A Polynomial Chaos Framework for Designing Linear Parameter Varying Control Systems
For control engineers, this provides a novel method to handle randomness in scheduling variables, but the improvement is demonstrated only on a single example.
This paper uses a polynomial chaos framework to design controllers for linear parameter varying (LPV) systems with random scheduling variables, achieving exponential mean-square stability. The proposed controllers outperform classical LPV controllers on an example nonlinear system.
Here we use polynomial chaos framework to design controllers for linear parameter varying (LPV) dynamical systems. We assume the scheduling variable to be random and use polynomial chaos approach to synthesize the controller for the resulting linear stochastic dynamical system. The stability of the LPV system is formulated as an exponential mean-square (EMS) stability problem. Two algorithms are presented that guarantee EMS stability of the stochastic system and correspond to parameter dependent and independent Lyapunov functions, respectively. LPV controllers from the polynomial chaos based framework is shown to outperform LPV controller from classical design for an example nonlinear system.