Multi-objective dynamic optimization of path-constrained switched systems

Abstract

A multi-objective dynamic optimization algorithm is proposed for path-constrained switched systems to locate approximated local Pareto solutions with specified tolerances. The algorithm is based on iteratively solving single-objective modified ϵ-constraint dynamic optimization problems to avoid generating weak Pareto solutions. These problems are first reduced to semi-infinite programs embedded with ordinary differential equations by performing the control vector parameterization technique. Then the guaranteed feasibility is attained within a finite number of iterations by enforcing the path constraints at discretized time points with a restriction parameter on the right-hand side. Furthermore, the approximation error of the obtained local Pareto solutions is quantitatively analyzed. The result shows that the Pareto approximation error can be directly controlled via user-specified parameters. Finally, the effectiveness of the algorithm is illustrated via a numerical example.