Model Reference Adaptive Control of Piecewise Affine Systems with State Tracking Performance Guarantees

In this paper, we investigate the model reference adaptive control approach for uncertain piecewise affine systems with performance guarantees. The proposed approach ensures the error metric, defined as the weighted Euclidean norm of the state tracking error, to be confined within a user-defined time-varying performance bound. We introduce an auxiliary performance function to construct a barrier Lyapunov function. This auxiliary performance signal is reset at each switching instant, which prevents the transgression of the barriers caused by the jumps of the error metric at switching instants. The dwell time constraints are derived based on the parameters of the user-defined performance bound and the auxiliary performance function. We also prove that the Lyapunov function is non-increasing even at the switching instants and thus does not impose extra dwell time constraints. Furthermore, we propose the robust modification of the adaptive controller for the uncertain piecewise affine systems subject to unmatched disturbances. A Numerical example validates the correctness of the proposed approach

Modeling and Control of Partial Differential Equations (PDE) Described Systems

This proposed research is aimed to develop a novel modeling and control algorithm for the PDE described systems. When dealing with time-dependent PDE problems, the partial derivatives of a function over spatial variables are obtained by approximating the function values at interpolation nodes and their corresponding neighbors as a finite summation of polynomial series. A cluster of interpolation nodes guarantees the boundedness of the residual derivatives. Substituting these approximations in the PDE and discretizing the spatial domain of variables while keeping the time domain continuous yields a system of ODEs. By using an eigenvalue-based technique, a reduced-order model is derived, which is incorporated with unmodeled dynamics described as bounded-input, bounded-output (BIBO) stable. To establish the equivalence with original PDE, the reduced-order ODE is augmented with nonlinear time-varying uncertainties and unmodeled dynamics. The final goal is to design an L1 adaptive controller for handling of model mismatch and delivering a good tracking performance