Closed-loop control of stochastic non-linear systems

✍ Scribed by G.T. Schmidt

• Publisher: Elsevier Science
• Year: 1971
• Tongue: English
• Weight: 814 KB
• Volume: 7
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/0005-1098(71)90021-5

✦ Synopsis

A simultaneous combined optimization of the reference trajectory, perturbation controller, and perturbation estimator .for stochastic non-linear systems can improve performance over quadratic synthesis optimization around a nominal trajectory.

Summnry--A new approach for optimum control of stochastic non-linear systems is developed from practical engineering assumptions. Systems amenable to this new approach include optimum guidance and navigation systems for space and terrestrial vehicles, optimum closed-loop process controllers and optimum controllers for systems with unknown parameters. The classical quadratic synthesis approach--optimization of a deterministic cost and perturbation estimation and control about that solution--is shown to give 24 per cent more cost and 97 per cent more mean-squared terminal error than the combined optimization approach presented for a sample problem involving control of a first-order system with an unknown time constant. A similar improvement in terminal error is shown for an atmospheric entry problem. Furthermore, the optimum controller automatically designs the best controller to minimize the effects of the unknown parameter without artificial augmentation of the cost function as is done in the sensitivity theory approach. The solution is obtained by expansion of the cost function in a power series around a deterministic trajectory with the assumption of linear perturbation estimation and control about that trajectory. Optimization of the expanded cost function gives necessary conditions dependent on the covariance matrices and the deterministic portion of the cost. When the necessary conditions are solved, a set of open-loop controls, perturbation controller gains, and perturbation estimator gains are obtained that can be precomputed and implemented into the system.