Showing papers on "State vector published in 1973"

Synthesis of an adaptive observer using Lyapunov's direct method

Abstract: An adaptive scheme is synthesized to estimate the state vector and identify all the parameters of a Single-input single-output nth order linear system, from only the input—output data. The scheme is proved to be asymptotically stable in the whole, thus ensuring the convergence of the identification process.

Observer design for a linear functional of the state vector

Abstract: A procedure is described for the design of an observer of minimum order with arbitrary dynamics to provide a specified linear functional of the state vector of a linear system.

On decentralized linear stochastic control problems with quadratic cost

Abstract: A decentralized stochastic optimal control problem is considered where agents have different a priori information on the system initial state. Agents are assumed to exchange their control values but not their state vector observation values. It is shown that this leads to a suboptimal control law, with correction terms being added to the well-known optimal proportional feedback control signal obtainable under the information centralization assumption of linear dynamics with quadratic cost, when person-by-person satisfactory team decisions are considered.

An innovations approach to least-squares estimation--Part V: Innovations representations and recursive estimation in colored noise

Abstract: We show that least-squares filtered and smoothed estimates of a random process given observations of another colored noise process can be expressed as certain linear combinations of the state vector of the so-called innovations representation (IR) of the observed process. The IR of a process is a representation of it as the response of a causal and causally invertible linear filter to a white-noise "innovations" process. For nonstationary colored noise processes, the IR may not always exist and a major part of this paper is devoted to the problem of identifying a proper class of such processes and of giving effective recursive algorithms for their determination. The IR can be expressed either in terms of the parameters of a known lumped model for the process or in terms of its covariance function. In the first case, our results on estimation encompass most of those found in the previous literature on the subject; in the second case, there seems to be no prior literature. Finally, we may note that our proofs rely on, and exploit in both directions, the intimate relation that exists between least-squares estimation and the innovations representation.

Partial reconstruction of state vectors in decentralized dynamic systems

Abstract: The extent to which the state vector information can be recovered in a decentralized control system from a partial observation record of the state vector measurement and also of the control vectors is discussed. That subspaces associated with partial reconstruction of the state space can be obtained recursively and that they have certain invariance properties is shown.

Sampled-data Nash controls in non-zero-sum differential games†

Abstract: Non-Zero-sum differential games where measurements of the state vector are possible only at discrete instants of time during the course of play are considered, and necessary conditions for the existence of a pair of sampled-data Nash controls are obtained. These conditions are different from those corresponding to the open-loop or closed-loop solutions. Linear quadratic games are then treated and a simple illustrative example which reduces to a pursuit-evasion game is presented.

An Application of Kalman Techniques to Aircraft and Missile Radar Tracking

Abstract: A real-time and postflight data reduction and error analysis program is developed with the ability to estimate either aircraft flight paths or missile trajectories with the same state vector and matrix dimension filter equations simply by input selection of the appropriate state transition matrix. A feature of the filter formulation is an analytical technique for computing the effects of measurement error parameters not explicitly included in the filter state vector on both the state vector estimate itself and the state covariance matrix. Examples of the processing of real tracking data for aircraft flight paths, missile trajectories, and some other more unusual applications are presented which illustrate both the data reduction and error analysis modes of program operation.

Estimation of Uncertain Systems

Abstract: Publisher Summary This chapter describes the state estimation problem with parameter uncertainties. The Kalman-Bucy filter gives the unbiased, minimum variance estimate of the state vector of a linear dynamic system that is disturbed by additive white noise when measurements of the state vector are linear, but disturbed by white noise. Such performance is not realized in actual practice because the information that is required to construct the Kalman-Bucy filter is approximately known. The noise parameters and models might be based upon few data points, computer round-off errors might be significant, and the system model might not be adequate. When it is impractical or impossible to arrive at accurate information upon which to base the filter design, suboptimal and adaptive techniques must be considered. The chapter discusses a technique that has been established to allow Kalman-Bucy filtering in an uncertain environment when the complexity of the estimation algorithm is constrained. The problem of the establishment of a method of Kalman-Bucy filter design, when the noise covariance matrices and the state matrix are uncertain, but bounded with known bounds has been presented in the chapter.

N-burn optimal analytic trajectories.

