bluuebunny/crossref_metadata_2025_split huggingface dataset:
Decentralized minimum‐energy control and coordination of large scale linear systems
Authors: Gruver W. A. , Hedges J. C. , Snyder W. E. 
Published: July 2007

AbstractA two‐level hierarchical algorithm of the interaction prediction type is derived for the decentralized optimal control of linear systems with fixed terminal state, linear interactions, and a minimum energy criterion. The algorithm is noniterative at the infimal level and utilizes successive approximation with averaging for the coordination. Numerical experiments compare the effect of the interactions, sampling times, and time horizon on the convergence of the algorithm.
Perturbation‐magnitude control for difference‐quotient estimation of derivatives
Authors: Kelley Henry J. , Lefton Leon , Johnson Ivan L. 
Published: July 2007

AbstractA process for adjusting perturbation magnitude for accurate difference‐quotient estimation of derivatives is described in the following. The process is intended to be carried out sequentially, alternating with iterations of a parameter‐optimization algorithm. A more complex and computationally‐expensive scheme for occasional auxiliary use is also described.
The automation of transversality conditions
Authors: Schappelle Robert H. , Brusch Richard G. 
Published: July 2007

AbstractThis paper presents a flexible, user‐oriented algorithm for the numerical implementation of the terminal point transversality conditions associated with optimal control problems. The method differs from the usual numerical implementation in that the constant Lagrange multipliers associated with terminal constraints are eliminated numerically during program execution rather than being eliminated analytically prior to program coding. This conceptual innovation gives the user considerable flexibility in specifying new sets of terminal boundary conditions without reprogramming.
Self‐scaling variable metric methods in hilbert space with applications to control problems
Authors: Turner P. R. , Huntley E. 
Published: July 2007

AbstractIn this paper the application of the self‐scaling variable metric methods to optimal control problems is considered. The convergence of such methods in Hilbert space, both with and without line searches, is established for a wide class of convex functionals. The methods are then tested numerically on control problems, and the results are compared with earlier results for other variable metric algorithms.
Minimum altitude‐loss soaring in a sinusoidal vertical wind distribution
Authors: Pierson Bion L. , Chen Imao 
Published: July 2007

AbstractMinimum altitude‐loss flight of a sailplane through a given vertical wind distribution is discussed. The problem is posed as a non‐linear optimalcontrol problem, and several numerical solutions are obtained using a gradient projection algorithm. The initial and final states are required to be equal, though they may be either fixed or free. An unexpected new optimal trajectory type is found to exist for relatively short ranges and free boundary conditions.
The solution of finite‐time optimal control problems with control time delays
Authors: Grimble M. J. 
Published: July 2007

AbstractThe design of deterministic LQP optimal control systems is considered for plants with control delays and a finite optimization interval. First, a solution is obtained to the fixed end‐point optimal control problem. An expression for the open‐loop optimal control is derived in the s‐domain. The closed‐loop optimal time‐varying gain matrix is then calculated from the s‐domain results. The open‐loop and closed‐loop solutions to the free end‐point optimal control problem are also given. The constant gain, infinite‐time, feedback control law is obtained as a limiting case of these results.The receding‐horizon optimal control problem for plants with control signal delays is also considered. The solution to this problem yields a constant feedback gain matrix which has obvious advantages for implementation. This gain matrix is not the same as the constant solution to the infinite‐time problem. The receding‐horizon control laws are derived for both the fixed and free end‐point problems, and these are shown to produce asymptotically stable closed‐loop systems.
Further properties of bounds on the quadratic cost of linear multivariable optimal regulators
Authors: Johnson M. A. 
Published: July 2007

