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At least 217 records · Page 12

The ergodic decomposition of stationary discrete random processes

The ergodic decomposition is discussed, and a version focusing on the structure of individual sample functions of stationary processes is proved for the special case of discrete-time random processes with discrete alphabets. The result is stronger in this case than the usual theorem, and the proof is both intuitive and simple. Estimation-theoretic and information-theoretic interpretations are developed and applied to prove existence theorems for universal source codes, both noiseless and with a fidelity criterion.

Gray, R. M.↗

Attitude estimation of earth orbiting satellites by decomposed linear recursive filters

Attitude estimation of earth orbiting satellites (including Large Space Telescope) subjected to environmental disturbances and noises was investigated. Modern control and estimation theory is used as a tool to design an efficient estimator for attitude estimation. Decomposed linear recursive filters for both continuous-time systems and discrete-time systems are derived. By using this accurate estimation of the attitude of spacecrafts, state variable feedback controller may be designed to achieve (or satisfy) high requirements of system performance.

Kou, S. R.↗

Adaptive control in the presence of unmodeled dynamics

Stability and robustness properties of a wide class of adaptive control algorithms in the presence of unmodeled dynamics and output disturbances were investigated. The class of adaptive algorithms considered are those commonly referred to as model reference adaptive control algorithms, self-tuning controllers, and dead beat adaptive controllers, developed for both continuous-time systems and discrete-time systems. A unified analytical approach was developed to examine the class of existing adaptive algorithms. It was discovered that all existing algorithms contain an infinite gain operator in the dynamic system that defines command reference errors and parameter errors; it is argued that such an infinite gain operator appears to be generic to all adaptive algorithms, whether they exhibit explicit or implicit parameter identification. It is concluded that none of the adaptive algorithms considered can be used with confidence in a practical control system design, because instability will set in with a high probability.

Rohrs, C. E.↗

Modular approach for satellite communication ground terminals

The trend in satellite communications is toward completely digital, time division multiple access (TDMA) systems with uplink and downlink data rates dictated by the type of service offered. Trunking terminals will operate in the 550 MBPS (megabit per second) region uplink and downlink, whereas customer premise service (CPS) terminals will operate in the 25 to 10 MBPS region uplink and in the 200 MBPS region downlink. Additional criteria for the ground terminals will be to maintain clock sychronization with the system and burst time integrity to within a matter of nanoseconds, to process required order-fire information, to provide adaptive data scrambing, and to compensate for variations in the user input output data rates, and for changes in range in the satellite communications links resulting from satellite perturbations in orbit. To achieve the required adaptability of a ground terminal to the above mentioned variables, programmable building blocks can be developed that will meet all of these requirements. To maintain system synchronization, i.e., all bursted data arriving at the satellite within assigned TDMA windows, ground terminal transmit data rates and burst timing must be maintained within tight tolerances. With a programmable synchronizer as the heart of the terminal timing generation, variable data rates and burst timing tolerances are achievable. In essence, the unit inputs microprocessor generated timing words and outputs discrete timing pulses.

Gould, G. R.↗

Robustness of adaptive control algorithms in the presence of unmodeled dynamics

This paper reports the outcome of an exhaustive analytical and numerical investigation of stability and robustness properties of a wide class of adaptive control algorithms in the presence of unmodeled dynamics and output disturbances. The class of adaptive algorithms considered are those commonly referred to as model-reference adaptive control algorithms, self-tuning controllers, and dead-beat adaptive controllers; they have been developed for both continuous-time systems and discrete-time systems. The existing adaptive control algorithms have been proven to be globally asymptotically stable under certain assumptions, the key ones being (1) that the number of poles and zeroes of the unknown plant are known, and (2) that the primary performance criterion is related to good command following. These theoretical assumptions are too restrictive from an engineering point of view. Real plants always contain unmodeled high-frequency dynamics and small delays, and hence no upper bound on the number of the plant poles and zeroes exists. Also real plants are always subject to unmeasurable output additive disturbances, although these may be guide small. Hence, it is important to critically examine the stability robustness properties of the existing adaptive algorithms when some of the theoretical assumptions are removed; in particular, their stability and performance properties in the presence of unmodeled dynamics and output disturbances. Previously announced in STAR as N83-16061

