Approximate optimal controls that maximize the probability of entering a target manifold

✍ Scribed by J.Y.S. Luh; G.E. O'Connor

• Publisher: Elsevier Science
• Year: 1969
• Tongue: English
• Weight: 843 KB
• Volume: 288
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(69)00199-2

✦ Synopsis

The linear time-dependent control processes subject to additive random dieturbances are discussed. An algorithm is developed for the control law which optimizes the adjustment of the trade-08 between the probability that the state of the process enters a given target manifold and the weighted control energy expenditure. The probability term satisfies the backward diffusion equation. An estimate of the solution to the equation is established. The optimal solution is then determined numerically on a digital computer. The computational scheme is based on two key techniques: the conjugate gradient procedure, and a Monte Carlo method for multidimensional integral computation. The Jlow charts which describe the algorithm are shown. An example is given as an illustration.