Optimal control in the presence of measurement uncertainties
Linear stochastic systems optimal feedback control with application to spacecraft minimum fuel midcourse guidance problems
Deyst, J. J., Jr.↗
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Dynamic stability of thin elastic plates under the action of non-deterministic loads.
Thin elastic plates dynamic stability under random distribution edge loading using theory of linear stochastic systems
Fontenot, L. L.↗
An analysis of the divergence problem in the Kalman filter.
Modeling errors in linear discrete stochastic system effects on Kalman filter state estimates
Price, C. F.↗
The effects of stability augmentation on the gust response of a STOL aircraft during a curved manual approach
The task of investigating the effect of SAS was formulated as two optimal control problems for stochastic systems: (1) to compute SAS gains with a rate model in the performance index algorithm; and (2) to calculate the pilot gains and system gust response using an optimal pilot model. Both problems were solved to yield reasonable low gains for the pilot and SAS, and the lateral directional mode poles and the longitudinal short period poles could be placed accurately by the model matching algorithm. Of the longitudinal (SAS) poles achieved, the vertical rms path error was least for the unaugmented poles. The lateral rms path error was an order of magnitude larger than the vertical error and showed a plus or minus 50 percent variation with SAS. It increased with dutch roll frequency and damping, and it decreased most significantly with increased roll stability. The variation in lateral error with bank angle for curved flight was also a significant function of the augmented poles.
Porter, M. B., Jr.↗
Specific-optimal control with a dual minimal-order observer-based compensator
The steady-state optimal control of a linear time-invariant stochastic system by means of a minimal-order dual-observer-based compensator is considered in this paper. The structure of the compensator is fixed while the associated gains are to be chosen so as to minimize a quadratic penalty on the plant state. Necessary and sufficient conditions for optimality are given, and an explicit solution is displayed. Salient features pertaining to the optimal system are: a decoupling property, a projection property, and an innovation property. Finally, it is shown that this design corresponds to a singular LQG problem, which is precisely the dual of another singular LQG problem: namely Newmann's problem. A complete picture is then given showing clearly the correspondence between the two designs.
Blanvillain, P. J.↗
The discrete-time compensated Kalman filter
A suboptimal dynamic compensator to be used in conjunction with the ordinary discrete-time Kalman filter is derived. The resultant compensated Kalman filter has the property that steady-state bias estimation errors, resulting from modelling errors, are eliminated. The implementation of the compensated Kalman filter involves the use of accumulators in the residual channels in addition to the nominal dynamic model of the stochastic system.
Lee, W.-H.↗
Stochastic control and the second law of thermodynamics
The second law of thermodynamics is studied from the point of view of stochastic control theory. We find that the feedback control laws which are of interest are those which depend only on average values, and not on sample path behavior. We are lead to a criterion which, when satisfied, permits one to assign a temperature to a stochastic system in such a way as to have Carnot cycles be the optimal trajectories of optimal control problems. Entropy is also defined and we are able to prove an equipartition of energy theorem using this definition of temperature. Our formulation allows one to treat irreversibility in a quite natural and completely precise way.
Brockett, R. W.↗
On-line methods for rotorcraft aeroelastic mode identification
The requirements for the on-line identification of rotorcraft aeroelastic blade modes from random response test data are presented. A recursive maximum likelihood (RML) technique is used in conjunction with a bandpass filter to identify isolated blade mode damping and frequency. The RML technique is demonstrated to have excellent convergence characteristics in random measurement noise and random process noise excitation. The RML identification technique uses an ARMA representation for the aeroelastic stochastic system and requires virtually no user interaction while providing accurate confidence bands on the parameter estimates. Comparisons are made with an off-line Newton type maximum likelihood algorithm which uses a state variable model representation. Results are presented from simulation random response data which quantify the identifed parameter convergence behavior for various levels of random excitation which is typical of wind tunnel turbulence levels. The RML technique is applied to hingless rotor test data from the NASA Langley Research Center Helicopter Hover Facility.