Rohrs, C. E.↗

Six-degree-of-freedom aircraft simulation with mixed-data structure using the applied dynamics simulation language, ADSIM

A realistic simulation of an aircraft in the flight using the AD 100 digital computer is presented. The implementation of three model features is specifically discussed: (1) a large aerodynamic data base (130,00 function values) which is evaluated using function interpolation to obtain the aerodynamic coefficients; (2) an option to trim the aircraft in longitudinal flight; and (3) a flight control system which includes a digital controller. Since the model includes a digital controller the simulation implements not only continuous time equations but also discrete time equations, thus the model has a mixed-data structure.

Savaglio, Clare↗

Recent developments in learning control and system identification for robots and structures

This paper reviews recent results in learning control and learning system identification, with particular emphasis on discrete-time formulation, and their relation to adaptive theory. Related continuous-time results are also discussed. Among the topics presented are proportional, derivative, and integral learning controllers, time-domain formulation of discrete learning algorithms. Newly developed techniques are described including the concept of the repetition domain, and the repetition domain formulation of learning control by linear feedback, model reference learning control, indirect learning control with parameter estimation, as well as related basic concepts, recursive and non-recursive methods for learning identification.

Phan, M.↗

Diagonally implicit Runge–Kutta schemes: Discrete energy-balance laws and compactness properties

Abstract We study diagonally implicit Runge–Kutta (DIRK) schemes when applied to abstract evolution problems that fit into the Gelfand-triple framework. We introduce novel stability notions that are well-suited to this setting and provide simple, necessary and sufficient, conditions to verify that a DIRK scheme is stable in our sense and in Bochner-type norms. We use several popular DIRK schemes in order to illustrate cases that satisfy the required structural stability properties and cases that do not. In addition, under some mild structural conditions on the problem we can guarantee compactness of families of discrete solutions with respect to time discretization.

Mathematics↗

On modeling of integrated communication and control systems

The mathematical modeling scheme proposed by Ray and Halevi (1988) for integrated communication and control systems is considered analytically, with an emphasis on the effect of introducing varying and distributed time delays to account for asynchronous time-division multiplexing in the communication part of the system. Ray and Halevi applied a state-transition concept to transform the original continuous-time model into a discrete-time model; the same approach was used by Kalman and Bertram (1959) to model various types of sampled data systems which are not subject to induced delays. The relationship between the two modeling schemes is explored, and it is shown that, although the Kalman-Bertram method has the advantage of a unified approach, it becomes inconvenient when varying delays appear in the control loop.

Liou, Luen-Woei↗

Linear system theory

The aim of this book is to provide a systematic and rigorous access to the main topics of linear state-space system theory in both the continuous-time case and the discrete-time case; and the I/O description of linear systems. The main thrusts of the work are the analysis of system descriptions and derivations of their properties, LQ-optimal control, state feedback and state estimation, and MIMO unity-feedback systems.

Callier, Frank M.↗

Interior Noise Reduction by Adaptive Feedback Vibration Control

The objective of this project is to investigate the possible use of adaptive digital filtering techniques in simultaneous, multiple-mode identification of the modal parameters of a vibrating structure in real-time. It is intended that the results obtained from this project will be used for state estimation needed in adaptive structural acoustics control. The work done in this project is basically an extension of the work on real-time single mode identification, which was performed successfully using a digital signal processor (DSP) at NASA, Langley. Initially, in this investigation the single mode identification work was duplicated on a different processor, namely the Texas Instruments TMS32OC40 DSP. The system identification results for the single mode case were very good. Then an algorithm for simultaneous two mode identification was developed and tested using analytical simulation. When it successfully performed the expected tasks, it was implemented in real-time on the DSP system to identify the first two modes of vibration of a cantilever aluminum beam. The results of the simultaneous two mode case were good but some problems were identified related to frequency warping and spurious mode identification. The frequency warping problem was found to be due to the bilinear transformation used in the algorithm to convert the system transfer function from the continuous-time domain to the discrete-time domain. An alternative approach was developed to rectify the problem. The spurious mode identification problem was found to be associated with high sampling rates. Noise in the signal is suspected to be the cause of this problem but further investigation will be needed to clarify the cause. For simultaneous identification of more than two modes, it was found that theoretically an adaptive digital filter can be designed to identify the required number of modes, but the algebra became very complex which made it impossible to implement in the DSP system used in this study. The on-line identification algorithm developed in this research will be useful in constructing a state estimator for feedback vibration control.

