| Summary: | 博士 === 國立中山大學 === 機械與機電工程學系研究所 === 97 === The dissertation addresses direct adaptive control frameworks for Lyapunov stabilization of the MIMO nonlinear uncertain systems for both uncertain
discrete-time and continuous-time systems. For system theory, the development of continuous-time theory always comes along with its discrete-time counterpart. However, for direct adaptive control frameworks we find relative few Lyapunov-based results published, which is mainly due to difficulty to find feasible Lyapunov candidates and to prove negative definiteness of the Lyapunov difference.
Furthermore, digital computer is widely used in
all fields. Most of time, we have to deal with the direct source of discrete-time signals, even the discrete-time signals arise from continuous-time settings as results of measurement or data collection process. These motivate our study in this field.
For discrete-time systems, we have investigated the results with trajectory dependent hypothesis, where the Lyapunov candidate function V combines the information from the current state k and one step ahead k-1 along the track x(k), for k≥0. The proposed frameworks guarantee partial stability
of the closed-loop systems, such that the feedback gains stabilize the closed-loop system without the knowledge of the system parameters. In addition,
our results show that the adaptive feedback laws can be characterized by Kronecker calculus.
Later, we release this trajectory dependent hypothesis
for normal discrete-time nonlinear systems. At the same time, the continuous-time cases are also studied when system with matched disturbances, where the disturbances can be characterized by
known continuous function matrix and unknown parameters. Here, the trajectory dependent Lyapunov candidates (tdLC), so long as the time step
|t(k)-t(k-1) | ≤ δ and the corresponding track |x(k)-x(k-1)| ≤ ε are sufficiently small, only exist in discrete-time case. In addition, we have extended the above control designs to systems with exogenous disturbances and
ι2 disturbances. Finally, we develop a robust direct adaptive control framework for linear uncertain
MIMO systems under the variance of unknow system matrix from given stable solution is bounded, that is |A-Ac| ≡ |B Kg| ≤ |ΔA|.
In general, through Lyapunov-based design we can obtain the global solutions and direct adaptive control design can simultaneously achieve parameter estimation and closed-loop stability.
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