Showing papers on "Optimal control published in 1980"

Feedback stabilization of linear systems with delayed control

Abstract: Feedback controls based on the receding horizon method have proven to be a useful and easy tool in stabilizing linear ordinary differential systems. In this paper the receding horizon method is applied to linear systems with delay in the control. An open-loop optimal control which minimizes control energy subject to certain side constraints is first derived and then transformed to a closed-loop control via the receding horizon concept. The resulting feedback system is shown to be asymptotically stable under a complete controllability condition. It is also shown how the receding horizon control suggests a more general class of stabilizing feedback control laws. The control laws of this paper are perhaps the easiest way to stabilize a linear system with delay in the control.

Discrete Linear Control: The Polynomial Equation Approach

Abstract: The replacement of the classical transfer-function approach (which has been proved natural and effective in many practical cases) by the state-space approach was one of the major developments in the theory of multivariable control systems.

Competition versus optimal control in groundwater pumping

Abstract: This article considers one of the most important issues in water resources research, namely, the management of groundwater. Economists have long taken it for granted that the temporal allocation of groundwater would lead to welfare losses if left to the free market because all farmers pump from a common aquifer. Hence water economists studied extensively optimal control of temporal groundwater allocation. They never paused to compare the temporal allocation yielded by optimal control with the free market. In this article we prove by comparing the two strategies analytically that if the storage capacity of the aquifer is relatively large, the difference between them is so small that it can be ignored for practical consideration.

On the numerical solution of the discrete-time algebraic Riccati equation

Abstract: In this paper we shall present two new algorithms for solution of the diserete-time algebraic Riccati equation. These algorithms are related to Potter's and to Laub's methods, but are based on the solution of a generalized rather than an ordinary eigenvalue problem. The key feature of the new algorithms is that the system transition matrix need not be inverted. Thus, the numerical problems associated with an ill-conditioned transition matrix do not arise and, moreover, the algorithm is directly applicable to problems with a singular transition matrix. Such problems arise commonly in practice when a continuous-time system with time delays is sampled.

Real‐time forecasting with a conceptual hydrologic model: 1. Analysis of uncertainty

Abstract: The optimal control of watershed systems requires accurate real-time short-term forecasts of river flows. For the first time, this paper formulates a large, nonlinear conceptual model (the National Weather Service catchment model) in a mode amenable to analysis of uncertainty and the utilization of real-time information (measurements, forecasts, guesses) to update system states and improve streamflow predictions. The proposed methodology is based on the state space formulation of the equations describing the hydrologic model and the assumption of sources of uncertainty in the data and in the model structure. The first two moments of random variables are estimated in a computationally efficient way using on-line linear estimation techniques. Linearization of functional relationships is performed with the uncommon but powerful multiple-input describing function technique for the most strongly nonlinear responses and Taylor expansion for the rest. The linear feedback rule developed is based on the Kalman filter.

A Dynamic Positioning System Based on Kalman Filtering and Optimal Control

Abstract: This paper describes a computer-based, dynamic positioning system for floating vessels. The system is based on a detailed mathematical model of vessel motion in response to forces from thrusters, wind, waves and water current. The system uses a Kalman filter for optimal estimation of vessel motions and environmental forces from wind, waves and current. The control system is based on feedback from the motion varibles where the oscillatory, wave-induced component is removed by the estimator. Feedback from the water current estimate provides the integral action of the system, and feed forward from the wind force estimates are implemented. Simulation results and recordings from actual operation of the system indicate an excellent system performance.

On global convergence of an algorithm for optimal control

Abstract: This paper presents an algorithm for the solution of optimal control problems with constraints on the control, but without constraints on the trajectory or the terminal state In this algorithm, reduction of a cost at each iteration is guaranteed Global convergence conditions for the algorithm are investigated and an example is worked out

Attitude Control of a Flexible Spacecraft

Abstract: An algorithm is presented for designing optimal low order compensators for high order systems and it is applied to the title problem where many vibration modes are excited by the control torque. These low order compensators are compared with the full order optimal compensator and found to be less sensitive to modeling errors and to provide near optimal attitude regulation.

A Successive Linear Optimization Approach to the Dynamic Traffic Assignment Problem

Abstract: A dynamic model for the optimal control of traffic flow over a network is considered. The model, which treats congestion explicitly in the flow equations, gives rise to nonlinear, nonconvex mathematical programming problems. It has been shown for a piecewise linear version of this model that a global optimum is contained in the set of optimal solutions of a certain linear program. This paper presents a sufficient condition for optimality which implies that a global optimum can be obtained by successively optimizing at most N + 1 objective functions for the linear program, where N is the number of time periods in the planning horizon. Computational results are reported to indicate the efficiency of this approach.