Molusis, J. A.↗
Effects of noise variance model on optimal feedback design and actuator placement
In optimal placement of actuators for stochastic systems, it is commonly assumed that the actuator noise variances are not related to the feedback matrix and the actuator locations. In this paper, we will discuss the limitation of that assumption and develop a more practical noise variance model. Various properties associated with optimal actuator placement under the assumption of this noise variance model are discovered through the analytical study of a second order system.
Ruan, Mifang↗
Iterative LQG Controller Design Through Closed-Loop Identification
This paper presents an iterative Linear Quadratic Gaussian (LQG) controller design approach for a linear stochastic system with an uncertain open-loop model and unknown noise statistics. This approach consists of closed-loop identification and controller redesign cycles. In each cycle, the closed-loop identification method is used to identify an open-loop model and a steady-state Kalman filter gain from closed-loop input/output test data obtained by using a feedback LQG controller designed from the previous cycle. Then the identified open-loop model is used to redesign the state feedback. The state feedback and the identified Kalman filter gain are used to form an updated LQC controller for the next cycle. This iterative process continues until the updated controller converges. The proposed controller design is demonstrated by numerical simulations and experiments on a highly unstable large-gap magnetic suspension system.
Hsiao, Min-Hung↗
Effect of Finite Computational Domain on Turbulence Scaling Law in Both Physical and Spectral Spaces
The well-known translation between the power law of energy spectrum and that of the correlation function or the second order structure function has been widely used in analyzing random data. Here, we show that the translation is valid only in proper scaling regimes. The regimes of valid translation are different for the correlation function and the structure function. Indeed, they do not overlap. Furthermore, in practice, the power laws exist only for a finite range of scales. We show that this finite range makes the translation inexact even in the proper scaling regime. The error depends on the scaling exponent. The current findings are applicable to data analysis in fluid turbulence and other stochastic systems.
Hou, Thomas Y.↗
A Probabilistic Framework for the Validation and Certification of Computer Simulations
The paper presents a methodology for quantifying, propagating, and managing the uncertainty in the data required to initialize computer simulations of complex phenomena. The purpose of the methodology is to permit the quantitative assessment of a certification level to be associated with the predictions from the simulations, as well as the design of a data acquisition strategy to achieve a target level of certification. The value of a methodology that can address the above issues is obvious, specially in light of the trend in the availability of computational resources, as well as the trend in sensor technology. These two trends make it possible to probe physical phenomena both with physical sensors, as well as with complex models, at previously inconceivable levels. With these new abilities arises the need to develop the knowledge to integrate the information from sensors and computer simulations. This is achieved in the present work by tracing both activities back to a level of abstraction that highlights their commonalities, thus allowing them to be manipulated in a mathematically consistent fashion. In particular, the mathematical theory underlying computer simulations has long been associated with partial differential equations and functional analysis concepts such as Hilbert spares and orthogonal projections. By relying on a probabilistic framework for the modeling of data, a Hilbert space framework emerges that permits the modeling of coefficients in the governing equations as random variables, or equivalently, as elements in a Hilbert space. This permits the development of an approximation theory for probabilistic problems that parallels that of deterministic approximation theory. According to this formalism, the solution of the problem is identified by its projection on a basis in the Hilbert space of random variables, as opposed to more traditional techniques where the solution is approximated by its first or second-order statistics. The present representation, in addition to capturing significantly more information than the traditional approach, facilitates the linkage between different interacting stochastic systems as is typically observed in real-life situations.
Ghanem, Roger↗
Life Prediction Issues in Thermal/Environmental Barrier Coatings in Ceramic Matrix Composites
Issues and design requirements for the environmental barrier coating (EBC)/thermal barrier coating (TBC) life that are general and those specific to the NASA Ultra-Efficient Engine Technology (UEET) development program have been described. The current state and trend of the research, methods in vogue related to the failure analysis, and long-term behavior and life prediction of EBCITBC systems are reported. Also, the perceived failure mechanisms, variables, and related uncertainties governing the EBCITBC system life are summarized. A combined heat transfer and structural analysis approach based on the oxidation kinetics using the Arrhenius theory is proposed to develop a life prediction model for the EBC/TBC systems. Stochastic process-based reliability approach that includes the physical variables such as gas pressure, temperature, velocity, moisture content, crack density, oxygen content, etc., is suggested. Benefits of the reliability-based approach are also discussed in the report.
