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Results for “Stochastic dynamical systems”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Integrated system identification and modal state estimation for control of flexible space structures

A novel approach of integrated system identification and modal state estimation is proposed for control of linear dynamical systems including flexible space structures. There are four steps involved in this approach. First, the relation between a stochastic state space model of a dynamical system and the coefficients of its autoregressive model with exogenous input is derived. Second, an adaptive least-squares transversal predictor is used to estimate the coefficients of the model. Third, a state space model and a steady state Kalman filter gain of the dynamical system are then identified from the coefficients of the model by using the eigensystem realization algorithm. Fourth, a modal state estimator is constructed using the modal parameters of the identified model. On-line implementation of this algorithm can continually improve the modal parameters and the filter gain. It can also gradually update the system model when the system characteristics are slowly changing. A numerical example is used to illustrate the feasibility of the new approach.

Chen, Chung-Wen↗
NASA NTRS1983

Guaranteed robustness properties of multivariable, nonlinear, stochastic optimal regulators

The robustness of optimal regulators for nonlinear, deterministic and stochastic, multi-input dynamical systems is studied under the assumption that all state variables can be measured. It is shown that, under mild assumptions, such nonlinear regulators have a guaranteed infinite gain margin; moreover, they have a guaranteed 50 percent gain reduction margin and a 60 degree phase margin, in each feedback channel, provided that the system is linear in the control and the penalty to the control is quadratic, thus extending the well-known properties of LQ regulators to nonlinear optimal designs. These results are also valid for infinite horizon, average cost, stochastic optimal control problems.

Tsitsiklis, J. N.↗
NASA NTRS1984

Guaranteed robustness properties of multivariable nonlinear stochastic optimal regulators

The robustness of optimal regulators for nonlinear, deterministic and stochastic, multi-input dynamical systems is studied under the assumption that all state variables can be measured. It is shown that, under mild assumptions, such nonlinear regulators have a guaranteed infinite gain margin; moreover, they have a guaranteed 50 percent gain reduction margin and a 60 degree phase margin, in each feedback channel, provided that the system is linear in the control and the penalty to the control is quadratic, thus extending the well-known properties of LQ regulators to nonlinear optimal designs. These results are also valid for infinite horizon, average cost, stochastic optimal control problems.

Tsitsiklis, J. N.↗
NASA NTRS1984

Multiobjective optimization in structural design with uncertain parameters and stochastic processes

The application of multiobjective optimization techniques to structural design problems involving uncertain parameters and random processes is studied. The design of a cantilever beam with a tip mass subjected to a stochastic base excitation is considered for illustration. Several of the problem parameters are assumed to be random variables and the structural mass, fatigue damage, and negative of natural frequency of vibration are considered for minimization. The solution of this three-criteria design problem is found by using global criterion, utility function, game theory, goal programming, goal attainment, bounded objective function, and lexicographic methods. It is observed that the game theory approach is superior in finding a better optimum solution, assuming the proper balance of the various objective functions. The procedures used in the present investigation are expected to be useful in the design of general dynamic systems involving uncertain parameters, stochastic process, and multiple objectives.

Rao, S. S.↗
NASA NTRS2011

Chance-Constrained Guidance With Non-Convex Constraints

Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of failure) is below a user-specified bound known as the risk bound. An example problem is to drive a car to a destination as fast as possible while limiting the probability of an accident to 10(exp -7). This framework allows users to trade conservatism against performance by choosing the risk bound. The more risk the user accepts, the better performance they can expect.

FROM↗
NASA NTRS1968

Optimal stochastic control.

Optimal stochastic control of small dynamic systems described by random differential equations, noting selective bibliography on several subjects

Wonham, W. M.↗
NASA NTRS1979

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.↗
NASA NTRS1985

Identification of dynamic systems, theory and formulation

The problem of estimating parameters of dynamic systems is addressed in order to present the theoretical basis of system identification and parameter estimation in a manner that is complete and rigorous, yet understandable with minimal prerequisites. Maximum likelihood and related estimators are highlighted. The approach used requires familiarity with calculus, linear algebra, and probability, but does not require knowledge of stochastic processes or functional analysis. The treatment emphasizes unification of the various areas in estimation in dynamic systems is treated as a direct outgrowth of the static system theory. Topics covered include basic concepts and definitions; numerical optimization methods; probability; statistical estimators; estimation in static systems; stochastic processes; state estimation in dynamic systems; output error, filter error, and equation error methods of parameter estimation in dynamic systems, and the accuracy of the estimates.

Maine, R. E.↗
NASA NTRS1972

Minimum-energy control of a class of electrically driven vehicles.

