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The problem of distributed identification of linear stochastic system with unknown coefficients over time-varying networks is considered. For estimating the unknown coefficients, each agent in the network can only access the input and the binary-valued output of the local system. Compared with the existing works on distributed optimization and estimation, the binary-valued local output observation considered in the paper makes the problem challenging. By assuming that the agent in the network can communicate with its adjacent neighbours, a stochastic approximation based distributed identification algorithm is proposed, and the consensus and convergence of the estimates are established. Finally, a numerical example is given showing that the simulation results are consistent with the theoretical analysis.

This paper studies a distributed stochastic optimization problem over random networks with imperfect communications subject to a global constraint, which is the intersection of local constraint sets assigned to agents. The global cost function is the sum of local cost functions, each of which is the expectation of a random cost function. By incorporating the augmented Lagrange technique with the projection method, a stochastic approximation based distributed primal-dual algorithm is proposed to solve the problem. Each agent updates its estimate by using the local observations and the information derived from neighbors. For the constrained problem, the estimates are first shown to be bounded almost surely (a.s.), and then are proved to converge to the optimal solution set a.s. Furthermore, the asymptotic normality and efficiency of the algorithm are addressed for the unconstrained case. The results demonstrate the influence of random networks, communication noises, and gradient errors on the performance of the algorithm. Finally, numerical simulations demonstrate the theoretic results.

In the paper, a novel distributed stochastic approximation algorithm (DSAA) is proposed to seek roots of the sum of local functions, each of which is associated with an agent from the multiple agents connected in a network. At any time, each agent updates its estimate for the root utilizing the observation of its local function and the information derived from the neighboring agents. The key difference of the proposed algorithm from the existing ones consists in the expanding truncations (so it is called as DSAAWET), by which the boundedness of the estimates can be guaranteed without imposing the growth rate constraints on the local functions. The convergence of the estimates generated by DSAAWET to a consensus set belonging to the root set of the sum function is shown under weaker conditions on the local functions and on the observation noise in comparison with the existing results. We illustrate our approach by two applications, one from signal processing and the other one from distributed optimization. Numerical simulation results are also included., 18 pages, 2 pictures

This paper deals with the parameter estimation problem of the Single-Input-Single-Output (SISO) switched Hammerstein system. Suppose that the switching law is arbitrary but can be observed online. All subsystems are parameterized and the Recursive Least Squares (RLS) algorithm is applied to estimate their parameters. To overcome the difficulty caused by coupling of data from different subsystems, the concept "intrinsic switch" is introduced. Two cases are considered: i) The input is taken to be a sequence of independent identically distributed (i.i.d.) random variables when identification is the only purpose; ii) A diminishingly excited signal is superimposed on the control when the adaptive control law is given. The strong consistency of the estimates in both cases is established and a simulation example is given to verify the theoretical analysis., Comment: 16 pages, 3 figures; Accepted for publication by Acta Mathematicae Applicatae Sinica (http://link.springer.com/journal/10255)

The continuous-time RM and KW procedures are modified to suit the case when the measurement error is the process of dependent increment. By using a combined method connecting the probabilistic method with the ordinary differential equation (ODE) method simple conditions are given to guarantee the convergence of algorithms to the zero and the extremum of regression functions.

The paper deals with the problem of destabilization of diffusively coupled identical systems. It is shown that the globally asymptotically stable systems being diffusively coupled may exhibit an oscillatory behavior. It is shown that if the diffusive medium consists of hyperbolically nonminimum phase systems and the diffusive factors exceed some threshold value the origin of the overall system undergoes a Poincaré-Andronov-Hopf bifurcation resulting in oscillatory behavior.

We continue considering the system described by (3.91)−(3.94), for which (p,q,r) are assumed to be the known upper bounds for system orders and d = 1 to be the lower bound for the time-delay of the system. The true orders may be strictly less than p, q and r respectively. The system coefficients written in the matrix form $${\theta ^r} = [ - {A_1} \ldots - {A_p}{\text{ }}{B_1} \ldots {B_q}{\text{ }}{C_1} \ldots {C_r}]$$ (5.1) are unknown.

In Chapter 4 we discussed the coefficient estimation problem for linear stochastic systems without monitoring, i.e. there is no specific purpose for the system input. In order for the coefficient estimate to be consistent, we have clarified how the stochastic regressors φ n or φ n 0 or ψ n should behave. Unfortunately, as to be shown in this chapter, the required properties of φ n or φ n 0 or ψ n , in general, may not be satisfied for adaptive control systems.

We start with the following standard linear state space model: $$ {\text{d}}{{\text{x}}_{\text{t}}}{\text{ = A}}{{\text{x}}_{\text{t}}}{\text{dt + B}}{{\text{u}}_{\text{t}}}{\text{dt + Dd}}{{\text{w}}_{\text{t}}} $$ (12.1) $$ {\text{d}}{{\text{y}}_{\text{t}}}{\text{= C}}{{\text{x}}_{\text{t}}}{\text{dt+d}}{{\text{w}}_{\text{t}}} $$ (12.2) where y t and u t are the scalar output and input, respectively, x t is the p-dimensional state vector and w t is a standard Wiener process (Brownian motion). A, B, C, D and F are real matrices of compatible dimensions.

