Mahyar Fazlyab

Parameter estimation and interval type-2 fuzzy sliding mode control of a z-axis MEMS gyroscope

This paper reports a hybrid intelligent controller for application in single axis MEMS vibratory gyroscopes. First, unknown parameters of a micro gyroscope including unknown time varying angular velocity are estimated online via normalized continuous time least mean squares algorithm. Then, an additional interval type-2 fuzzy sliding mode control is incorporated in order to match the resonant frequencies and to compensate for undesired mechanical couplings. The main advantage of this control strategy is its robustness to parameters uncertainty, external disturbance and measurement noise. Consistent estimation of parameters is guaranteed and stability of the closed-loop system is proved via the Lyapunov stability theorem. Finally, numerical simulation is done in order to validate the effectiveness of the proposed method, both for a constant and time-varying angular rate.

Interior point method for dynamic constrained optimization in continuous time

This paper considers a class of convex optimization problems where both the objective function and the constraints have a continuous dependence on time. We develop an interior point method that asymptotically succeeds in tracking the optimal point in nonstationary settings. The method utilizes a time-varying constraint slack and a prediction-correction structure that relies on time derivatives of functions and constraints and Newton steps in the spatial domain. Error free tracking is guaranteed under customary assumptions on the optimization problems and time differentiability of objective and constraints. The effectiveness of the method is illustrated in a target tracking problem.

Robust topology identification and control of LTI networks

This paper reports a robust scheme for topology identification and control of networks running on linear dynamics. In the proposed method, the unknown network is enforced to asymptotically follow a reference dynamics using the combination of Lyapunov based adaptive feedback input and sliding mode control. The adaptive part controls the dynamics by learning the network structure, while the sliding mode part rejects the input uncertainty. Simulation studies are presented in several scenarios (detection of link failure, tracking time varying topology, achieving dynamic synchronization) to give support to theoretical findings.

Self-triggered time-varying convex optimization

In this paper, we propose a self-triggered algorithm to solve a class of convex optimization problems with time-varying objective functions. It is known that the trajectory of the optimal solution can be asymptotically tracked by a continuous-time state update law. Unfortunately, implementing this requires continuous evaluation of the gradient and the inverse Hessian of the objective function which is not amenable to digital implementation. Alternatively, we draw inspiration from self-triggered control to propose a strategy that autonomously adapts the times at which it makes computations about the objective function, yielding a piece-wise affine state update law. The algorithm does so by predicting the temporal evolution of the gradient using known upper bounds on higher order derivatives of the objective function. Our proposed method guarantees convergence to arbitrarily small neighborhood of the optimal trajectory in finite time and without incurring Zeno behavior. We illustrate our framework with numerical simulations.

A variational approach to dual methods for constrained convex optimization

We approach linearly constrained convex optimization problems through their dual reformulation. Specifically, we derive a family of accelerated dual algorithms by adopting a variational perspective in which the dual function of the problem represents the scaled potential energy of a synthetic mechanical system, and the kinetic energy is defined by the Bregman divergence induced by the dual velocity flow. Through application of Hamiltons principle, we derive a continuous-time dynamical system which exponentially converges to the saddle point of the Lagrangian. Moreover, this dynamical system only admits a stable discretization through accelerated higher-order gradient methods, which precisely corresponds to accelerated dual mirror ascent. In particular, we obtain discrete-time convergence rate O(1/kp), where p − 1 is the truncation index of the Taylor expansion of the dual function. For practicality sake, we consider p = 2 and p = 3 only, respectively corresponding to dual Nesterov acceleration and a dual variant of Nesterovs cubic regularized Newton method. This analysis provides an explanation from whence dual acceleration comes as the discretization of the Euler-Lagrange dynamics associated with the constrained convex program. We demonstrate the performance of the aforementioned continuous-time framework with numerical simulations.