A minimum-energy controller is designed and built for a class of electrically driven vehicles according to the theoretical concepts determined by the application of modern control theory. Theoretical results are obtained by making several justifiable assumptions in the dynamical equations of the system and solving the resulting stochastic optimal control problem by Bellman's dynamic programming technique. Several practical and economical considerations are taken into account for the mechanization of the minimum-energy control law.

Sahinkaya, Y. E.↗
NASA NTRS1996

On the Stochastic Quantization Method: Characteristics and Applications to Singular Systems

Introducing the generalized Langevin equation, we extend the stochastic quantization method so as to deal with singular dynamical systems beyond the ordinary territory of quantum mechanics. We also show how the uncertainty relation is built up to the quantum mechanical limit with respect to fictitious time, irrespective of its initial value, within the framework of the usual stochastic quantization method.

Kanenaga, Masahiko↗
NASA NTRS2005

Generic Kalman Filter Software

The Generic Kalman Filter (GKF) software provides a standard basis for the development of application-specific Kalman-filter programs. Historically, Kalman filters have been implemented by customized programs that must be written, coded, and debugged anew for each unique application, then tested and tuned with simulated or actual measurement data. Total development times for typical Kalman-filter application programs have ranged from months to weeks. The GKF software can simplify the development process and reduce the development time by eliminating the need to re-create the fundamental implementation of the Kalman filter for each new application. The GKF software is written in the ANSI C programming language. It contains a generic Kalman-filter-development directory that, in turn, contains a code for a generic Kalman filter function; more specifically, it contains a generically designed and generically coded implementation of linear, linearized, and extended Kalman filtering algorithms, including algorithms for state- and covariance-update and -propagation functions. The mathematical theory that underlies the algorithms is well known and has been reported extensively in the open technical literature. Also contained in the directory are a header file that defines generic Kalman-filter data structures and prototype functions and template versions of application-specific subfunction and calling navigation/estimation routine code and headers. Once the user has provided a calling routine and the required application-specific subfunctions, the application-specific Kalman-filter software can be compiled and executed immediately. During execution, the generic Kalman-filter function is called from a higher-level navigation or estimation routine that preprocesses measurement data and post-processes output data. The generic Kalman-filter function uses the aforementioned data structures and five implementation- specific subfunctions, which have been developed by the user on the basis of the aforementioned templates. The GKF software can be used to develop many different types of unfactorized Kalman filters. A developer can choose to implement either a linearized or an extended Kalman filter algorithm, without having to modify the GKF software. Control dynamics can be taken into account or neglected in the filter-dynamics model. Filter programs developed by use of the GKF software can be made to propagate equations of motion for linear or nonlinear dynamical systems that are deterministic or stochastic. In addition, filter programs can be made to operate in user-selectable "covariance analysis" and "propagation-only" modes that are useful in design and development stages.

Lisano, Michael E., II↗
NASA NTRS1993

Control of Complex Dynamic Systems by Neural Networks

This paper considers the use of neural networks (NN's) in controlling a nonlinear, stochastic system with unknown process equations. The NN is used to model the resulting unknown control law. The approach here is based on using the output error of the system to train the NN controller without the need to construct a separate model (NN or other type) for the unknown process dynamics. To implement such a direct adaptive control approach, it is required that connection weights in the NN be estimated while the system is being controlled. As a result of the feedback of the unknown process dynamics, however, it is not possible to determine the gradient of the loss function for use in standard (back-propagation-type) weight estimation algorithms. Therefore, this paper considers the use of a new stochastic approximation algorithm for this weight estimation, which is based on a 'simultaneous perturbation' gradient approximation that only requires the system output error. It is shown that this algorithm can greatly enhance the efficiency over more standard stochastic approximation algorithms based on finite-difference gradient approximations.