AbstractSome new results continuing the development of a theory for bounding the optimal value of a quadratic cost function subject to a linear system constraint are presented.The observed property of the nesting of increasing orders of bounds is formalized and proven. This property is shown to be related to the successive inclusion of the constraint sets. A unified result for the nesting and convergence of the bound sequences is also given to conclude this analysis.Extension of the bound derivation to that of a limiting situation based on the introduction of an asymptotic parameter into the control weight is developed in detail. The upper bounds are shown to collapse into a single value, and the lower bounds form a set of nested limit values.
Optimal shape of an elastic structure
Authors: Sakawa Yoshiyuki , Ukai Hiroyuki 
Published: July 2007

AbstractThis paper treats an optimal design problem of an elastic upright structure which can be regarded as a column. The optimal shape of the structure, which makes the lowest natural frequency as large as possible, is determined under several equality and inequality constraints. A necessary condition for optimality is derived, and a numerical procedure for obtaining the optimal shape is discussed. The piecewise Hermite interpolation technique and the Rayleigh‐Ritz method are employed for computing the smallest eigenvalue and the corresponding eigenfunction. Several numerical results are presented.
The effects of non‐linear kinematics in optimal evasion
Authors: Forte I. , Steinberg A. , Shinar J. 
Published: July 2007

AbstractThe effects of non‐linear kinematics on optimal evasive strategies from a pursuer guided by proportional navigation are investigated in a plane. Non‐linear analysis is mandatory since, for certain values of system parameters and initial conditions, linearized kinematic models are not valid. The investigation discloses two principles of optimal evasion. For long pursuit time, both principles are satisfied and the relatively large miss distance is almost independent of the initial conditions. Short pursuit time does not allow simultaneous satisfaction of both principles, and the two‐dimensional optimal compromise results in a reduced miss distance. The inability to satisfy both principles suggests a three‐dimensional manoeuvre perpendicular to the initial collision plane.
Optimal forest fire control with limited reinforcements
Authors: Parlar Mahmut 
Published: July 2007

AbstractA forest fire fighting model is generalized to include the possibility of dispatching reinforcements whose size may be limited for the particular fire. The resulting deterministic optimal control problem with free final time and a moving boundary equality constraint on the final state and with bounded state and control variables is solved by the maximum principle. The optimal control is found to be a bang‐bang control which can switch at most twice until the final time.
An explicit feedback approximation for medium‐range interceptions in a vertical plane
Authors: Shinar J. , Negrin M. 
Published: July 2007

AbstractMinimum‐time interception of a target flying at a constant speed and altitude by a missle‐carrying fighter aeroplane is analysed using the method of forced singular perturbations (FSP). The engagement starts beyond visual range and terminates when the firing envelope of the missile is reached. Since in a medium‐range scenario the interceptor does not reach its maximum specific energy, the solution consists of matched initial and terminal boundary layers. The paper concentrates on interception of high flying targets for which the terminal phase is also a climbing subarc. The solution of this problem is approximated in a uniformly valid explicit feedback form using a range‐dependent weighting parameter. Application to an interceptor with realistic aerodynamic and propulsion models serves as an illustrative example.
A navigation algorithm using measurement‐based extrapolation
Authors: Stubberud Allen R. 
Published: July 2007

AbstractAn element in the guidance loop of any aircraft is the navigation system. This system derives position (and sometimes velocity) information by combining data from various on‐board and external measurement devices and transmits it to the guidance algorithm.In this paper a navigation algorithm is designed for an aircraft which has on‐board inertial measurements, range measurements from a TACAN station, and range, elevation and azimuth measurements from a ground‐based radar. The basic design philosophy is the predictor‐corrector form for a recursive estimator. State prediction is accomplished by extrapolation of the inertial measurements rather than from Newton's second law. This eliminates major modelling problems caused by the aircraft's aerodynamics. State correction is accomplished using optimal linear stochastic estimation methods. The resulting estimator (navigation algorithm) is essentially an ‘extended Kalman filter’ which processes the above‐mentioned inputs and generates optimal (in a linearized sense) estimates of the aircraft's latitude, longitude and altitude.
A dual formulation of the algebraic riccati equation problem
Authors: Incertis Fernando 
Published: July 2007

