Decentralized Stackelberg Strategies for Interconnected Stochastic Dynamic Systems

The main problem with the soft-computing algorithms is a determination of their parameters. The tuning rules are very general and need experiments during a trial and error method. The equations describing the bat algorithm have the form of difference equations, and the algorithm can be treated as a stochastic discrete-time system. The behaviour of this system depends on its dynamic and preservation stability conditions. The paper presents the stability analysis of the bat algorithm described as a stochastic discrete-time state-space system. The observability and controllability analyses were made in order to verify the correctness of the model describing the dynamic of BA. Sufficient conditions for stability are derived based on the Lyapunov stability theory. They indicate the recommended areas of the location of the parameters. The analysis of the position of eigenvalues of the state matrix shows how the different values of parameters affect the behaviour of the algorithm. They indicate the recommended area of the location of the parameters. Simulation results confirm the theory-based analysis.

This paper presents the stabilization problem of a class of discrete-time stochastic linear systems with time delay using an event-triggered control(ETC) strategy. For the general linear systems, we propose a new event triggering mechanism and deduce sufficient conditions for mean square exponentially stabilizability(MSES) and almost sure exponentially stabilizability(ASES) via ETC. The results show that the stability of the system depends on the system parameters (time delay, noise, event trigger threshold parameter, and unstable characteristic value of the original system). When the feedback control is disturbed by low-intensity noise, the unstable system can be stable in the mean square. Finally, the validity of the theoretical results is illustrated through a simulation example.

Bayesian optimal control for a non-autonomous stochastic discrete time system

In this paper, an adaptive optimal control is investigated for a stochastic linear discrete-time system with multiplicative state-dependent noise and control-dependent noise without knowledge of the system dynamics. With the framework of Q-learning, an off-policy state feedback solution for stochastic linear quadratic tracking (SLQT) problem has been proposed. First, an augmented system of the original system and the reference command generator is established to solve SLQT problem. Then, we present an optimal control by solving stochastic algebraic Riccati equation (SARE). Next, we present the on-policy and off-policy algorithms to achieve an adaptive optimal control without knowing the system dynamics. Finally, a simulation test is finally setup to verify the performance of the proposed adaptive optimal control.

Closed-Loop Strategy for Stackelberg Game Problem with Incomplete Information Structures

This paper derives conditions under which co-diagonalization of the controllability and observability Gramians can be performed in a physically consistent manner for the class of linear quantum stochastic systems that are common in the fields of quantum optics and related areas like quantum nano- and optomechanical systems. Such a class is essentially a quantum analogue of classical (non-quantum) linear stochastic systems. However, unlike their classical counterparts, the laws of quantum mechanics impose nonlinear equality constraints on the system matrices of linear quantum stochastic systems, the so-called physical realizability constraints. Therefore, a meaningful model reduction procedure must yield a physically realizable reduced model satisfying these constraints. Previous work has shown that model reduction by subsystem truncation preserves physical realizability, but did not propose a method for truncating a subsystem. One candidate approach for this truncation is a quantum adaptation of the well-known balanced truncation method for classical linear time-invariant systems. It is shown in this paper that balanced realization for linear quantum stochastic systems is only possible under a strongly restrictive necessary and sufficient condition. However, the paper also derives less restrictive necessary and sufficient conditions for other realizations with simultaneously diagonal controllability and observability Gramians, and introduces the notion of a quasi-balanced realization. An example of the application of the results is provided to demonstrate quasi-balanced truncation in the linear quantum stochastic setting.

This paper proposes an incentive Stackelberg strategy for the mean‐field type Itô stochastic systems with Poisson jumps in finite horizon and infinite horizon, respectively. Unlike the regular Stackelberg strategy, the obtained incentive Stackelberg strategy allows the leader to achieve his desired goal, that is, attaining his global optimum. Also, the mean‐square stability of the system is investigated, and it can be achieved by the follower. In addition, an algorithm procedure is introduced to derive the incentive feedback Stackelberg strategy in an infinite horizon. Finally, two examples are provided to highlight the effectiveness of the proposed results.

