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Large scale systems are defined as systems requiring more than one decision maker to control the system. Decentralized control and decomposition are discussed for large scale dynamic systems. Information and many-person decision problems are analyzed.
Classes of large scale dynamic systems were discussed in the context of modern control theory. Specific examples discussed were in the technical fields of aeronautics, water resources and electric power.
Techniques of predicting and/or controlling the dynamic behavior of large scale systems are discussed in terms of decentralized decision making. Topics discussed include: (1) control of large scale systems by dynamic team with delayed information sharing; (2) dynamic resource allocation problems by a team (hierarchical structure with a coordinator); and (3) some problems related to the construction of a model of reduced dimension.
The classes of large-scale dynamic systems are discussed in terms of modeling with emphasis on air transportation system modeling.
We consider the class of large-scale dynamical systems consisting of identical subsystems, but with complex connectivity. It is shown that the irreducibility of this large system is directly related to the irreducibility of a simple system, which is obtained by a replacement of the subsystems by integrators.
Some notions of decentralization and coordination in the control of large-scale dynamic systems are discussed. Decentralization and coordination have always been important concepts in the study of large systems. Roughly speaking decentralization is the process of dividing a large problem into subproblems so that it can be handled more easily. Coordination is the manipulation of the subproblem so that the original problem is solved. The various types of decentralization and coordination that have been used to control dynamic systems are discussed. The emphasis was to distinguish between on-line and off-line operations to understand the results available by indicating the aspects of the problem which are decentralized.
A multilevel feedback control scheme is proposed for optimization of large-scale systems composed of a number of (not necessarily weakly coupled) subsystems. Local controllers are used to optimize each subsystem, ignoring the interconnections. Then, a global controller may be applied to minimize the effect of interconnections and improve the performance of the overall system. At the cost of suboptimal performance, this optimization strategy ensures invariance of suboptimality and stability of the systems under structural perturbations whereby subsystems are disconnected and again connected during operation.
The improved cost effectiveness using better models, more accurate and faster algorithms and large scale computing offers more representative dynamic analyses. The band Lanczos eigen-solution method was implemented in Rockwell's version of 1984 COSMIC-released NASTRAN finite element structural analysis computer program to effectively solve for structural vibration modes including those of large complex systems exceeding 10,000 degrees of freedom. The Lanczos vectors were re-orthogonalized locally using the Lanczos Method and globally using the modified Gram-Schmidt method for sweeping rigid-body modes and previously generated modes and Lanczos vectors. The truncated band matrix was solved for vibration frequencies and mode shapes using Givens rotations. Numerical examples are included to demonstrate the cost effectiveness and accuracy of the method as implemented in ROCKWELL NASTRAN. The CRAY version is based on RPK's COSMIC/NASTRAN. The band Lanczos method was more reliable and accurate and converged faster than the single vector Lanczos Method. The band Lanczos method was comparable to the subspace iteration method which was a block version of the inverse power method. However, the subspace matrix tended to be fully populated in the case of subspace iteration and not as sparse as a band matrix.
Increasing demands on the fidelity of simulations for real-time and high-fidelity simulations are stressing the capacity of modern processors. New integration techniques are required that provide maximum efficiency for systems that are parallelizable. However many current techniques make assumptions that are at odds with non-cascadable systems. A new serial multi-step/multi-rate integration algorithm for dual-timescale continuous state systems is presented which applies to these systems, and is extended to a parallel multi-step/multi-rate algorithm. The superior performance of both algorithms is demonstrated through a representative example.
A large-scale dynamic system is considered as composed of a number of interconnected subsystems. Input and output reachability of the system is defined as a structural counterpart to controllability and observability. When the system is subject to structural perturbations due to on-off participation of the subsystems, conditions are provided for reachability to be connective, that is, to be invariant under the perturbations. The concept of input and output reachability leads naturally to formulations of input and output decentralized systems. It is shown that such systems are connectively reachable, which is an important structural property of 'large' and 'small' decentralized systems alike. Finally, a procedure is outlined to transform a centralized system into an input or output decentralized system with distinct inputs or outputs assigned to each subsystem separately.
Artificial intelligence techniques are applied to the problems of model form and parameter identification of large-scale dynamic systems. The object-oriented knowledge representation is discussed in the context of causal modeling and qualitative reasoning. Structured sets of rules are used for implementing qualitative component simulations, for catching qualitative discrepancies and quantitative bound violations, and for making reconfiguration and control decisions that affect the physical system. These decisions are executed by backward-chaining through a knowledge base of control action tasks. This approach was implemented for two examples: a triple quadrupole mass spectrometer and a two-phase thermal testbed. Results of tests with both of these systems demonstrate that the software replicates some or most of the functionality of a human operator, thereby reducing the need for a human-in-the-loop in the lower levels of control of these complex systems.
