Dan Yu

Dan Yu, Suman Chakravorty

In this paper, we consider the model reduction problem of large-scale systems, such as systems obtained through the discretization of partial differential equations. We propose a computationally optimal randomized proper orthogonal decomposition (RPOD*) technique to obtain the reduced order model by perturbing the primal and adjoint system using Gaussian white noise. We show that the computations required by the RPOD* algorithm is orders of magnitude cheaper when compared to the balanced proper orthogonal decomposition (BPOD) algorithm and BPOD output projection algorithm while the performance of the RPOD* algorithm is much better than BPOD output projection algorithm. It is optimal in the sense that a minimal number of snapshots is needed. We also relate the RPOD* algorithm to random projection algorithms. The method is tested on two advection-diffusion equations.

Dan Yu, Mohammandhussen Rafieisakhaei, Suman Chakravorty

This paper studies the stochastic optimal control problem for systems with unknown dynamics. A novel decoupled data based control (D2C) approach is proposed, which solves the problem in a decoupled "open loop-closed loop" fashion that is shown to be near-optimal. First, an open-loop deterministic trajectory optimization problem is solved using a black-box simulation model of the dynamical system using a standard nonlinear programming (NLP) solver. Then a Linear Quadratic Regulator (LQR) controller is designed for the nominal trajectory-dependent linearized system which is learned using input-output experimental data. Computational examples are used to illustrate the performance of the proposed approach with three benchmark problems.

Dan Yu, Mohammadhussein Rafieisakhaei, Suman Chakravorty

This paper studies the partially observed stochastic optimal control problem for systems with state dynamics governed by Partial Differential Equations (PDEs) that leads to an extremely large problem. First, an open-loop deterministic trajectory optimization problem is solved using a black box simulation model of the dynamical system. Next, a Linear Quadratic Gaussian (LQG) controller is designed for the nominal trajectory-dependent linearized system, which is identified using input-output experimental data consisting of the impulse responses of the optimized nominal system. A computational nonlinear heat example is used to illustrate the performance of the approach.

Dan Yu, Mohammadhussein Rafieisakhaei, Suman Chakravorty

This paper studies the stochastic optimal control problem for systems with unknown dynamics. First, an open-loop deterministic trajectory optimization problem is solved without knowing the explicit form of the dynamical system. Next, a Linear Quadratic Gaussian (LQG) controller is designed for the nominal trajectory-dependent linearized system, such that under a small noise assumption, the actual states remain close to the optimal trajectory. The trajectory-dependent linearized system is identified using input-output experimental data consisting of the impulse responses of the nominal system. A computational example is given to illustrate the performance of the proposed approach.