Control of stochastic parameter-varying uncertain systems with application to the launch vehicle

  • Ilan Rusnak RAFAEL

Abstract

The problem of optimal control of stochastic discrete parameter-varying uncertain linear systems is formulated and partially solved. The solution is achieved by a generalization of the State and Parameters Observability Canonical form – SPOC to parameter varying systems. This representation of linear time-variant systems enables the application of tools from the LQR-LQG theory of control and estimation of discrete linear parameter-varying systems. The optimal solution is exact and noncausal. A causal suboptimal controller, using certainty equivalence, is proposed as an ad-hoc solution. This controller needs only the knowledge of the order of the system. The scheme is BIBO stable for sufficiently low noises and sufficiently slowly varying parameters. As an example, the proposed algorithm is applied to a difficult problem: control of an unstable nonminimum phase parameter-varying model of a dynamic launch vehicle with very large uncertainty, and unmodelled dynamics.  Care is devoted to an analysis of the robustness of the control algorithm. It is demonstrated via simulations that as long as the assumptions are valid the algorithm remains stable and preserves performance.

Published
2020-05-25