Shah, Ashwin R.↗
Exploring the Connection Between Sampling Problems in Bayesian Inference and Statistical Mechanics
The Bayesian and statistical mechanical communities often share the same objective in their work - estimating and integrating probability distribution functions (pdfs) describing stochastic systems, models or processes. Frequently, these pdfs are complex functions of random variables exhibiting multiple, well separated local minima. Conventional strategies for sampling such pdfs are inefficient, sometimes leading to an apparent non-ergodic behavior. Several recently developed techniques for handling this problem have been successfully applied in statistical mechanics. In the multicanonical and Wang-Landau Monte Carlo (MC) methods, the correct pdfs are recovered from uniform sampling of the parameter space by iteratively establishing proper weighting factors connecting these distributions. Trivial generalizations allow for sampling from any chosen pdf. The closely related transition matrix method relies on estimating transition probabilities between different states. All these methods proved to generate estimates of pdfs with high statistical accuracy. In another MC technique, parallel tempering, several random walks, each corresponding to a different value of a parameter (e.g. "temperature"), are generated and occasionally exchanged using the Metropolis criterion. This method can be considered as a statistically correct version of simulated annealing. An alternative approach is to represent the set of independent variables as a Hamiltonian system. Considerab!e progress has been made in understanding how to ensure that the system obeys the equipartition theorem or, equivalently, that coupling between the variables is correctly described. Then a host of techniques developed for dynamical systems can be used. Among them, probably the most powerful is the Adaptive Biasing Force method, in which thermodynamic integration and biased sampling are combined to yield very efficient estimates of pdfs. The third class of methods deals with transitions between states described by rate constants. These problems are isomorphic with chemical kinetics problems. Recently, several efficient techniques for this purpose have been developed based on the approach originally proposed by Gillespie. Although the utility of the techniques mentioned above for Bayesian problems has not been determined, further research along these lines is warranted
Pohorille, Andrew↗
Open-loop-feedback-optimal adaptive stochastic control of linear systems
This paper considers the suboptimal stochastic control of linear discrete-time dynamical systems with unknown or stochastically varying parameters. The suboptimal scheme is based upon the use of the open-loop-feedback-optimal method. The state and parameter estimates are generated by an extended Kalman filter algorithm. Numerical results for first-order systems are presented.
Ku, R.↗
Linear System Control Using Stochastic Learning Automata
This paper explains the use of a Stochastic Learning Automata (SLA) to control switching between three systems to produce the desired output response. The SLA learns the optimal choice of the damping ratio for each system to achieve a desired result. We show that the SLA can learn these states for the control of an unknown system with the proper choice of the error criteria. The results of using a single automaton are compared to using multiple automata.
Ziyad, Nigel↗
Mathematical problems of modeling stochastic nonlinear dynamic systems
Systems analysis logic applied to mathematical modeling of dynamic nonlinear stochastic processes
Mortensen, R. E.↗
Performance evaluation of automated manufacturing systems using generalized stochastic Petri Nets
The main objective of this research is to develop a generic modeling methodology with a flexible and modular framework to aid in the design and performance evaluation of integrated manufacturing systems using a unified model. After a thorough examination of the available modeling methods, the Petri Net approach was adopted. The concurrent and asynchronous nature of manufacturing systems are easily captured by Petri Net models. Three basic modules were developed: machine, buffer, and Decision Making Unit. The machine and buffer modules are used for modeling transfer lines and production networks. The Decision Making Unit models the functions of a computer node in a complex Decision Making Unit Architecture. The underlying model is a Generalized Stochastic Petri Net (GSPN) that can be used for performance evaluation and structural analysis. GSPN's were chosen because they help manage the complexity of modeling large manufacturing systems. There is no need to enumerate all the possible states of the Markov Chain since they are automatically generated from the GSPN model.
Al-Jaar, Robert Y.↗