This paper presents a Fuzzy Mathematical Programming (FMP) approach for solving Multilevel Decentralized Programming Problems (ML(D)PPs). The higher level Decision Maker(DM) makes the decision first to provide preferred values of the decision variables under control and the follower reacts by optimizing the objective function conditioned on the higher level DM’s decision. A simple method is employed to find a satisfactory solution under fuzziness with linear fractional objectives overcoming the selection of membership functions and tolerance values and terminates in a finite number of steps. The methodology proposes small number of iterations and aims at reducing the feasible space of a decision variable at each level of the hierarchical system until a satisfactory solution is obtained at the last level. The Stackelberg strategy is employed as a solution concept when decision problems are modeled as two-level programming problems, whether there is a cooperative relationship between the decision makers or not. Illustrative numerical example is provided to demonstrate the feasibility of the proposed method.

In this paper we propose definitions of equivalence via stochastic bisimulation and of equivalence of stochastic external behavior for the class of discrete-time stochastic nonlinear control systems with possibly degenerate distributed disturbances. The notions are inspired by the analogue notions that exist for probabilistic chains and for behavioral systems, respectively. Connections between the two notions and also with stochastic reachability are discussed. For the subclass of discrete-time stochastic linear control systems with multivariate possibly degenerate normal distributed disturbances, geometric necessary and sufficient conditions for checking stochastic bisimulation equivalence and stochastic external behavior equivalence are derived. The proposed results nicely extend the theory of bisimulation equivalence and equivalence of external behavior known for non-deterministic control systems to a stochastic setting.

The decentralized control of discrete time stochastic linear systems is considered in this paper. The decentralized control laws are obtained by determining a sequential Nash equilibrium point for a set of quadratic cost functions. In the absence of disturbances, the Nash equilibrium set has the property of driving the state of the closed-loop system to the origin in finite time or asymptotically. In addition, the control law is a linear function of the instantaneous output measurements and can be computed on-line using relatively simple algorithms.

One common way for users to organize personal interests is to categorize information by topics. Each area of interest could be represented either by a simple concept label or by more complex information structures that include concepts linked to each other by user defined relationships. We believe that this type of information structure could be easily represented by domain ontologies. The increasing interest in the Semantic Web has been producing a growing number of publicly available ontologies. This is a rich source of information that could be very helpful during the process of engineering other domain ontologies. Still, we need automatic tools that help non-expert users build and maintain their own ontologies. To make this process more accessible, we introduce Miology, a Web-based application that helps users automatically select and adapt existing ontologies to represent their personal interests.

Intermittent fault detection for linear discrete-time stochastic multi-agent systems

This paper is concerned with reduced-order /sub /spl infin// filtering of stochastic systems. Based on linear matrix inequality (LMI) technique, a new design method is proposed for the reduced-order filtering of stochastic linear systems. The method is derived from decomposing the key matrix in LMIs which determines the order of designed filters. Different from the existing methods, the proposed method first minimizes the upper bound of the key matrix and then eliminates its near-zero eigenvalues, which results in a simpler, more direct and reliable design procedure. The method is applicable to both continuous and discrete time stochastic systems. Its effectiveness is illustrated by an example.

In this paper, an H ∞ filter design problem is studied for networked stochastic linear discrete-time systems with mixed uncertainties of random measurement delays, packet dropouts and missing measurements. We model the packet delivery characteristics of the network as a four-state Markov process and note that the results for discrete-time linear systems with Markovian jumping parameters can be applied. We focus on the design problem of a full-order H ∞ filter such that for all possible uncertain measurements the filtering error dynamics is exponentially mean square stable and a prescribed H ∞ performance bound is guaranteed. Necessary and sufficient bilinear matrix inequality (BMI) condition for the synthesis of the aforementioned filter for a discrete-time jump system is presented. Some simulation examples are presented to show the applicability and effectiveness of the proposed approach.

ON THE DYNAMICS OF INTERACTION IN LARGE ECONOMIES