The main concepts of control theory for linear systems with known parameters are needed in order to work on problems arising from the control system with unknown parameters which is the subject of the present book. Aiming at those who are not in the field of control theory, this chapter provides the necessary concepts and results of control theory which will be used in later chapters.

The system considered in this chapter is the same as that described by (3.91)−(3.94), for which it is assumed that (p,q,r) are the known upper bounds for system orders and d = 1 is the lower bound for time-delay. The assumption d = 1 is not a constraint, because in the case of d > 1 we may regard B i as zero for 1 ≤ i < d.

In preceding chapters, we have studied finite dimensional linear systems of the form (3.91), or $$ {y_n} = [I - {C^{ - 1}}(z)A(z)]{y_n} + {C^{ - 1}}(z)B(z){u_n} + {w_n}, $$ (9.1) where C−1(z)A(z) and C−1(z)B(z) are rational transfer matrices.

Tracking or estimating a system or a signal whose properties vary with time is a fundamental problem in system identification as well as in signal processing. The basic time-varying model is that of a regression: $$ {y_k} = \varphi _k^\tau {\theta _k} + vk,{\text{ }}\forall k \geqslant 0 $$ (10.1) where yk and v k are the scalar output and the noise respectively, and φ k and θ k are, respectively, the r-dimensional stochastic regressor and the unknown time-varying parameter. It is convenient to denote the parameter variation at time k by Δ k : $${\Delta _k} \triangleq {\theta _k} - {\theta _{k - 1}},\forall k \geqslant 1.$$ (10.2)

The martingale method is a powerful tool for analyzing recursive identification algorithms and stochastic adaptive control systems. In this chapter, we first present classical convergence theorems for martingales [Do], [Cho], [St], [N], [LSh]. Then we estimate the sums of martingale difference sequence with single- and double-indexed random weights [St], [LW1], [CG3], [GHH], [HG]. These results are the bases of analysis for the least-square-based estimates for coefficients and orders which will be considered in later chapters.

In this chapter we introduce the main concepts and some basic results of probability theory for convenience of reference. They are presented mostly without proof, but are explained by examples for those who are not familiar with measure-theory-based probability theory. For detailed material we refer readers to standard texts, for example, [Do], [Chu2], [Lo], [CT] and [Sh].

The adaptive tracking problem is considered for discrete-time stochastic systems consisting of a modeled part being a stable ARMAX process and unmodeled dynamics dominated by a small constant epsilon multiplied by a quantity independent of epsilon but tending to infinity as the past input, output, and noise grow. The adaptive control law proposed is switched at stopping times and is disturbed by a sequence of random vectors bounded by an arbitrary small but fixed constant sigma . It is shown that the closed-loop system is globally stable, the estimation errors for parameters contained in the modeled part of the order epsilon , and the tracking error differs from the minimum tracking error for systems without unmodeled dynamics by value of O( epsilon /sup 2/)+O( sigma /sup 2/). >

Simple identification algorithms are proposed for both continuous- and discrete-time systems with correlated noise. By a combined method connecting the martingale method with the ordinary differential equation method, quite simple conditions are obtained to guarantee strong consistency of the proposed algorithms, which give estimates for the unknown coefficients in both the dynamic system and the noise model.

In this paper the system identification problem under correlated noise is considered. By a new combined method connecting the ordinary differential equation method with the probabilistic method the simple sufficient conditions are given to guarantee the strong consistency of certain Recursive algorithms which give the estimates for the cofficient matrices in both the dynamic system and the noise model simultaneously. Besides. the strong consistent estimate for the covariance matrix of the noise is also obtained. For the continuous-time system the similar results are demonstrated.

In this paper the tracking and control problems of a multi-input multi-output system with unknown coefficients and with quadratic index are considered. Estimates of the unknown parameters are first given, and based on them the self-tuning control law is formed. Sufficient conditions for the parameter estimates to converge to the true ones, and for the difference between the self-tuning control and the optimal control to tend to zero, are considered.

The stochastic controls and strategies for linear quadratic Gaussian systems are considered in this paper. We have obtained the unified suboptimal controls and strategies applicable to the general case, whether the covariance matrix of the measurement noise and the weighting matrix of the control action are degenerate or not, and also have given the optimal control and strategy applicable to both the degenerate and the non-degenerate co-variance matrix of the measurement noise when the initial information is unknown.

The paper deals with the influence of fuzzy logic based controller on stability of isolated termo power systems. The comparison, with respect to the quality of stabilization, of the systems with a conventional and a fuzzy controller was performed by analyzing the simulation results on a suitable mathematical model. It is shown that fuzzy logic based controller improves stability of an isolated termo power systems. The cases in which the fuzzy logic approach gives better quality performance of the system than the conventional approach are considered.

In the last ten years several new conceptions for the design of production systems have been developed (Lean Production, Fractal Factory, Business Process Reengineenng, Virtual Factory etc.). As a country in transition Croatia is at the turning point between the planned economy and the market-based economy. It is therefore necessary during the process of privatization to restructure the existing enterprises and to introduce new organization structures. These structures must be adapted to the present situation regarding culture, the levels of education and technology, and other conditions. The paper describes the results of research performed so far regarding the new forms of organizational structures, as wsll as the research being planned for the future.