Abstract: Derivation of N-burn analytic solutions for propellant-optimal transfer trajectories of a vehicle in a vacuum between arbitrary boundary conditions. Variational changes in the desired boundary conditions are expressed, in general, in terms of variational changes in the control vector and in the initial state vector. All coefficient matrices are computed recursively in terms of the analytic matrices established from the subarcs of the N-burn solution. The solution is applicable to shuttle ascent (exoatmospheric), rendezvous, and deorbit problems. Consideration is also given to state-variable and control-variable inequality constraints.

On subspaces associated with partial reconstruction of state vectors, the structure algorithm, and the predictable directions of Riccati equations

Abstract: The close relations are discussed that exist among the three subspaces that arise in three apparently unrelated problem areas: 1) the subspace associated with the error of state vector reconstruction in informationally decentralized control problems; 2) the subspace associated with the solution of the Riccati equation; and 3) the null space of the certain observation matrix constructed by the structure algorithm.

Suboptimal stochastic controller for an n-body spacecraft

Abstract: Considerable attention, in the open literature, is being focused on the problem of developing a suitable set of deterministic dynamical equations for a complex spacecraft. This paper considers the problem of determining a stochastic optimal controller for an n-body spacecraft. The approach used in obtaining the stochastic controller involves the application, interpretation, and combination of advanced dynamical principles and the theoretical aspects of modern control theory. The stochastic controller obtained herein for a complicated model of a spacecraft uses sensor angular measurements associated with the base body to obtain smoothed estimates of the entire state vector. It can be easily implemented, and it enables system performance to be significantly improved.

Optimization of costly measurements in stochastic decision processes

Abstract: Two kinds of problems regarding measurement optimization in stochastic decision processes, when measurements are costly or constrained not to exceed a given number, have been investigated in the last years: the first one refers to the optimum timing of observations on the state vector of the process, while the second refers to the convenience of buying information on the random actions exerted by a stochastic environment. In this paper the two problems are considered from a unified point of view. In other words, the decision maker has to determine the optimal observation policy, under the assumption that both state and random vectors are measurable. A solution based on the application of dynamic programming is discussed for a general class of multistage processes. Analytical results are then obtained for scalar linear systems with quadratic cost on state and control. In this case, an efficient algorithm to determine the optimal sequence of measurements is presented, on the base of which a sensitivity analysis with respect to the process parameters is also carried out.

Computer-aided-design procedure for reduced-order observers. Estimate of entire state vector

Abstract: A systematic design procedure for reduced-order observers for linear time-invariant dynamical systems described by state-space equations is presented, using an alternative canonical form to that considered by Luenberger. The algorithm developed is suitable for the case where an estimate of the entire state vector is required, and can be extended to the case where only an estimate of a single linear functional of the state is required. The paper is concerned with the computer-aided design of reduced-order observers which will reconstruct an estimate of the entire state vector. The procedure presented is illustrated by an example.

Bias estimation error induced by parameter uncertainties

Abstract: The effect of a class of plant parameter uncertainties upon the state vector estimation of a system driven by a deterministic forcing function is considered. For this problem the minimization of mean-square error and the minimization of bias error are opposing goals. The set of noninferior solutions for the optimal control problem whose performance index has components mean-square error and bias error is considered, and evaluated.

An Analysis of Methods for Extracting Aerodynamic Coefficients from Test Data

Abstract: : An analysis of numerical methods for extracting aerodynamic coefficients from dynamic test data has been conducted The emphasis of the analysis is on the effects that random measurement errors in the data and random disturbances in the system have on the accuracy with which the coefficients for linear and nonlinear systems can be determined Both deterministic and stochastic methods for extracting the coefficients and determining their uncertainties are considered The deterministic technique considered, due to Chapman and Kirk, provides excellent estimates of both linear and nonlinear static pitching moment coefficients for the range of measurement efforts and system noise considered Somewhat less accurate estimates of pitch damping coefficients are obtained The stochastic approach considered demonstrates the feasibility of using an extended Kalman filter, with a parameter augmented state vector, for determining the values of the aerodynamic coefficients and their uncertainties from noisy dynamic test data Parameter estimates obtained from the extended filter compare favorably with previously obtained results using deterministic techniques Estimates of the parameter uncertainties provided by the filter are generally superior to those obtained with deterministic techniques particularly when system noise has corrupted the data

Design of Optimal Incomplete State Feedback Controllers for Large Linear Constant Systems

Abstract: In this paper the theory of linear optimal output feedback control is investigated in relation to its applicability in the design of high-dimensional linear multivariable control systems. A method is presented which gives information about the relative importance of the inclusion of a state vector element in the output feedback. The necessary conditions of the optimization problem are shown to be a set of linear/quadratic algebraic matrix equations. Numerical algorithms are presented which take account of this linear/quadratic character.