The purpose of this paper is to develop new methods for constructing vector Lyapunov functions and broaden the application of Lyapunov's theory to stability analysis of large-scale dynamic systems. The application, so far limited by the assumption that the large-scale systems are composed of exponentially stable subsystems, is extended via the general concept of comparison functions to systems which can be decomposed into asymptotically stable subsystems. Asymptotic stability of the composite system is tested by a simple algebraic criterion. By redefining interconnection functions among the subsystems according to interconnection matrices, the same mathematical machinery can be used to determine connective asymptotic stability of large-scale systems under arbitrary structural perturbations.
The purpose of this paper is to develop new methods for constructing vector Liapunov functions and broaden the application of Liapunov's theory to stability analysis of large-scale dynamic systems. The application, so far limited by the assumption that the large-scale systems are composed of exponentially stable subsystems, is extended via the general concept of comparison functions to systems which can be decomposed into asymptotically stable subsystems. Asymptotic stability of the composite system is tested by a simple algebraic criterion. With minor technical adjustments, the same criterion can be used to determine connective asymptotic stability of large-scale systems subject to structural perturbations. By redefining the constraints imposed on the interconnections among the subsystems, the considered class of systems is broadened in an essential way to include composite systems with unstable subsystems. In this way, the theory is brought substantially closer to reality since stability of all subsystems is no longer a necessary assumption in establishing stability of the overall composite system.
This paper establishes the connective stability concept in the framework of the comparison principle and vector Liapunov functions, as a natural setting for resolving the complexity vs reliability problem in the control of large-scale dynamic systems. The central result is the following: a stable complex system when composed as a competitive structure of the interconnected stable subsystems remains stable despite the on-off participation of the subsystems. This result is important in that it can be used efficiently to synthesize reliable complex systems by multilevel feedback control.
Subspace iteration has been a major advance in solving large eigen problems when only a subset of eigen-pairs is required. The essence of this method is a transformation from displacement coordinates of an n-th order eigensystem to generalized coordinates of a smaller q-th order. The eigenvalue problem is then solved in the reduced space. The method was first developed by Clint and Jennings for real symmetric systems and was then called 'simultaneous iteration'. The success of the method prompted further research along this line and there have been many improved algorithms developed. This approach has been widely used by structural engineers for extracting the most useful natural frequencies and mode shapes of large-scale dynamic systems. This paper exploits into a new direction which is in the form of iterative process for simultaneously calculating eigenvector derivatives of many eigenvectors with respect to multi-variables. The method fully uses all the available information from preceding eigenvalue solution and, thus, effectively economizes computational efforts. It iterates through two equations derived from the first variation of the two fundamental equations used in subspace iteration method. There is no expensive large matrix decomposition required and the process converges to acceptable solution in a finite number of iterations. Therefore, the procedure increases its efficiency superiority over the others as the system size or the number of interested eigenvectors become larger and larger.
Phase variable transformations are used to construct the mathematical model of an aeroelastic aircraft in a form that is amenable to partial or piecemeal acceptance of parameters estimated from flight data. The problem is one of parameter identification of large scale dynamic systems involving a system matrix characterized by about 200 elements. A mathematical model of the USAF Total In-Flight Simulator was computed using the FLEXSTAB program. As data became available during the progress of the flight test program, it was processed and substituted in the mathematical model for parameters obtained from the FLEXSTAB program. Results tend to show a progressive and orderly transition from an analytically defined mathematical model to one obtained from the flight tests of the actual aircraft.
The problem of the parameter identification of large scale dynamic systems involving a system matrix characterized by approximately 200 elements is addressed. By using phase variable transformations, a mathematical model of an aeroelastic airplane is described in a form that is amenable to partial or piecemeal acceptance of parameters estimated from flight data. A mathematical model of the U.S. Air Force Total In-Flight Simulator was computed using the FLEXSTAB digital computer program. As data became available during the progress of the flight test program, this data was processed and substituted in the mathematical model for parameters analytically obtained from the FLEXSTAB program. The results tend to show a progressive and orderly transition from an analytically defined mathematical model to one obtained from the flight tests of the actual aircraft.
Range scheduling for satellite control presents a classical problem: supervisory control of a large-scale dynamic system, with unwieldy amounts of interrelated data used as inputs to the decision process. Increased automation of the task, with the appropriate human-computer interface, is highly desirable. The development and user evaluation of a semi-automated network range scheduling system is described. The system incorporates a synergistic human-computer interface consisting of a large screen color display, voice input/output, a 'sonic pen' pointing device, a touchscreen color CRT, and a standard keyboard. From a human factors standpoint, this development represents the first major improvement in almost 30 years to the satellite control network scheduling task.