http://popups.lib.uliege.be/1373-5411/index.php?id=259 Index terms fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=925 This paper deals with the stochastic adaptive linear quadratic optimal control problems which have been an active area of research for many years. It has been known that these problems could be treated by dynamic programming. However, it has been conceded that explicit solution of the dynamic programming equations for these problems is generally not possible and that numerical solution of these equations is a difficult computational procedure. This has led to many approximation techniques. In the paper, a variational approach is used to obtain optimality conditions for the stochastic linear quadratic adaptive control problems. These conditions lead to an algorithm for computing optimal control laws which differs from the dynamic programming algorithm. If the unknown parameters enter into the state equation additively, and the prior distribution of the unknown parameters is normal, the algorithm can be carried out in closed form. The examples are given to illustrate the proposed technique. Mon, 01 Jul 2024 14:08:23 +0200 Thu, 10 Oct 2024 16:17:00 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=925 http://popups.lib.uliege.be/1373-5411/index.php?id=860 The stochastic dynamical system with the states described by elements u of a Hilbert space is considered. There is a deterministic system considered as its nonperturbed variant. An outcome y is observed under random perturbations. The probability distribution P(y, u) of the measurements results in the fixed states u is analysed. A class of stochastic systems marked by the full determination of the law P(y, u) via equations of the nonperturbed system is found. We also find the distributions P(y, u). These distributions prove to be similar to the quantum laws of probability distribution of observable quantities including the principles of superposition and uncertainty and the phenomenon of quantization. Mon, 01 Jul 2024 14:03:02 +0200 Thu, 10 Oct 2024 10:42:58 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=860 http://popups.lib.uliege.be/1373-5411/index.php?id=258 In this paper, the problem of determining the optimal control law for discrete-time stochastic linear systems with respect to a quadratic performance criterion is considered. It is assumed that the system is subject to additive system noise and that the state variables are measured with additive measurement noise, without specifying the specific characteristics of random variables. It is shown that the problem of stochastic optimal control can be reduced to two independent problems, one of equivalent deterministic optimal control and the other of stochastic estimation of underlying uncertainties. This holds even if the system noise, the measurement noise and/or the initial state of the system are non-Gaussian, mutually and time-wise dependent. The aim of the present paper is to show how the invariant embedding technique and fiducial approach may be used to solve the problem of adaptive cautious controlling a discrete-time stochastic linear system in which the state transition matrix and the control driven matrix are unknown. This is the case when the certainty equivalence principle does not yield the admissible adaptive control laws for the present problem. The proposed approach does not require the arbitrary selection of priors as in the Bayesian approach. It makes it possible to simplify the problem of adaptive optimization of stochastic systems and, if the system noise and/or the measurement noise are Gaussian, to carry out the algorithm in closed form. The examples are given to illustate the suggested methodology. Wed, 19 Jun 2024 15:17:36 +0200 Wed, 19 Jun 2024 15:17:46 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=258