Aspects of automatic train control

Abstract: This thesis describes research and development. work carried out by the author into the control of traction and braking systems on rail vehicles. After a review of recent developments, the problem of. driving a train under minimum-energy control subject·to timetable and operational constraints is discussed. This is partitioned into two sections. Firstly, target time and velocities for key pOints on the journey are computed; these are communicated to or stored on the train, together with route and vehicle data. Secondly, an on-board digital system drives the train to each target according to control algorithms which incorporate a predictorcorrector module, whose function is to determine which of two criteria of performance is to be used (minimum-energy when running early or on-time, minimum-time when running late). Most of the thesis is devoted to the analysis and design of the train-borne control system. The general form of the optimal control (of tractive or braking effort) is determined by the application of Pontryagin's Maximum Principle over each section of the journey. However, the moments of transition between the various modes of control are calculated by a method which involves a lookahead model in the predictor module, rather than by iterative solution of the state and co-state equations . An important aspect of the design is the dynamic response of the braking SUb-system, which may include a substantial pneumatic transport lag within the control loop. S-plane and z-plane design procedures for the required discrete control algorithms to.achieve a specified transient response are derived. The thesis concludes with a chapter on the instrumentation required for the train-borne control system.

Generalization of results on multivariable adaptive control

Abstract: This paper shows that previous results on multi-input multi-output discrete time deterministic and stochastic adaptive control can be extended to a wider class of systems. It is shown that global convergence can be established for an adaptive control algorithm applied to the general class of stably invertible systems.

Three-dimensional optimal pursuit and evasion with bounded controls

Abstract: The missile-aircraft pursuit-evasion problem is formulated by a three-dimensional linearized kinematic model with bounded control. The formulation is valid both for the optimal control (against a known adversary strategy) and the zero sum differential game versions. Assuming perfect information, the linearized kinematic model yields for both versions a solution which can be impletemented in real time for airborne application. The avoidance of a known pursuer by an evader who has no state information is solved by a stochastically optimal periodical maneuver. Other examples of imperfect information are briefly discussed.

Sequential conjugate gradient-restoration algorithm for optimal control problems with non-differential constraints and general boundary conditions, part I

Abstract: In this paper, a new member of the family of sequential gradient-restoration algorithms for the solution of optimal control problems is presented. This is an algorithm of the conjugate gradient type, which is designed to solve two classes of optimal control problems, called Problem P1 and Problem P2 for easy indentification. Problem P1 involves minimizing a functional I subject to differential constraints and general boundary conditions. It consists of finding the state x(t), the control u(t), and the parameter pi so that the functional I is minimized, while the constraints and the boundary conditions are satisfied to a predetermined accuracy. Problem P2 extends Problem P1 to include non-differential constraints to be satisfied everywhere along the interval of integration. The approach taken is a sequence of two-phase cycles, composed of a conjugate gradient phase and a restoration phase. The conjugate gradient phase involves one iteration and is designed to decrease the value of the functional, while the constraints are satisfied to first order. The restoration phase involves one or more iterations; each restorative iteration is designed to force constraint satisfaction to first order, while the norm squared of the variations of the control, the parameter, and the missing components of the initial state is minimized. The resulting algorithm has several properties: (i) it produces a sequence of feasible solutions; (ii) each feasible solution is characterized by a value of the functional I which is smaller than that associated with any previous feasible solution; and (iii) for the special case of a quadratic functional subject to linear constraints, the variations of the state, control, and parameter produced by the sequence of conjugate gradient phases satisfy various orthogonality and conjugacy conditions. The algorithm presented here differs from those of References 1-4, in that it is not required that the state vector be given at the initial point. Instead, the initial conditions can be absolutely general. In analogy with References 1-4, the present algorithm is capable of handling general final conditions; therefore, it is suitable for the solution of optimal control problems with general boundary conditions. The importance of the present algorithm lies in that many optimal control problems either arise naturally in the present format or can be brought to such a format by means of suitable transformations.5 Therefore, a great variety of optimal control problems can be handled. This includes: (i) problems with control equality constraints, (ii) problems with state equality constraints, (iii) problems with state-derivative equality constraints, (iv) problems with-control inequality constraints, (v) problems with state inequality constraints, (vi) problems with state-derivative inequality constraints, and (vii) Chebyshev minimax problems. Several numerical examples are presented in Part 2 (Reference 6) in order to illustrate the performance of the algorithm associated with Problem P1 and Problem P2. The numerical results show the feasibility as well as the convergence characteristics of the present algorithm.