AbstractBy introducing a set of matrix transformations, the algebraic Riccati equation (ARE) is converted into a ‘dual’ matrix quadratic equation (DARE) where the unknown belongs to the field of skew‐symmetric matrices. As a consequence of this reformulation for a matrix space Rnxn the system of n(n+ 1)/2 coupled quadratic equations associated to ARE is shown to be equivalent to another system of n(n‐1)/2 coupled quadratic equations. An efficient computational algorithm is given for solving the dual Riccati equation and closed form analytical solutions of ARE are derived for the case in which n=2 or when some special, but non‐trivial, commutativity conditions are fulfilled in the transformed space.
A new approach to identification of linear systems and the optimal solution of a class of synthesis problems
Authors: Emre Erol 
Published: July 2007

AbstractA unifying solution is given to the problems of optimal deadbeat control, disturbance decoupling, exact model matching and system identification. It is shown that the optimal solutions of these problems can be obtained by solving a new type optimization problem. Our solution makes use of certain recent results on system structure and on geometric and polynomial theories of linear systems.
Comparison of two optimal feedback controls for parabolic systems
Authors: Amouroux M. , Courdesses M. , Jai A. El. 
Published: July 2007

AbstractTwo numerical methods for solving minimum energy control problem with final state constraints are presented for parabolic systems. In infinite dimensions, the functional analysis approach gives an explicit solution from which an approximation method is developed to allow the removal of the indetermination which causes numerical difficulties. The Riccati equation approach about the penalized criterion is also studied and the two solutions are compared on the implemented control laws (in finite dimensions). An example is presented.
Optimal employment strategies of profit‐maximizing and labour‐managed firms
Authors: Feichtinger Gustav 
Published: July 2007

AbstractThis paper deals with the problem of finding optimal hiring and firing policies for profit‐maximizing and labour‐managed firms whose objective is to maximize profits and net income per worker, respectively. Assuming a concave production function with labour force as a variable production factor, a non‐linear demand function, increasing marginal production costs, and convex costs of changing the labour force, we determine the optimal employment strategies by the maximum principle. By using phase portrait analysis, we prove that for a relatively small manpower stock the optimal policies of the profit‐maximizing firms are to increase its labour force over time such that the increase is largest in the beginning. However, for a ‘large’ initial stock, firing can be optimal at the beginning. For a labour‐managed firm, the same behaviour is shown to be optimal for the infinite‐time‐horizon problem only under additional assumptions. The joint analysis of profit‐maximizing and labour‐managed firms provides a possibility to compare the optimal stationary employment policies.
On the hierarchical algorithms for nonlinear systems with bounded control
Authors: Mahmoud Magdi S. , Fawsy Ahmed S. 
Published: July 2007

AbstractHierarchical algorithms for the dynamic optimization of non‐linear systems with control bound inequality, constraints are considered. Three different computational schemes are developed, based on the costate prediction co‐ordination. Each scheme consists of four levels; of which the second level manipulates the control constraints in an explicit way. Digital simulation of the developed algorithms on a typical power control system is presented.
Optimal pricing of a monopoly against a competitive producer
Authors: Dockner Engelbert 
Published: July 2007

AbstractIn 1977, Lieber and Barnea presented an investment and pricing differential game. There are two players, a monopoly possessing some exhaustible resource and a price‐taking competitor. The monopoly wishes to determine an optimal price, whereas the competitor wishes to choose optimal investment in an alternative production. This paper presents a non‐linear extension of the game. The special structure of the game permits a complete solution in the state—costate phase plane as well as in the control phase plane. The monopoly plays an optimal decreasing price strategy and the competitor plays an optimal decreasing investment strategy with an increasing production capacity.
Optimal impulsive manoeuvres and aerodynamic braking
Authors: Jezewski D. J. 
Published: July 2007

