Model with coupled subsystems

Consideration was given to the model with coupled subsystems. In the absence of relations between the subsystems, the MIS falls down into independent systems of autonomous ordinary differential equations. In the structure of the entire system, the subsystems make up hierarchical levels. Sun-planets-satellites, interacting moving objects, and so on exemplify the models with coupled subsystems. The problem of studying dynamics of such models was posed. The following natural approach to their analysis was proposed: classification of the subsystems by types (dynamic properties), specification of various bundles of subsystems, and subsequent analysis of these bundles. Realization of the approach to oscillations, stability, stabilization, bifurcation, and resonance was given. These problems were solved for the model with coupled subsystems having two second-kind subsystems in the basic combination of the oscillation modes in the subsystem.     

A quasi-parallel method for the simulation of loosely coupled continuous subsystems

The concept of a quasi-parallel integration method is proposed as a potentially efficient way of handling the simulation of continuous systems that can be decomposed into a collection of loosely coupled sub-systems. Possible measures for evaluating the computational advantage of such an approach are formulated and then used to identify characteristics of the given system that would assure substantial gains if the method were applied. A particular implementation of such a quasi-parallel method is described and the results of a series of numerical experiments are given. These provide some insight into the question of trade-offs between accuracy and computational gain.     

Model containing coupled subsystems with oscillations of different types

Consideration was given to an autonomous model containing coupled subsystems (MCCS) and, in the absence of couplings between the subsystems, falling down into systems of ordinary differential equations. It is assumed that the subsystems admit different types of nondegenerate single-frequency oscillations. Solved were the problems of oscillations in MCCS, their stability, and stabilization of MCCS oscillation by smooth autonomous coupling controls. It was shown how the developed theory is applied to the coupled Duffing and Van der Pol oscillators.     

Designing a stable cycle in weakly coupled identical systems

Consideration was given to a dynamic model containing weakly coupled identical subsystems. The subsystem was assumed to admit a family of periodic solutions where the period is a monotonic function of one parameter. Requirements on the coupling under which the model has an asymptotic orbital stable cycle were established. The problem of stabilization of the model oscillations by a small smooth autonomous coupling control was solved using the results obtained. The system of two coupled conservative systems with one degree of freedom was considered individually.     

Optimal control of weakly coupled bilinear systems

The optimization of the time-invariant bilinear weakly coupled system with a quadratic performance criterion is considered. A sequence of linear state and costate equations is constructed such that the open-loop solution of the optimization problem is obtained in terms of the reduced-order subsystems. This leads to a reduction in the size of the required computations and allows parallel processing of information. The near-optimal closed-loop control is obtained in the form of a linear feedback law, with the feedback gains calculated from two reduced-order independent time-varying linear-quadratic optimal control problems.     

Decoupling transformation for weakly coupled linear systems

The non-singular transformation that completely decouples a weakly coupled linear system under non-restrictive conditions is defined. The transformation matrices are obtained from two algebraic matrix equations. Algorithms that efficiently generate solutions to these equations are derived. The proposed transformation also completely decouples the corresponding Lyapunov matrix differential equation.     

Oscillation family in weakly coupled identical systems

Consideration was given to an autonomous model with weakly coupled identical subsystems. Existence of a family of periodic solutions which is similar to the family in a subsystem was established. A scenario of bifurcations of the characteristic exponents was given, and the stabilization problem was solved. An example was given.     

Optimal reduced-order solution of the weakly coupled discreteRiccati equation

The optimal solution of the weakly coupled algebraic discrete Riccati equation is obtained in terms of a reduced-order continuous-type algebraic Riccati equation via the use of a bilinear transformation. The proposed method has a rate of convergence of O(ε² ) where ε represents a small coupling parameter. A real-world physical example (a chemical plant model) demonstrates the efficiency of the proposed method. Simulation results obtained using a package for a computer-aided control system are presented. For this specific real-world example, the algorithm perfectly matches the presented theory, since convergence, with an accuracy of 10^-4, is achieved after nine iterations (i.e., 0.68¹⁸=10^-4)     

