| The intent of this dissertation is to present novel approaches of synthesizing controllers for Hybrid Dynamical Systems (HDS). These are systems that configure embedded control which takes into account the interactions between a computer program modeled as an automaton and continuous systems modeled by nonlinear ordinary differential equations.;The two problems we address are as follows. We develop a non-restrictive and general approach of designing HDS stabilization algorithms using nonlinear feedback linearization techniques. In doing so, we were able to completely bypass the issue of characterization of inherent switching boundaries in the HDS plant model. This latter property was the major hindering factor of deriving stabilizing controllers from prevailing HDS asymptotic stability results. Next, we construct a new architecture for implementing suboptimal HDS controllers using wavelet calculus. Our Wavelets Control Architecture (WCA) is amenable to efficient high performance computing, thereby satisfactorily addressing the dimensionality issue pertaining to any Galerkin method of estimating the optimal solution by solving the associated Hamiltonian-Jacobian-Bellman (HJB) partial differential equation. In addition, multiresolution analysis of compact wavelets enable us to estimate the discontinuities in HJB fairly well compared to other orthogonal bases. Moreover, we exploit these properties to reduce HDS Plant's logic decision making capability to a much simpler digital switching device consisting of, say, the JK Flip-Flops. Hence, both the HDS Plant's logic semantics and WCA can be completely realized in a hardware form taking advantage of the current paradigm in VLSI technology - system on a chip. |