Lim, Tae W.↗

Stability and Conservation properties of Hermite-based approximations of the Vlasov-Poisson System

Spectral approximation based on Hermite-Fourier expansion of the Vlasov-Poisson model for a collisionless plasma in the electro-static limit is provided by adding high-order artificial collision operators of Lenard-Bernstein type. These differential operators are suitably designed in order to preserve the physically-meaningful invariants (number of particles, momentum, energy). In view of time-discretization, stability results in appropriate norms are presented. In this study, necessary conditions link the magnitude of the artificial collision term, the number of spectral modes of the discretization, as well as the time-step. The analysis, carried out in full for the Hermite discretization of a simple linear problem in one-dimension, is then partly extended to cover the complete nonlinear Vlasov-Poisson model.

97 MATHEMATICS AND COMPUTING↗

Windowed least-squares model reduction for dynamical systems

Here we propose a windowed least-squares (WLS) approach for model reduction of dynamical systems. The proposed approach sequentially minimizes the time-continuous full-order-model residual within a low-dimensional space–time trial subspace over time windows. The approach comprises a generalization of existing model reduction approaches, as particular instances of the methodology recover Galerkin, least-squares Petrov–Galerkin (LSPG), and space–time LSPG projection. In addition, the approach addresses key deficiencies in existing model reduction techniques, e.g., the dependence of LSPG and space–time LSPG projection on the time discretization and the exponential growth in time exhibited by a posteriori error bounds for both Galerkin and LSPG projection. We consider two types of space–time trial subspaces within the proposed approach: one that reduces only the spatial dimension of the full-order model, and one that reduces both the spatial and temporal dimensions of the full-order model. For each type of trial subspace, we consider two different solution techniques: direct (i.e., discretize then optimize) and indirect (i.e., optimize then discretize). Numerical experiments conducted using trial subspaces characterized by spatial dimension reduction demonstrate that the WLS approach can yield more accurate solutions with lower space–time residuals than Galerkin and LSPG projection.

97 MATHEMATICS AND COMPUTING↗

Measurand transient signal suppressor

A transient signal suppressor for use in a controls system which is adapted to respond to a change in a physical parameter whenever it crosses a predetermined threshold value in a selected direction of increasing or decreasing values with respect to the threshold value and is sustained for a selected discrete time interval is presented. The suppressor includes a sensor transducer for sensing the physical parameter and generating an electrical input signal whenever the sensed physical parameter crosses the threshold level in the selected direction. A manually operated switch is provided for adapting the suppressor to produce an output drive signal whenever the physical parameter crosses the threshold value in the selected direction of increasing or decreasing values. A time delay circuit is selectively adjustable for suppressing the transducer input signal for a preselected one of a plurality of available discrete suppression time and producing an output signal only if the input signal is sustained for a time greater than the selected suppression time. An electronic gate is coupled to receive the transducer input signal and the timer output signal and produce an output drive signal for energizing a control relay whenever the transducer input is a non-transient signal which is sustained beyond the selected time interval.

