.     

Optimum reduction of large dynamic system†

A performance index connecting the correlation measures of feedback errors of two unity feedback systems is suggested for obtaining the optimum simplified models of large, linear, time-invariant systems. To ensure the suitability of the index a simplification procedure by eliminating the remote poles in sequence is adopted. The examples indicate that the index is a useful criterion for optimum reduction of large dynamic systems.     

Synthesis of adaptive sub-optimal feedback control laws†

In this paper a method for synthesizing a sub-optimal feedback controller which is sensitive to variations in plant parameters is presented. The structure of the sub-optimal control is a linear combination of suitably chosen basis functions multiplied by coefficients which are functions of the varying plant parameters. The coefficient multipliers are determined by the minimization of a mean-square error using data obtained from numerically computed optimal trajectories. The controller may be called adaptive since it uses identification of the varying plant parameters to modify the coefficient multipliers. Examples are included which show that with relative sensitivity as the criterion the method is superior to other methods of suboptimal control design.     

Performance characteristics of an adaptive hydraulic servo-mechanism†

This paper presents the results of an extensive set of experiments which were carried out on an adaptive hydraulic servo-mechanism: this system embodied adaptive controllers designed on the basis of Liapunov's direct method.     

Suboptimization techniques for improving transients in adaptive control†

Two possible optimization techniques for on-line adjustment of the design parameters involved in the adaptation algorithms of adaptive control schemes for minimum phase plants arc discussed. Sensitivity corrections adapled to this particular problem are introduced for correcting inaccuracies in an auxiliary model derived in order to be able to apply classical optimization techniques to the whole scheme. The main objective of such techniques is to improve the adaptation transient performances. The resulting strategies are discussed from the point of view of performance and possible implementation. Simulations illustrate the feasibility of the proposed optimizing procedures which are an extension, using a more general optimization theory and/or a sensitivity approach, of previous results and an alternative to the adaptive sampling approach of De la Sen (1984 c).     

Search for the optima of stochastic functions†

A method is proposed for search for extrema in stochastic systems. Search algorithms which were developed and are successful in noise-free systems are used in the noise-corrupted systems except that minimum variance estimators are substituted for direct functional measurements. The optimal programme of estimators is obtained by solving a variational calculus problem. An example showing significant improvement in search response over traditional stochastic approximation methods is presented.     

Chemical process control—A new technique for adaptive tuning of controllers†

This paper presents a new technique for determining the optimum settings of the conventional two-mode and three-mode controllers. The procedure which utilizes the practically available on-line closed loop data is an extension of the classical work of Ziegler and Nichols (1942). The advantages of the present method over that of Ziegler and Nichols are (i) that it does not require the process to undergo sustained oscillations, (ii) that the tuning constants are determined iteratively (and not by hit-and-miss technique) thereby making the tuning adaptive in nature and (iii) that it is possible to select a criterion of optimality other than the usual 1:4 decay ratio.     

An approximation for the time optimal bounded output problem for linear systems†

An effective means for obtaining approximations to the time optimal bounded output problem is presented. The approximation is obtained from the results of a convex programming problem which is rapidly solved by computer. Moreover, the original optimization problem can be approximated to any desired degree of accuracy,