AbstractAn impulsive optimization method and the results of a suboptimal atmospheric guidance program are combined to produce an efficient solution to the aero‐braking problem. For a specified initial and final orbit, the solution determines: (1) the minimum of the sum of the magnitudes of the impulse vectors, (2) the optimal atmospheric entry and exit state vectors (subject to both equality and inequality constraints) and (3) the optimal coast times. Numerical solutions are presented to illustrate characteristics of the solution.
Optimal boundary impedance for the minimization of reflection: (I) Asymptotic solutions by the geometrical optics method
Authors: Chen Goong , Bridges Thomas J. 
Published: July 2007

AbstractIn the design of surfaces which absorb waves, the impedance boundary condition is used as an effective means of diminishing the reflection. In this paper, we use the geometrical optics method to approximate the optimal impedance value which minimizes the reflected field for the scalar wave equation with a monochromatic source. Our treatment yields good results for optimal impedance in the asymptoticity region of the geometrical optics solution.
The adjustment and integration of accelerometer data using steady‐state feedback gains
Authors: Murray Daniel M. 
Published: July 2007

AbstractThe adjustment of noisy accelerometer data to prevent drift in the velocity and displacement trajectories is formulated as a discrete‐time optimal control problem. It is shown that large penalties on the terminal velocity and displacement produce large feedback gains towards the end of the time interval and result in unrealistic adjustments. An adjustment procedure is proposed in which a small penalty is placed on the entire time history of the velocity and displacement. The solution of the associated algebraic Riccati equation yields steady‐state feedback gains which produce satisfactory adjustments of the acceleration measurements and generate realistic velocity and displacement trajectories.
Block‐independent control of distributed structures
Authors: Silverberg L. M. , Meirovitch L. 
Published: July 2007

AbstractAs a compromise between coupled control and independent modal‐space control, a block‐independent control method is proposed. The computational difficulties encountered in coupled control are thereby reduced significantly. The requirement on the number of actuators is shown to be lower for block‐independent control than for independent modal‐space control, but only moderately so. A numerical example is presented.
Optimal control analysis of a simple criminal prosecution model
Authors: Gerchak Yigal , Parlar Mahmut 
Published: July 2007

AbstractThis paper analyzes an optimal control model dealing with a problem in criminal justice policy. It is assumed that a society generates criminals at a constant rate. The size of the criminal population at any time depends on the criminal generation rate and the number of criminals prosecuted and imprisoned. Optimal prosecution rate over time is found by using Pontryagin's principle. The objective is to minimize the total discounted cost of the damages inflicted by the criminals plus the cost of law enforcement. Explicit forms of the optimal trajectories are found in both the finite and infinite horizon cases. In the latter case, a stability analysis of the optimal steady‐state is also presented. The paper concludes with a comparative statics analysis of the equilibrium and a description of the optimal control of a more detailed criminal justice system model.
A unified approach to reduced‐order modelling and control of large‐scale systems with multiple decision makers
Authors: Saksena Vikram R. , Cruz J. B. 
Published: July 2007

AbstractThis paper presents a unified approach to reduced‐order modelling and control of large‐scale systems with multiple decision makers. The ‘core’ of a large game problem is identified through the information structure and the class of structure preserving strategies. The induced decomposition results in a low‐order game problem and two decentralized optimal control problems. An example of a two‐area power system demonstrates the computational attractiveness of the proposed design methodology.
Numerical simulation of a non‐linear feedback controller for a wind tunnel model involving a time delay
Authors: Manitius A. , Tran H. 
Published: July 2007

AbstractThis paper describes a non‐linear, S‐minimum time, feedback controller for a wind tunnel model and a numerical simulation of its performance. The model is a linear third‐order system with delay and a state‐variable constraint; it represents the dynamics of a Mach number control loop in a cryogenic wind tunnel. The design method involves a singular perturbation technique, an impulse control and a compensation of delay. Peformance of linear and non‐linear S‐minimum time control is compared in various operating conditions. The closed‐loop dynamics of the non‐linear system is examined by numerical simulations which exhibit the boundary‐layer phenomena in the control and the effects of various changes in parameters.
On the solution of the decoupling problem in lqg optimal systems
Authors: Chen Bor‐Sen , Kung Chung‐Chun 
Published: July 2007