Conic state extrapolation

Abstract: The Conic State Extrapolation Routine provides the capability to conically extrapolate any spacecraft inertial state vector either backwards or forwards as a function of time or as a function of transfer angle. It is merely the coded form of two versions of the solution of the two-body differential equations of motion of the spacecraft center of mass. Because of its relatively fast computation speed and moderate accuracy, it serves as a preliminary navigation tool and as a method of obtaining quick solutions for targeting and guidance functions. More accurate (but slower) results are provided by the Precision State Extrapolation Routine.

An approach via state estimation to differential games with information time lag

Abstract: This paper deals with zero-sum two-person differential games in which one player has a deferred information on the state vector. This player mends this lack of information by using an adaptative deterministic extrapolation to estimate the plant state, and then, makes his decisions by means of the datas so obtained. An analysis of the phenomenon yields a criterion for optimizing the estimation which is based upon the Hamiltonian estimation of the perfect information game. A class of extrapolators is given by its dynamical equation. Then, the initial game is reduced to a new game containing pure time delay in the state and the controls.

Aircraft Range Optimization Using Singular Perturbations

Abstract: An approximate analytic solution is developed for the problem of maximizing the range of an aircraft for a fixed end state. The problem is formulated as a singular perturbation and solved by matched inner and outer asymptotic expansions and the minimum principle of Pontryagin. Cruise in the stratosphere, and on transition to and from cruise at constant Mach number are discussed. The state vector includes altitude, flight path angle, and mass. Specific fuel consumption becomes a linear function of power approximating that of the cruise values. Cruise represents the outer solution; altitude and flight path angle are constants, and only mass changes. Transitions between cruise and the specified initial and final conditions correspond to the inner solutions. The mass is constant and altitude and velocity vary. A solution is developed which is valid for cruise but which is not for the initial and final conditions. Transforming of the independent variable near the initial and final conditions result in solutions which are valid for the two inner solutions but not for cruise. The inner solutions can not be obtained without simplifying the state equations. The singular perturbation approach overcomes this difficulty. A quadratic approximation of the state equations is made. The resulting problem is solved analytically, and the two inner solutions are matched to the outer solution.

Optimal observers for time varying linear systems

Abstract: A method is presented for generating the optimal control of a linear system from measurements of the system input and output. The systems considered are n-th order, time invariant or time varying forced linear systems which are restricted to be bounded and uniformly completely state reconstructible. The control is generated from an estimate of the state vector which is obtained from an observer. The observer dynamics are derived from an optimal estimation formulation which is closely related to the concept of observability. Asymptotic stability of the observer is demonstrated and the effects of initial errors are considered. The result is a practical method of estimating the state of a linear system from noiseless measurements of the input and output. Additionally, theoretical results are obtained concerning the existence of observers for time varying linear systems.

Dual amplitudes constructed onJ>0 integer pointSU1,1 representations

Abstract: One studies the possibility of constructing factorizable dual amplitudes based on positive integer pointSU 1,1 representations. The (2J+1) invariant subspace inD (χ) leads in this case to a (2J+1)-dimensional generalized zero mode that can be interpreted in terms of an internal spin of the ground state. Typically, Born-term amplitudes constructed in this manner will exhibit multipole ghosts on nonleading levels. A divergence is also present at the Born-term level. It is suggested that these models can also be formulated as Lagrangian field theories on a two-dimensional manifold. This may yield a way of formulating auxiliary conditions and investigating whether the state vector space can be divided in physical and nonphysical sectors.

Adaptive control utilizing optimally sensitive design techniques

Abstract: In the recent literature a control problem in which both the initial state vector as well as a vector of constant plant parameters ore unknown ha3 been treated utilizing sensitivity techniques referred to as optimally sensitive control. In this paper the concepts of optimally sensitive control as developed by Kokotovic, Perkins, Cruz and others are extended to the problem in which the state dynamics contain a vector of stochastic inputs which can be represented as Martingale processes. The resulting optimally sensitive system is shown to be an effective and realistic adaptive controller for systems containing unknown time-varying parameters. A numerical example is presented to demonstrate the effectiveness of the resulting control system at identifying and adapting to the levels of the unknown time-varying inputs.