Spall, James C.↗
NASA NTRS2010

Physics-Based Methods of Failure Analysis and Diagnostics in Human Space Flight

The Integrated Health Management (IHM) for the future aerospace systems requires to interface models of multiple subsystems in an efficient and accurate information environment at the earlier stages of system design. The complexity of modern aeronautic and aircraft systems (including e.g. the power distribution, flight control, solid and liquid motors) dictates employment of hybrid models and high-level reasoners for analysing mixed continuous and discrete information flow involving multiple modes of operation in uncertain environments, unknown state variables, heterogeneous software and hardware components. To provide the information link between key design/performance parameters and high-level reasoners we rely on development of multi-physics performance models, distributed sensors networks, and fault diagnostic and prognostic (FD&P) technologies in close collaboration with system designers. The main challenges of our research are related to the in-flight assessment of the structural stability, engine performance, and trajectory control. The main goal is to develop an intelligent IHM that not only enhances components and system reliability, but also provides a post-flight feedback helping to optimize design of the next generation of aerospace systems. Our efforts are concentrated on several directions of the research. One of the key components of our strategy is an innovative approach to the diagnostics/prognostics based on the real time dynamical inference (DI) technologies extended to encompass hybrid systems with hidden state trajectories. The major investments are into the multiphysics performance modelling that provides an access of the FD&P technologies to the main performance parameters of e.g. solid and liquid rocket motors and composite materials of the nozzle and case. Some of the recent results of our research are discussed in this chapter. We begin by introducing the problem of dynamical inference of stochastic nonlinear models and reviewing earlier results. Next, we present our analytical approach to the solution of this problem based on the path integral formulation. The resulting algorithm does not require an extensive global search for the model parameters, provides optimal compensation for the effects of dynamical noise, and is robust for a broad range of dynamical models. In the following Section the strengths of the algorithm are illustrated illustrated by inferring the parameters of the stochastic Lorenz system and comparing the results with those of earlier research. Next, we discuss a number of recent results in application to the development of the IHM for aerospace system. Firstly, we apply dynamical inference approach to a solution of classical three tank problems with mixed unknown continuous and binary parameters. The problem is considered in the context of ground support system for filling fuel tanks of liquid rocket motors. It is shown that the DI algorithm is well suited for successful solution of a hybrid version of this benchmark problem even in the presence of additional periodic and stochastic perturbation of unknown strength. Secondly, we illustrate our approach by its application to an analysis of the nozzle fault in a solid rocket motor (SRM). The internal ballistics of the SRM is modelled as a set of one-dimensional partial differential equations coupled to the dynamics of the propellant regression. In this example we are specifically focussed on the inference of discrete and continuous parameters of the nozzle blocking fault and on the possibility of an application of the DI algorithm to reducing the probability of "misses" of an on-board FD&P for SRM. In the next section re-contact problem caused by first stage/upper stage separation failure is discussed. The reaction forces imposed on the nozzle of the upper stage during the re-contact and their connection to the nozzle damage and to the thrust vector control (TVC) signal are obtained. It is shown that transient impact induced torquean be modelled as a response of an effective damped oscillator. A possible application of the DI algorithm to the inference of damage parameters and predicting fault dynamics ahead of time using the actuator signal is discussed. Finally, we formulate Bayesian inferential framework for development of the IHM system for in-flight structural health monitoring (SHM) of composite materials. We consider the signal generated by piezoelectric actuator mounted on composite structure generating elastic waves in it. The signal received by the sensor is than compared with the baseline signal. The possibility of damage inference is discussed in the context of development of the SHM.

Smelyanskiy, Vadim N.↗
NASA NTRS1971

On the minimax feedback control of uncertain dynamic systems.

In this paper the problem of optimal feedback control of uncertain discrete-time dynamic systems is considered where the uncertain quantities do not have a stochastic description but instead are known to belong to given sets. The problem is converted to a sequential minimax problem and dynamic programming is suggested as a general method for its solution. The notion of a sufficiently informative function, which parallels the notion of a sufficient statistic of stochastic optimal control, is introduced, and conditions under which the optimal controller decomposes into an estimator and an actuator are identified.

Bertsekas, D. P.↗
NASA NTRS1973

Sufficiently informative functions and the minimax feedback control of uncertain dynamic systems.

The problem of optimal feedback control of uncertain discrete-time dynamic systems is considered where the uncertain quantities do not have a stochastic description but instead are known to belong to given sets. The problem is converted to a sequential minimax problem and dynamic programming is suggested as a general method for its solution. The notion of a sufficiently informative function, which parallels the notion of a sufficient statistic of stochastic optimal control, is introduced, and conditions under which the optimal controller decomposes into an estimator and an actuator are identified.

Bertsekas, D. P.↗
NASA NTRS2004

Complexity of life via collective mind

e mind is introduced as a set of simple intelligent units (say, neurons, or interacting agents), which can communicate by exchange of information without explicit global control. Incomplete information is compensated by a sequence of random guesses symmetrically distributed around expectations with prescribed variances. Both the expectations and variances are the invariants characterizing the whole class of agents. These invariants are stored as parameters of the collective mind, while they contribute into dynamical formalism of the agents' evolution, and in particular, into the reflective chains of their nested abstract images of the selves and non-selves. The proposed model consists of the system of stochastic differential equations in the Langevin form representing the motor dynamics, and the corresponding Fokker-Planck equation representing the mental dynamics (Motor dynamics describes the motion in physical space, while mental dynamics simulates the evolution of initial errors in terms of the probability density). The main departure of this model from Newtonian and statistical physics is due to a feedback from the mental to the motor dynamics which makes the Fokker-Planck equation nonlinear. Interpretation of this model from mathematical and physical viewpoints, as well as possible interpretation from biological, psychological, and social viewpoints are discussed. The model is illustrated by the dynamics of a dialog.

collective intelligence↗