AbstractIn this paper, we study the input‐output decoupling of the LQG optimal system. Two frequency dependent weighting matrices, Q(s) and R(s), in the cost functional J are specified to achieve the desired decoupled design. Furthermore, the pole‐zero placement in the LQG decoupled system is also discussed. The Wiener‐Hopf approach (frequency domain technique) will be applied to solve the above problems.
Energy state revisited
Authors: Kelley Henry J. , Cliff Eugene M. , Weston Alan R. 
Published: July 2007

AbstractMinimum‐time climbs in the ‘energy’ approximation are reviewed and further consideration given to choice of variables. A pair of variables which seems to offer an attractive replacement for altitude and air‐speed in singular‐perturbation procedures is suggested. Use of the new variables in an energy‐modelled climb‐dash problem is illustrated.
The effect of sample period on optimally designed servomechanism control systems
Authors: Diduch C. P. , Doraiswami R. 
Published: July 2007

AbstractA uniform approach for comparing sampled‐data servomechanism control systems with respect to the sample period is formulated such that a quadratic performance measure of the augmented continuous system states and discrete controller states is used both for controller design and performance evaluation. The structure of the controller and performance cost is optimally designed as a function of the sample period and converges to an optimal continuous control system as the sample period approaches zero. Extensive simulation reveals that the performance cost increases and that the norm of the controller gains decreases monotonically with the sample period.
Two pursuers and one evader in the plane: A stochastic pursuit‐evasion differential game
Authors: Yavin Y. 
Published: July 2007

AbstractA stochastic pursuit‐evasion differential game involving three players moving in the plane is considered. The players are E, the evader, and Pi (where i = 1,2), the pursuers. It is assumed that all players have complete observation of each other's positions. Also, each of the pursuers has a killing range and a detection range. If player E is intercepted by at least one of the pursuers before leaving the detection range of either of them, then the pursuers win the game. If, on the other hand, E leaves the detection range of one (or both) of the pursuers before being intercepted, then player E wins the game. Sufficient conditions on max‐min pursuit‐evasion strategies are derived. These conditions require the existence of a properly smooth solution to a non‐linear partial differential equation on a torus in R3. By applying a finite‐difference method, the equation is solved numerically, and the max‐min pursuit‐evasion strategies are computed.
Optimum rate allocation in quantized control
Authors: Meadow Charles J. , Fischer Thomas R. , Gibson Jerry D. 
Published: July 2007

AbstractA linear‐quadratic‐Gaussian (LQG) delocalized control problem is formulated to require both specification of a control law and communication of measurements to controller and controls to plant. Efficient communication requires quantization of both measurement and control signals. The basic design problem is to allocate in an optimum fashion a fixed total communication rate to the measurement and control communication systems.A dynamic communication‐rate allocation algorithm is developed on the basis of prediction error and entropy power. As intuitively expected, the rate allocation depends on both the measurement and plant noise powers as well as the overall quadratic performance measure. Solely on the basis of entropy power considerations, a larger rate should be allocated for communication of measurements than for communication of controls.
Strategy of evasion from many pursuers
Authors: Zak V. L. 
Published: July 2007

AbstractA differential game of evasion with many participants (a game of kind in the terminology of Isaacs1) is considered. One controlled object (the evader) seeks to avoid contact with each of several pursuers. The motion of the evader is subject to a phase constraint. An efficient method (up to the explicit formulae) of constructing the evader's strategy is proposed. This strategy ensures evasion on the infinite time interval and the fulfilment of the phase constraint. The evader's control corresponding to this strategy is always a piecewise‐programme function of time, and the number of programme pieces is finite (there is an upper estimate for this number). There is a lower estimate for the minimal distance between the evader and the pursuers.