Structural Analysis for the Design of Reliable Controllers and State Estimators for Continuous-Time Dynamical Systems with Uncertainties

The task of designing feedforward control strategies for finite-dimensional systems in such a way that the output variables match predefined trajectories is a common goal in control engineering. Besides the widely used formulation of the corresponding system models as explicit sets of ordinary differential equations, differential-algebraic representations allow for a unified treatment of both system analysis and synthesis. For modeling and analysis of many real-life dynamic processes, differential-algebraic equations are a natural description to take into account interconnections between different physical components. Each component of such interconnected systems is described by a separate dynamic model, for instance the electric drive and the mechanical components in power trains.Moreover, side conditions are required to connect these component models by a description of power flow or, for example, geometric constraints imposed by links and joints. During system synthesis, control design tasks can be formulated in terms of initial value problems for sets of differential-algebraic equations. To check solvability, verified and nonverified algorithms are applicable which analyze the underlying system structures. The same holds for the reconstruction of internal variables and parameters on the basis of measured data. In this contribution, constructive approaches are discussed for solving both the control and estimator design using differential-algebraic formulations. It is demonstrated how these approaches can be used to show controllability and observability of dynamical systems. Numerical results for two applications conclude this paper.

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