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The letter treats a class of nonlinear control systems in state-space form. The problem considered is that of choosing two nonlinear feedback matrix functions F(x, t) and G(x, t) which decouple a candidate subset of the output set. The conditions under which this problem has a solution are derived and the procedure for computing the two nonlinear State feedback gain matrix functions required is given. An illustrative example is fully worked out.

An indirect state-feedback technique for matching a controllable multicontroller system to a given model is presented. By this technique the multicontroller system is transformed to its Asseo phase-variable canonical form prior to the application of the state-feedback control. The cases where the system under control and the model are equidimensional or not are considered, and a solution to the model-matching problem by using output feedback is provided. The theory is illustrated by three examples.

The problem of choosing the buffer length for a maximum allowed fractional loss, in a situation where the feeding rate is Erlangian, and where the service is effected through multiple output lines with regular and synchronous removal rates, is studied. Design curves are provided which can be used as a guide for the practical buffer-length choice.

The maximum-likelihood approach to the lumped-parameter filtering estimation theory is extended to a general class of nonlinear distributed-parameter systems with additive Gaussian disturbances and measurement noise. The concept of conventional finite-dimensional-likelihood function is replaced by the likelihood functional which determines the statistical characteristics of an infinite-dimensional Gaussian random variable. First, the nonlinear filtering problem is considered. Using the differential dynamic-programming technique, an approximate nonlinear filter is derived which is shown to be the most natural nonlinear analogue of Kalman's linear distributed-parameter filter, presented in two recent papers. Secondly, the nonlinear prediction is treated by simple extrapolation. Thirdly, the smoothing problem is solved by the well known technique of decomposing the likelihood function(a1) in two parts. Finally, computational results are provided which show the effectiveness of the theory.

The paper treats the optimal distributed and boundary control problem for a general class of linear stochastic distributed-parameter systems. A quadratic cost functional is used, and the stochastic distributed Hamilton-Jacobi equation, which is derived by the dynamic-programming technique, is solved explicitly. Analogously to the lumped-parameter case, the result is a pair of linear optimal feedback controllers, their common weighting function being described by a matrix partial-integrodilferential equation of the Riccati form. When the state of the system is not exactly measured, the distributed Kalman's filter, derived in a recent paper, is used, the decoupling of the optimal controllers and the optimal estimator being proved. Kalman's duality principle is extended to the distributed systems under investigation, the canonical equations of Hamilton are derived and a version of Pontryagin's minimum principle is proved.

The optimal-filtering problem of linear distributed-parameter systems corrupted by boundary and/or volume stochastic disturbances is considered. The optimal filter is shown to be a generalisation of that previously derived for pure volume noise.

Moment equations are derived for a general class of distributed-parameter dynamic processes corrupted by white in time distributed disturbances. An integrodifferential equation for the expected value of an arbitrary functional of the process is first derived simply by using the whiteness property of the stochastic disturbance. In this way there is no need to utilise the forward Kolmogorov's equation, which at present is not available for distributed-parameter processes. The moment equations are then derived as special cases of this functional integrodifferential equation.

The problem of choosing the buffer size for a given waiting time or fractional loss in a situation where the input rate is Poissonian and the output rate is periodically regular is considered. The value of the results lies in that they give a practical way to a compromise between buffer fractional loss and buffer waiting time in those applications where both quantities are of interest. The periodically regular service-time distribution allows for more than one stream of queuing customers to be served by only one servicing channel.

This paper extends the optimal linear filtering and prediction theory of Kalman and Bucy to a general class of linear distributed-parameter systems. The filter equations for the optimal estimate and its variance are replaced by partial integrodifferential equations, the complexity of which depends on the form of the particular system under investigation. A solution to the smoothing problem for the same class of distributed systems, analogous to that suggested by Kwakernaak, is given, and the problem of integrating the filtering and smoothing equations is discussed.

The optimal distributed and boundary control of nonlinear distributed-parameter systems with nonlinear cost functionals is treated. First- and second-order algorithms for improving a nominal distributed and/or boundary-control function are developed. The approach of iteratively solving the distributed-parameter Hamilton-Jacobi equation, known as differential dynamic-programming technique, is followed. A simple example illustrates the theory.

International audience; Intelligence and learning are intimately connected. They need each other to be at their peak. This is why, since its inception in the fifties, Artificial Intelligence has been preoccupied with the study of learning, as testified by the pioneering works devoted to the first cybernetic" turtles" or" mouses", or the CHECKERS program [1]. Aside from this fundamental interest in learning that, in a way, dates back to the Greek philosophers, there are more practical reasons why" intelligent" systems should be endowed with learning capacities. Numerous tasks are indeed intrinsically quite difficult to program, if only because they imply seemingly infinite numbers of unpredictable situations. For example, in the domain of pattern recognition or obstacle avoidance, it is impossible to enumerate all possible cases. Likewise, the knowledge acquisition phase has long been identified as a major problem in the development of knowledge-based systems. The prospect of a machine capable of automatically acquiring the competencies needed to face up new and unknown situations is therefore quite attractive. Furthermore, there is a need for systems that can adapt in face of changing environments, improve their performance and update their knowledge while carrying on their duties. Here too, learning is required, possibly involving longer timescale. Finally, there are activities like scientific discovery that are learning problems in themselves. For all these reasons, machine learning is an active field of research experiencing a vigorous development.This chapter is intended to provide an introductory survey of some achievements in machine learning and of the main issues that are currently of central concern.