Soft-constrained stochastic Nash games for weakly coupled large-scale systems

In this paper, we discuss infinite-horizon soft-constrained stochastic Nash games involving state-dependent noise in weakly coupled large-scale systems. First, we formulate linear quadratic differential games in which robustness is attained against model uncertainty. It is noteworthy that this is the first time conditions for the existence of robust equilibria have been derived based on the solutions of sets of cross-coupled stochastic algebraic Riccati equations (CSAREs). After establishing an asymptotic structure with positive definiteness for CSAREs solutions, we derive a recursive algorithm by means of Newton’s method so that it can be used to obtain solutions for CSAREs. As another important feature, we propose a high-order approximate Nash strategy based on iterative solutions. Finally, we provide a numerical example to verify the efficiency of the proposed algorithms.     

Asymptotic solutions to weakly coupled stochastic teams withnonclassical information

The authors develop a new iterative approach toward the solution of a class of two-agent dynamic stochastic teams with nonclassical information when the coupling between the agents is weak, either through the state dynamics or through the information channel. In each case, the weak coupling is characterized in terms of a small (perturbation) parameter. When this parameter value (say, ∈) is set equal to zero, the original fairly complex dynamic team, with a nonclassical information pattern, is decomposed into or converted to relatively simple stochastic control or team problems, the solution of which makes up the zeroth-order approximation (in a function space) to the team-optical solution of the original problem. The fact that the zeroth-order solution approximates the optimal cost up to at least O(∈) is shown. It is also shown that approximations of all orders can be obtained by solving a sequence of stochastic control and/or simpler team problems     

On synchrony of weakly coupled neurons at low firing rate

The dynamics of a pair of weakly interacting conductance-based neurons, firing at low frequency, nu, is investigated in the framework of the phase-reduction method. The stability of the antiphase and the in-phase locked state is studied. It is found that for a large class of conductance-based models, the antiphase state is stable (resp., unstable) for excitatory (resp., inhibitory) interactions if the synaptic time constant is above a critical value tau(c)(s), which scales as the absolute value of log nu when nu goes to zero.     

Distributed model predictive control of constrained weakly coupled nonlinear systems

This paper proposes a distributed model predictive control (MPC) strategy for a large-scale system that consists of several dynamically coupled nonlinear systems with decoupled control constraints and disturbances. In the proposed strategy, all subsystems compute their control signals by solving local optimizations constrained by their nominal decoupled dynamics. The dynamic couplings and the disturbances are accommodated through new robustness constraints in the local optimizations. The paper derives relationships among, and designs procedures for, the parameters involved in the proposed distributed MPC strategy based on the analysis of the recursive feasibility and the robust stability of the overall system. The paper shows that, for a given bound on the disturbances, the recursive feasibility is guaranteed if the sampling interval is properly chosen. Moreover, it establishes sufficient conditions for the overall system state to converge to a robust positively invariant set. The paper illustrates the effectiveness of the proposed distributed MPC strategy by applying it to three coupled cart-(nonlinear) spring–damper subsystems.     

Method of some inverse geophysical problem solution by using weakly coupled connected distributed computing systems

In this work a possible model for organizing a grid-based application that performs the solution of several inverse geophysical problems is described. As an example, we consider the problem of determining the parameters of seismic anisotropy in the Earth’s mantle by the inversion of seismic waveforms. It is shown that this class of problems is reduced to the tabulation of a complicated multidimensional function. In this approach, the calculation at each point in a definition interval is calculated independently, so this is ideally appropriate for calculations that use a loosely connected distributed computing infrastructure.     

