Adaptive Control of Nonlinear Systems via Approximate Linearization
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We present a direct adaptive tracking control scheme for nonlinear systems that do not have a well defined (vector) relative degree and hence are not feedback linearizable. This techniques uses feedback and coordinate changes to transform a nonlinear system with parameter uncertainty into an approximate input-output linearized one. Our result is also applicable to slightly non-minimum phase nonlinear systems with unknown parameters. We prove that the presented adaptive design scheme results in an asymptotically stable closed loop system and show that the controller can achieve adaptive tracking of reasonable trajectories with bounds on the tracking error. We also present a state regulation scheme based on state approximate linearization. We demonstrate the adaptive approximate tracking results using a simplified model of an aircraft which is slightly non-minimum phase. The usefulness of our approach is also illustrated on a "benchmark" example that is not feedback linearizable.