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NASA NTRS1972

Theory of a general class of dissipative processes.

Development of a theory of periodic processes that is of sufficient generality for being applied to systems defined by partial differential equations (distributed parameter systems) and functional differential equations of the retarded and neutral type (hereditary systems), as well as to systems arising in the theory of elasticity. In particular, the attempt is made to develop a meaningful general theory of dissipative periodic systems with a wide range of applications.

Hale, J. K.↗

NASA NTRS1981

Problems in the application of multivariable adaptive control to flexible spacecraft

The present investigation is concerned with the application of adaptive control to distributed parameter systems (DPS) which arise in the modeling of large space structures (LSS). Distributed parameter and multivariable models for LSS are introduced and the decoupled adaptive control of such models is considered. Possibilities to achieve adaptive control in connection with a more general model are also examined. It is found that, in concept, adaptive control appears to be a natural choice for solving attitude and shape perturbation problems in LSS. However, due to the distributed parameter nature of such structures and the current lack of experience in their control, the problem must be phrased in general terms which are very difficult to deal with. In particular, detailed a priori plant knowledge is currently required so that decoupling and/or reduced order models of sufficient accuracy can be provided.

Lawrence, D. A.↗

NASA NTRS1992

A fundamental theorem for the model reduction of nonlinear systems

A simple, but fundamental, theorem is given on the extent to which a nonlinear system model can have its order reduced. Essentially, the result is that the order, or the dimension of the state space representation, cannot be reduced to, or below, the dimension of the system's attractor. Several examples are given to illustrate this point. The result is especially applicable to higher order systems such as the infinite dimensional systems arising from the modeling of distributed parameter systems.

Mossayebi, Faramarz↗

NASA NTRS1981

Parameter estimation of large flexible aerospace structures with application to the control of the Maypole Deployable Reflector

Systems such as the Maypole deployable reflector have a distributed parameter nature. The flexible column and hoop structure and the circular antenna of 30-100 meter diameter which it supports are described by partial, rather than ordinary, differential equations. Progress completed in reduced order modelling andd controller design and digital parameter estimation and control is summarized. Topics covered include depolyment and on-orbit operation; quasi-static (steady state) operation; dynamic distributed parameter system; autoregressive moving average identification; frequency domain procedures; direct or implicit active control; adaptive observers; parameter estimation using a linear reinforcement learning factor; feedback control; and reduced order modeling for nonlinear systems.

Balas, M. J.↗

NASA NTRS1972

Optimal control of first order distributed systems

The problem of characterizing optimal controls for a class of distributed-parameter systems is considered. The system dynamics are characterized mathematically by a finite number of coupled partial differential equations involving first-order time and space derivatives of the state variables, which are constrained at the boundary by a finite number of algebraic relations. Multiple control inputs, extending over the entire spatial region occupied by the system ("distributed controls') are to be designed so that the response of the system is optimal. A major example involving boundary control of an unstable low-density plasma is developed from physical laws.

Johnson, T. L.↗

NASA NTRS1968

An invariance principle for dynamical systems in Hilbert spaces

Invariance method for extending Liapunov function to distributed parameter system

Infante, E. F.↗

NASA NTRS1982

Reconstruction of atmospheric pollutant concentrations from remote sensing data - An application of distributed parameter observer theory

The reconstruction of a concentration distribution from spatially averaged and noise-corrupted data is a central problem in processing atmospheric remote sensing data. Distributed parameter observer theory is used to develop reconstructibility conditions for distributed parameter systems having measurements typical of those in remote sensing. The relation of the reconstructibility condition to the stability of the distributed parameter observer is demonstrated. The theory is applied to a variety of remote sensing situations, and it is found that those in which concentrations are measured as a function of altitude satisfy the conditions of distributed state reconstructibility.

Koda, M.↗

NASA NTRS1974

A minimum principle for smooth first-order distributed systems

Consideration of the problem of characterizing optimal controls for a class of distributed parameter systems. The system dynamics are characterized mathematically by a finite number of coupled partial differential equations involving first-order time and space derivatives of the state variables. Boundary conditions on the state are in the form of a finite number of algebraic relations between the state and boundary control variables. A few directions are outlined in which the results obtained may be extended further.

Johnson, T. L.↗

NASA NTRS1971

Optimal startup control of a jacketed tubular reactor.

The optimal startup policy of a jacketed tubular reactor, in which a first-order, reversible, exothermic reaction takes place, is presented. A distributed maximum principle is presented for determining weak necessary conditions for optimality of a diffusional distributed parameter system. A numerical technique is developed for practical implementation of the distributed maximum principle. This involves the sequential solution of the state and adjoint equations, in conjunction with a functional gradient technique for iteratively improving the control function.

