Fixed Time Fuel Optimal Control Of Linear State Constrained Systems By Use Of Linear Programming Techniques
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Author | : A. Frederick Fath |
Publisher | : |
Total Pages | : 25 |
Release | : 1967 |
Genre | : |
ISBN | : |
A procedure is developed for obtaining a numerical approximation to the fixed-time fuel-optimal control for a state-constrained linear system. The constraints on both the state variable and the control variable are given by systems of linear inequalities describing convex polygonal sets which are allowed to be time-varying. The initial state and the final state can be explicitly given or specified as members of certain convex polygonal sets. The numerical approximation is obtained by reformulating the control problem into a form that is solvable by linear programming techniques. (Author).
Author | : August Frederick Fath |
Publisher | : |
Total Pages | : 34 |
Release | : 1968 |
Genre | : Rockets (Aeronautics) |
ISBN | : |
A procedure is given for the computation of the fuel-optimal control for linear state-constrained systems where convex polygonal (possibly time-varying) sets are used for specifying the allowable control vectors and the allowable state vectors. The terminal condition can be imposed through a convex target set or through exact specification of the terminal state. The solution is obtained by formulating the problem so that the techniques of linear programming with upper bounds can be used. The use of these techniques and the special structure of the reformulated problem results in a computationally efficient algorithm. As an example, the algorithm is used for the solution of a space rendezvous problem. (Author).
Author | : August Frederick Fath |
Publisher | : |
Total Pages | : 588 |
Release | : 1967 |
Genre | : Linear programming |
ISBN | : |
Author | : |
Publisher | : |
Total Pages | : 1572 |
Release | : 1992 |
Genre | : Aeronautics |
ISBN | : |
Author | : Walter Charles Lipinski |
Publisher | : |
Total Pages | : 260 |
Release | : 1969 |
Genre | : Liquid metal fast breeder reactors |
ISBN | : |
Author | : Defense Documentation Center (U.S.) |
Publisher | : |
Total Pages | : 784 |
Release | : 1967 |
Genre | : Science |
ISBN | : |
Author | : Zhongjing Ma |
Publisher | : Springer Nature |
Total Pages | : 355 |
Release | : 2021-01-30 |
Genre | : Technology & Engineering |
ISBN | : 9813362928 |
This book focuses on how to implement optimal control problems via the variational method. It studies how to implement the extrema of functional by applying the variational method and covers the extrema of functional with different boundary conditions, involving multiple functions and with certain constraints etc. It gives the necessary and sufficient condition for the (continuous-time) optimal control solution via the variational method, solves the optimal control problems with different boundary conditions, analyzes the linear quadratic regulator & tracking problems respectively in detail, and provides the solution of optimal control problems with state constraints by applying the Pontryagin’s minimum principle which is developed based upon the calculus of variations. And the developed results are applied to implement several classes of popular optimal control problems and say minimum-time, minimum-fuel and minimum-energy problems and so on. As another key branch of optimal control methods, it also presents how to solve the optimal control problems via dynamic programming and discusses the relationship between the variational method and dynamic programming for comparison. Concerning the system involving individual agents, it is also worth to study how to implement the decentralized solution for the underlying optimal control problems in the framework of differential games. The equilibrium is implemented by applying both Pontryagin’s minimum principle and dynamic programming. The book also analyzes the discrete-time version for all the above materials as well since the discrete-time optimal control problems are very popular in many fields.
Author | : |
Publisher | : |
Total Pages | : 542 |
Release | : 1972 |
Genre | : Mechanics, Applied |
ISBN | : |
Author | : Daniel Tabak |
Publisher | : Prentice Hall |
Total Pages | : 264 |
Release | : 1971 |
Genre | : Mathematics |
ISBN | : |
Author | : A. Frederick Fath |
Publisher | : |
Total Pages | : 30 |
Release | : 1967 |
Genre | : |
ISBN | : |
A procedure is presented for approximating the time-optimal control for linear state-constrained systems. The constraint sets on both the state variable and the control vector can be any sets able to be approximated by piecewise-constant convex polygonal sets. The target set can be specified as any convex polygonal set about the origin in state space. The approximation is obtained by reformulating the problem such that iteration on a scalar quantity (the final time) is needed with a linear programming problem solved at each iteration. An example using a fourth order system is presented. (Author).