Bozeman, Richard J., Jr.↗

Hybrid particle-spectral method for kinetic plasma simulations

A hybrid model for numerical solutions of the Vlasov–Poisson equations is presented, which blends spectral and particle approaches. The model splits the distribution function for plasma species into both spectral and particle representations in the velocity space to combine the advantages of each approach. The spectral representation leverages asymmetrically weighted Hermite basis, whereas the particle representation leverages the particle-in-cell method. Configuration phase space is decomposed with the Fourier method, which is well suited for periodic problems. We derive conservation equations for mass, momentum, and energy for the proposed combined method. It is shown that the coupling error between the two methods is absent in the semi-discrete setting (not taking into account time discretization). Finally, numerical test cases are presented simulating a weak electron beam interaction with plasma, leading to beam–plasma instability. The initially localized electron beam evolved into a highly non-equilibrium distribution function in the velocity space. A small growth rate and the resonance nature of instability make it difficult to obtain accurate solutions for purely particle methods due to noise, which falls as ∼1/Np with a number of particles. At the same time, purely spectral methods may require a large number of modes to capture the highly non-equilibrium state of the evolved beam. We show that the hybrid method is well suited for such problems: it reproduces the linear stage as well as nonlinear dynamics with sufficient accuracy using a highly non-equilibrium distribution function.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Hybrid particle-spectral method for kinetic plasma simulations

A hybrid model for numerical solutions of the Vlasov–Poisson equations is presented, which blends spectral and particle approaches. The model splits the distribution function for plasma species into both spectral and particle representations in the velocity space to combine the advantages of each approach. The spectral representation leverages asymmetrically weighted Hermite basis, whereas the particle representation leverages the particle-in-cell method. Configuration phase space is decomposed with the Fourier method, which is well suited for periodic problems. We derive conservation equations for mass, momentum, and energy for the proposed combined method. It is shown that the coupling error between the two methods is absent in the semi-discrete setting (not taking into account time discretization). Finally, numerical test cases are presented simulating a weak electron beam interaction with plasma, leading to beam–plasma instability. The initially localized electron beam evolved into a highly non-equilibrium distribution function in the velocity space. A small growth rate and the resonance nature of instability make it difficult to obtain accurate solutions for purely particle methods due to noise, which falls as ~1/$\sqrt{N_p}$ with a number of particles. At the same time, purely spectral methods may require a large number of modes to capture the highly nonequilibrium state of the evolved beam. We show that the hybrid method is well suited for such problems: it reproduces the linear stage as well as nonlinear dynamics with sufficient accuracy using a highly non-equilibrium distribution function.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Issues in modeling and controlling the SCOLE configuration

The parametric study of the in-plane Spacecraft Control Laboratory Experiment (SCOLE) system, the Floquet Stability Analysis, and three dimensional formulations of the SCOLE system dynamics are examined. Control issues are discussed, such as: control of large structures with delayed input in continuous time; control with delayed input in discrete time; control law design for SCOLE using Linear Quadratic Gaussian (LQC)/TRR technique; and optimal torque control for SCOLE slewing maneuvers.

Bainum, Peter M.↗

On the discretization error of the discrete generalized quantum master equation

The transfer tensor method (TTM) [Cerrillo and Cao, Phys. Rev. Lett. 112 , 110401 (2014)] can be considered a discrete-time formulation of the Nakajima–Zwanzig quantum master equation (NZ-QME) for modeling non-Markovian quantum dynamics. A recent paper [Makri, J. Chem. Theory Comput. 21 , 5037 (2025)] raised concerns regarding the consistency of the TTM discretization, particularly a spurious term at the initial time t = 0. Here, this work presents a detailed analysis of the discretization structure of the TTM, clarifying the origin of the initial-time correction and establishing a consistent relationship between the TTM discrete-time memory kernel K N and the continuous-time NZ-QME kernel $\mathscr{K}$( N Δ t ). This relationship is validated numerically using the spin-boson model, demonstrating convergence of reconstructed memory kernels and accurate dynamical evolution as Δ t → 0. While the TTM provides a consistent discretization, we note that alternative schemes are also viable, such as the midpoint derivative/midpoint integral scheme proposed in Makri’s work. The relative performance of various schemes for either computing accurate $\mathscr{K}$( N Δ t ) from exact dynamics or obtaining accurate dynamics from exact $\mathscr{K}$( N Δ t ) warrants further investigation.

Density-matrix↗