MirSaleh Bahavarnia

Closed-loop feedback sparsification under parametric uncertainties

We consider the problem of output feedback controller sparsification for systems with parametric uncertainties. We develop an optimization scheme that minimizes the performance deterioration from that of a well-performing pre-designed centralized controller, while enhancing sparsity pattern of the feedback gain. In order to improve temporal proximity of the pre-designed control system and its sparsified counterpart, we also incorporate an additional constraint into the problem formulation such that the output of the controlled system is enforced to stay in the vicinity of the output of the pre-designed system. It is shown that the resulting non-convex optimization problem can be equivalently reformulated into a rank-constrained problem. We then formulate a bi-linear minimization problem to obtain a sub-optimal solution which satisfies the rank constraint with arbitrary tolerance. Finally, a sub-optimal sparse controller synthesis for IEEE 39-bus New England power network is used to showcase the effectiveness of our proposed method.

Periodic time-triggered sparse Linear Quadratic Controller design

This paper investigates the periodic time-triggered sparse Linear Quadratic Controller (LQC) design for the class of Linear Time Invariant (LTI) systems. Given a time period and keeping the control input fixed during such a time period, an optimization problem is formulated in which the objective function consists of a quadratic performance term along with an ℓ0-regularization term. Recasting such an optimization problem as a rank-constrained optimization problem and utilizing the weighted ℓ1-relaxation enable us to apply so-called bi-linear rank penalty technique to design periodic time-triggered sparse LQC. Employing the various test cases and running our proposed algorithm for different values of time period, performance/sparsity trade-off curves are visualized which suggest a helpful criterion to choose the time period in a way that the desired balance between controller sparsity and rate of periodic triggering is made.

Non-Fragile Tuning of Fractional-Order PD Controllers for IPD-Modelled Processes

Abstract This paper deals with introducing non-fragile algebraic tuning rules for fractional-order PD controllers where they are used in controlling processes modeled in Integral Plus Delay (IPD) forms. These tuning rules are obtained based on a recently introduced approach, named as the centroid approach, which results in non-fragile tuning methods. Based on this approach, the centroids of two-dimensional admissible regions or the center of gravity of three-dimensional admissible regions in controller parameter space give non-fragile options for choosing controller parameters.

Performance bounds and optimal design of randomly switching linear consensus networks

We analyze the steady-state performance of randomly switching linear consensus networks subject to an additive noise. Our focus is on a class of discrete-time linear consensus networks whose dynamics evolve in time by switching between symmetric doubly-stochastic matrices that are drawn from a given finite set of realizations, which are dictated by a discrete random variable with a known probability mass function (pmf). The mean square deviation of the output from zero is utilized as a performance measure to quantify the noise propagation across the network. The direct computation of the performance measure, however, suffers from the curse of dimensionality. The first objective of this paper is to report a rather tight lower-bound for the performance measure that requires comparably less computations. Our second goal is to design a randomly switching network by minimizing the overall performance measure with respect to the vector of switching probabilities between consecutive realizations. Indeed, we prove that the performance measure is a convex function of the vector of switching probabilities, and furthermore, the optimal network design problem can be cast as a Semi-Definite Program (SDP). Moreover, we show that the performance measure is a convex function of the link weights of all underlying graphs, which implies that one can perform a reweighting procedure to minimize the performance measure using convenient convex programming tools. Different aspects of our theoretical results are illustrated via numerous examples and simulations.

Row-column sparse linear quadratic controller design via Bi-linear rank penalty technique and non-fragility notion

We consider the problem of row-column sparse linear quadratic controller (LQC) design. An optimization problem is formulated in which the quadratic performance loss is minimized subject to satisfaction of m+n sparsity constraints to obtain the row-column (r, c)-sparse LQC design where m and n refer to the number of inputs and states, respectively and r/c represent the maximum allowed density level for each row/column of controller. It is expressed that the obtained non-convex optimization problem can equivalently be reformulated as a rank-constrained problem with m+n +1 rank constraints. After applying the non-fragility notion provided by [1] to such a rank-constrained problem, bi-linear rank penalty technique is deployed to find a sub-optimal row-column (r, c)-sparse LQC design which fulfills the rank constraint with desired tolerance. At last, to verify our proposed algorithm, given a randomly generated system, a sub-optimal row-column (r, c)-sparse LQC design is proposed and subsequently, the fundamental trade-off between r/c and quadratic performance loss is visualized.