Hahn, D. R.↗

NASA NTRS1972

An approximate method for the synthesis of optimal control of distributed systems.

An approximate method is presented for the synthesis of an optimal control of distributed parameter systems, based on a combination of the ideas of Lyapunov's direct method and those of Bellman's successive approximation in policy space. The method is such that the approximate equation is improved after each iteration in the sense of the performance index being used.

Park, K. E.↗

NASA NTRS1988

On the inclusion principle and spillover effect in the identification of distributed structures

Distributed structures are Distributed-Parameter Systems (DPS) and must be modeled by large-dimensional systems. Practical limitations require that only a subset of the modes be actively controlled. Control of the residual (uncontrolled) modes is known as control spillover, and it can degrade the system performance. The contamination of the sensor signals by the residual modes is known as observation spillover and it can destabilize the system. An analogous effect exists in the identification problem. Distributed structures must be represented by discretized (finite-dimensional) models or lumped-parameter systems. The contamination of the measurements by the residual (unmodeled) modes is referred to as identification spillover, and it is the object of this study. To study the effects of identification spillover, we use a variational formulation to obtain the natural frequencies and mode shapes. This formulation has direct application to DPS. The identification technique consists of finding the stationary values of a pseudo-Rayleigh quotient.

Norris, Mark. A.↗

NASA NTRS1988

Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems

An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.

Banks, H. T.↗

NASA NTRS1985

Stable Direct Adaptive Control of Linear Infinite-dimensional Systems Using a Command Generator Tracker Approach

A command generator tracker approach to model following contol of linear distributed parameter systems (DPS) whose dynamics are described on infinite dimensional Hilbert spaces is presented. This method generates finite dimensional controllers capable of exponentially stable tracking of the reference trajectories when certain ideal trajectories are known to exist for the open loop DPS; we present conditions for the existence of these ideal trajectories. An adaptive version of this type of controller is also presented and shown to achieve (in some cases, asymptotically) stable finite dimensional control of the infinite dimensional DPS.

Balas, M. J.↗

NASA NTRS1977

Solar sail attitude dynamics and control

This paper describes some results of an attitude dynamics and control study for a solar sailing vehicle. This type of vehicle is currently under study and evaluation at JPL and has very high potential for interplanetary missions in and beyond the 1980s. Crucial to the success of such a vehicle would be the performance of its onboard attitude control system. Because of the vehicle's large size and its flexibility, vehicle deformations may have a potential for causing a degradation in vehicle performance. It may therefore be necessary for the control system to take into account the vehicle deformations as well as its rigid-body motions. Distributed parameter system analysis techniques are used in the paper to study certain fundamental aspects of such a control system for the sail vehicle. The techniques can, however, be more generally applicable to other large flexible vehicles.

Rodriguez, G.↗

NASA NTRS1979

The dual-momentum control device for large space systems

The dual-momentum control device being studied for large spacecraft consists of two counter-rotating rings, each designated as an annular momentum control device (AMCD). For large rings, flexibility is appreciable and it becomes necessary to account for the distributed nature of the rings in the design of the magnetic bearing controllers. Also, ring behavior is unpredictably sensitive to ring temperature, spin rate, manufacturing imperfections, and other variables. For that reason, an adaptive control system is being sought for ring stabilization and maneuvering. This paper details an original adaptive control methodology for distributed parameter systems and illustrates this technique by application to AMCD stabilization.

Montgomery, R. C.↗

NASA NTRS1989

Optimal feedback control infinite dimensional parabolic evolution systems: Approximation techniques

A general approximation framework is discussed for computation of optimal feedback controls in linear quadratic regular problems for nonautonomous parabolic distributed parameter systems. This is done in the context of a theoretical framework using general evolution systems in infinite dimensional Hilbert spaces. Conditions are discussed for preservation under approximation of stabilizability and detectability hypotheses on the infinite dimensional system. The special case of periodic systems is also treated.

Banks, H. T.↗

NASA NTRS1989

Optimal feedback control of infinite-dimensional parabolic evolution systems - Approximation techniques

Banks, H. T.↗

NASA NTRS1972

Stability of distributed systems with feedback via Michailov's criterion.

Development of a stability criterion of the Nyquist type from Michailov's criterion for a large class of distributed parameter systems, in particular, for a large class of transmission line systems with feedback. Following a generalization of Michailov's criterion, simplifying assumptions, usually valid in practice, are shown to yield a simplified test for determining whether 'encirclement-counting' constitutes a valid stability test. The results are reformulated for an open-loop analysis. Three examples show various aspects of the theoretical analysis.

Reis, G. C.↗