Dynamic positioning of floating vessles based on Kalman filtering and optimal control

Abstract: This paper describes computer-based, dynamic positioning system for floating vessels. The system is based on a detailed mathematical model of vessel motion in response to forces from thrusters, wind, waves and water current. The system uses a Kalman filter for optimal estimation of vessel motions and environmental forces from wind, waves and current. The control system is based on feedback from the motion variables where the oscillatory, wave-induced component is removed by the estimator. Feedback from the water current estimate provides the integral action of the system and feed forward from the wind force estimates are implemented. Simulation results and recordings from actual operation of the system indicate an excellent system performance. Reference is given to installations made on actual vessels.

Analysis and Optimal Design of a Packet-Voice Receiver

Abstract: The analysis problems arising from a digital packet switched speech network are outlined in a wide statistical environment. The statistical models assumed are discussed with respect to practical applications. Particular attention is devoted to a formal description of the influence of the packet voice receiver on the system behavior in terms of the delay pdf. The optimization of the system performance, in order to obtain the best voice quality, is stated as an optimal control problem, and the analysis results play a central role in the construction of the objective functions. The problem is solved in a particular analytical environment. The outlined analytical results are supported by critical comments on their comparison with practical implementations, allowing the designer a better capability in handling any problems.

Optimal periodic control: The π test revisited

Abstract: The paper examines second-order conditions for both steady-state and dynamic optimality in a periodic control problem. It centers on the π condition of Bittanti, Fronza, and Guardabassi [2] and has three main objectives: 1) to form a π "test" for a somewhat more general problem than considered in [2]; 2) to point out that certain auxiliary conditions must be added if the results of [2] are to be valid; and 3) to explore more fully the relationships between second-order conditions for steady-state optimality and second-order conditions for optimality in the dynamic problem.

Modal-Space Control of Large Flexible Spacecraft Possessing Ignorable Coordinates

Abstract: One problem peculiar to spacecraft in free space is that of ignorable coordinates, which are present when the spacecraft has no natural ability of preventing rigid-body motions. Ignorable coordinates can be eliminated from the problem formulation by introducing a reduced state vector. However, this results in having the ignorable coordinates uncontrolled. This paper solves this problem by introducing a dual-level control. The firstlevel controls are designed to control the ignorable coordinates and they lead to a positive definite "augmented system" and the second-level controls are designed for the final control of the complete state vector, including the ignorable coordinates. The second-level controls are designed in modal space and can be based on several types of control laws. In particular, proportional control providing artificial viscous damping, proportional optimal control, and nonlinear on-off control are discussed. A numerical example, illustrating all of these control laws, is presented.

Eigenspace selection procedures for closed loop response shaping with modal control

Abstract: Procedures are discussed for selecting closed loop eigenvalues and eigenvectors to achieve desired transient response behavior. The admissible eigenvector subspace is defined with basis vectors calculated using a singular value decomposition. These vectors are optimally combined to 1) minimize the vector element errors between desired and achievable eigenvectors, or 2) blend the control effort to exactly place desired eigenvectors, or 3) a combined optimization. Appropriate transmission zeros reveal tradeoffs between eigenvalue and eigenvector placement. Modal control ls used to realize the eigenspace placement goals using output feedback and user supplied compensation. Two aerospace examples demonstrate techniques for achieving desired response characteristics consistent with conventional design specifications.

Decentralized control of finite state Markov processes

Abstract: We are concerned with the control of a particular class of dynamic systems -- finite state Markov chains. The information pattern available is the so-called one step delay sharing information pattern. Using this information pattern, the dynamic programming algorithm can be explicitly carried out to obtain the optimal policy. The problems are discussed under three different cost criteria -- finite horizon problem with expected total cost, infinite horizon problem with discounted cost, and infinite horizon problem with average expected cost. The solution of the problem is possible with the one step delay sharing decentralized pattern because, as in the centralized control of Markov chains, a separation principle holds (this is not true for multiple step delay sharing). Hence the decentralized problem can essentially be reduced to a (more complicated) centralized one; this reduction is carried out in detail. With some modifications, the "Policy Iteration Algorithm" and "Sondik's Algorithm" are readily applied to find the optimal policies for these problems.