Multivariable Adaptive Control via Non-Convex Optimization

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CTS-9508654 Ydstie Carnegie Mellon The objective of this research is to develop design theory for a singularity free multivariable adaptive controller. This will be done by combining adaptive control theory with non-convex optimization, an approach which represents a departure from current design philosophies based on convexification, switching logic and/or persistent excitation. Fast adaptation based on second order information and nonlinear programming should improve the convergence rate. Matched control and estimation objectives will be applied so that optimal steady state performance can be achieved. The optimization based algorithm will be based on theory and have few ad hoc tuning parameters. The new concepts in this research are the "centered parameter", which gives optimal performance of a parameterized control system, the use of non-convex optimization to solve singularity problems and the use of adaptive filters to match design and optimization objectives. The theory will apply to a broad class of certainty equivalence adaptive control algorithms including H infinity, LQG and predictive control. The PIs will work on implementation of adaptive control to large scale industrial processes. Experiments show that it is in multivariable applications that adaptive control shows greatest potential giving improvement in process operation.