Gain switching control law for dynamic inversion based adaptive control with unknown sign of control effectiveness

One way control reversal will appear in the plant dynamics is as an opposite to expected (incorrect) sign of control. Adaptive control laws can correct for many plant parameter errors, but some struggle with this phenomenon. A more specific explanation will be posed for the issues direct model reference adaptive control (MRAC) has with opposite to expected sign of control for multiple input multiple output (MIMO) systems, namely that they will fail to satisfy sufficient conditions for matching the adaptive control approximation of plant error in a fixed point solution. A so called "inverse gain switching control" (IGSC) is presented as an adaptive control law for such an MRAC to successfully correct for plant parametric errors, including the sign of the control. The MRAC will include a dynamic inverse (DI). To realize this, an adaptive gain as a function of control signal was utilized. This creates a non-causal dependence that must be broken by solving explicitly for the control signal. As a result, there is a singularity in a term containing said adaptive gain. This will be remedied with a switching control law to appropriately move it around the singularity and retain stability. An example two degree of freedom, four state, spring mass damper system was used to first demonstrate the existing state of practice architecture using Chebyshev polynomial adaptive control in addition to the proposed inverse switching gain control. Results show successful performance and improved convergence of tracking error and adaptive gains in correct and opposite to expected sign of control cases for IGSC. The polynomial adaptive control became unstable and failed for the case of opposite to expected sign of control. The use of the control signal in the adaptive law shows promise for addressing an opposite to expected (or unknown) sign of control. It also presents potential increased robustness as it may better match plant structured parametric error and it promises a potentially more direct route to satisfying a fixed point solution assumption to the matching conditions.