A Data-driven Approach to Robust Control of Multivariable Systems by Convex Optimization

The frequency-domain data of a multivariable system in different operating points is used to design a robust controller with respect to the measurement noise and multimodel uncertainty. The controller is fully parametrized in terms of matrix polynomial functions and can be formulated as a centralized, decentralized or distributed controller. All standard performance specifications like $H_2$, $H_\infty$ and loop shaping are considered in a unified framework for continuous- and discrete-time systems. The control problem is formulated as a convex-concave optimization problem and then convexified by linearization of the concave part around an initial controller. The performance criterion converges monotonically to a local optimal solution in an iterative algorithm. The effectiveness of the method is compared with fixed-structure controllers using non-smooth optimization and with full-order optimal controllers via simulation examples. Finally, the experimental data of a gyroscope is used to design a data-driven controller that is successfully applied on the real system

Incorporating Physics-Based Patterns into Geophysical and Geostatistical Estimation Algorithms

Geophysical imaging systems are inherently non-linear and plagued with the challenge of limited data. These drawbacks make the solution non-unique and sensitive to small data perturbations; hence, regularization is performed to stabilize the solution. Regularization involves the application of a priori specification of the target to modify the solution space in order to make it tractable. However, the traditionally applied regularization model constraints are independent of the physical mechanisms driving the spatiotemporal evolution of the target parameters. To address this limitation, we introduce an innovative inversion scheme, basis-constrained inversion, which seeks to leverage advances in mechanistic modeling of physical phenomena to mimic the physics of the target process, to be incorporated into the regularization of hydrogeophysical and geostatistical estimation algorithms, for improved subsurface characterization. The fundamental protocol of the approach involves the construction of basis vectors from training images, which are then utilized to constrain the optimization problem. The training dataset is generated via Monte Carlo simulations to mimic the perceived physics of the processes prevailing within the system of interest. Two statistical techniques for constructing optimal basis functions, Proper Orthogonal Decomposition (POD) and Maximum Covariance Analysis (MCA), are employed leading to two inversion schemes. While POD is a static imaging technique, MCA is a dynamic inversion strategy. The efficacies of the proposed methodologies are demonstrated based on hypothetical and lab-scale flow and transport experiments

Globally Optimal Resource Allocation Design for Discrete Phase Shift IRS-Assisted Multiuser Networks with Perfect and Imperfect CSI

Intelligent reflecting surfaces (IRSs) are a promising low-cost solution for achieving high spectral and energy efficiency in future communication systems by enabling the customization of wireless propagation environments. Despite the plethora of research on resource allocation design for IRS-assisted multiuser communication systems, the optimal design and the corresponding performance upper bound are still not fully understood. To bridge this gap in knowledge, in this paper, we investigate the optimal resource allocation design for IRS-assisted multiuser systems employing practical discrete IRS phase shifters. In particular, we jointly optimize the beamforming vector at the base station (BS) and the discrete IRS phase shifts to minimize the total transmit power for the cases of perfect and imperfect channel state information (CSI) knowledge. To this end, two novel algorithms based on the generalized Benders decomposition (GBD) method are developed to obtain the globally optimal solution for perfect and imperfect CSI, respectively. Moreover, to facilitate practical implementation, we propose two corresponding low-complexity suboptimal algorithms with guaranteed convergence by capitalizing on successive convex approximation (SCA). In particular, for imperfect CSI, we adopt a bounded error model to characterize the CSI uncertainty and propose a new transformation to convexify the robust quality-of-service (QoS) constraints. Our numerical results confirm the optimality of the proposed GBD-based algorithms for the considered system for both perfect and imperfect CSI. Furthermore, we unveil that both proposed SCA-based algorithms can achieve a close-to-optimal performance within a few iterations. Moreover, compared with the state-of-the-art solution based on the alternating optimization (AO) method, the proposed SCA-based scheme achieves a significant performance gain with low complexity