Geometrical optimization of trusses by a two-level approximation concept

Geometrical optimization of trusses, i.e. optimization of the cross-sectional areas of the members and the coordinates of the joints, is solved by atwo-level approximation concept (TLAC). Displacements and element forces are approximated by first order Taylor series expansions in terms of generalized variables (or their reciprocal) which define the geometrical properties of the elements. This approximation leads to a high-qualityfirst level approximate problem (FA) which is solved by considering a sequence ofsecond level approximate problems (SA) in the design variable space. The method presented here represents a new approach to the solution of geometrical optimization problems. Numerical examples are given to demonstrate the high efficiency of the proposed method.The method described in this paper was originally formulated by the author in the PR China     

BLISS/S: a new method for two-level structural optimization

The paper describes a two-level method for structural optimization for a minimum weight under the local strength and displacement constraints. The method divides the optimization task into separate optimizations of the individual substructures (in the extreme, the individual components) coordinated by the assembled structure optimization. The substructure optimizations use local cross-sections as design variables and satisfy the highly nonlinear local constraints of strength and buckling. The design variables in the assembled structure optimization govern the structure overall shape and handle the displacement constraints. The assembled structure objective function is the objective in each of the above optimizations. The substructure optimizations are linked to the assembled structure optimization by the sensitivity derivatives. The method was derived from a previously reported two-level optimization method for engineering systems, e.g. aerospace vehicles, that comprise interacting modules to be optimized independently, coordination provided by a system-level optimization. This scheme was adapted to structural optimization by treating each substructure as a module in a system, and using the standard finite element analysis as the system analysis. A numerical example, a hub structure framework, is provided to show the new method agreement with a standard, no-decomposition optimization. The new method advantage lies primarily in the autonomy of the individual substructure optimization that enables concurrency of execution to compress the overall task elapsed time. The advantage increases with the magnitude of that task. Received December 5, 1999?Revised mansucript received April 26, 2000     

A two-level parallelization method for distributed hydrological models

This paper proposes a scalable two-level parallelization method for distributed hydrological models that can use parallelizability at both the sub-basin level and the basic simulation-unit level (e.g., grid cell) simultaneously. This approach first uses the message-passing programming model to dispatch parallel tasks at the sub-basin level to different nodes with multi-core CPUs in the cluster. Each node is responsible for some of the sub-basins. Parallel tasks for each sub-basin at the basic simulation-unit level are then dispatched to multiple cores within each node using the shared-memory programming model. A grid-based distributed hydrological model was parallelized to demonstrate the performance of the proposed method, which was tested in different scenarios (e.g., different data volume, different numbers of sub-basins). Results show that the proposed two-level parallelization method had better scalability than the parallel computation at sub-basin level alone, and the parallel performance increased with data volume and the number of sub-basins.     

Reduced-order solution to the finite-time optimal-control problemsof linear weakly coupled systems

The optimal solution to the finite-time optimal-control problem of weakly coupled linear systems is found in terms of completely decoupled reduced-order differential equations for both closed-loop and open-loop control. This is achieved through the use of the decoupling transformation that block diagonalizes the Hamiltonian matrix of the weakly coupled linear-quadratic control problem. The convergence to the optimal solution is pretty rapid. The proposed technique is very well suited for parallel computations     

A two-level iteration method for solution of contact problems

The merits and limitations of some existing procedures for the solution of contact problems, modeled by the finite element method, are examined. Based on the Lagrangian multiplier method, a partitioning scheme can be used to obtain a small system of equation for the Lagrange multipliers which is then solved by the conjugate gradient method. A two-level contact algorithm is employed which first linearizes the nonlinear contact problem to obtain a linear contact problem that is in turn solved by the Newton method. The performance of the algorithm compared to some existing procedures is demonstrated on some test problems.     

Sliding mode control of continuous-time weakly coupled linear systems with external disturbances

We investigate the problem of sliding mode control for continuous-time weakly coupled linear systems with external disturbances. This is the first study of sliding mode control for continuous-time weakly coupled systems. Using a decoupling transformation, a weakly coupled system is first internally decoupled into two subsystems that are weakly coupled through control inputs only. Then, two sliding mode surfaces are designed for each subsystem using two sliding mode control techniques. The presented procedure greatly simplifies design due to reduced dimensions of subsystems, while providing good approximate results with the accuracy of $O\left(?\right)$, where $?$ is a small weak coupling parameter.