Control System Design of Nonlinear Systems via Numeric and Symbolic Computation

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The research has investigated a methodology of control system design of nonlinear systems, in particular nonlinear polynomial systems via numeric and symbolic computation. The methods of state feedback controller design, observer design and input-to-state system analysis have proposed for nonlinear polynomial systems using sum of squares relaxation and solving semidefinite programming problems. An optimization of nonlinear gain functions has also proposed by a combined use of sum of squares and quantifier elimination. The research also has investigated a design method on gain scheduling controller for the Acrobot, in which effectiveness of several reduction approaches of computation are verified.