Design of nonuniform near allpass complementary FIR filters via a semi-infinite programming technique

In this paper, we consider the problem of designing a set of nonuniform near allpass complementary FIR filters. This problem can be formulated as a quadratic semi-infinite programming problem, where the objective is to minimize the sum of the ripple energy for the individual filters, subject to the passband and stopband specifications as well as to the allpass complementary specification. The dual parameterization method is used for solving the linear quadratic semi-infinite programming problem

Efficient algorithm for solving semi-infinite programming problems and their applications to nonuniform filter bank designs

An efficient algorithm for solving semi-infinite programming problems is proposed in this paper. The index set is constructed by adding only one of the most violated points in a refined set of grid points. By applying this algorithm for solving the optimum nonuniform symmetric/antisymmetric linear phase finite-impulse-response (FIR) filter bank design problems, the time required to obtain a globally optimal solution is much reduced compared with that of the previous proposed algorith

Optimum design of discrete-time differentiators via semi-infinite programming approach

In this paper, a general optimum full band high order discrete-time differentiator design problem is formulated as a peak constrained least square optimization problem. That is, the objective of the optimization problem is to minimize the total weighted square error of the magnitude response subject to the peak constraint of the weighted error function. This problem formulation provides a great flexibility for the tradeoff between the ripple energy and the ripple magnitude of the discrete-time differentiator. The optimization problem is actually a semi-infinite programming problem. Our recently developed dual parametrization algorithm is applied for solving the problem. The main advantage of employing the dual parameterization algorithm for solving the problem is the guarantee of the convergence of the algorithm and the obtained solution being the global optimal solution that satisfies the corresponding continuous constraints. Moreover, the computational cost of the algorithm is lower than that of algorithms implementing the semi-definite programming approach

Optimization approach for solving problems in signal processing and communications systems

This invited seminar is discussed on optimization approach for solving problems in signal processing and communications systems

A dual parametrization approach to Nyquist filter design

In this paper, the optimum design of a factorable Nyquist filter with the intersymbol interference (ISI) being exactly zero is formulated as a nonlinear optimization problem with continuous inequality constraints. An iterative scheme is developed for solving this semi-infinite optimization problem, where an improved dual parametrization method is utilized in each iteration of the iterative scheme. Trade-off between robustness against timing jitter and small stopband attenuation is achieved via an adjustment of a parameter. Some examples are solved using the proposed iterative method

On Control and Estimation of Large and Uncertain Systems

This thesis contains an introduction and six papers about the control and estimation of large and uncertain systems. The first paper poses and solves a deterministic version of the multiple-model estimation problem for finite sets of linear systems. The estimate is an interpolation of Kalman filter estimates. It achieves a provided energy gain bound from disturbances to the point-wise estimation error, given that the gain bound is feasible. The second paper shows how to compute upper and lower bounds for the smallest feasible gain bound. The bounds are computed via Riccati recursions. The third paper proves that it is sufficient to consider observer-based feedback in output-feedback control of linear systems with uncertain parameters, where the uncertain parameters belong to a finite set. The paper also contains an example of a discrete-time integrator with unknown gain. The fourth paper argues that the current methods for analyzing the robustness of large systems with structured uncertainty do not distinguish between sparse and dense perturbations and proposes a new robustness measure that captures sparsity. The paper also thoroughly analyzes this new measure. In particular, it proposes an upper bound that is amenable to distributed computation and valuable for control design. The fifth paper solves the problem of localized state-feedback L2 control with communication delay for large discrete-time systems. The synthesis procedure can be performed for each node in parallel. The paper combines the localized state-feedback controller with a localized Kalman filter to synthesize a localized output feedback controller that stabilizes the closed-loop subject to communication constraints. The sixth paper concerns optimal linear-quadratic team-decision problems where the team does not have access to the model. Instead, the players must learn optimal policies by interacting with the environment. The paper contains algorithms and regret bounds for the first- and zeroth-order information feedback

A System Level Approach to Optimal Controller Design for Large-Scale Distributed Systems

Modern cyber-physical systems, such as the smart grid, software-defined networks, and automated highway systems, are large-scale, physically distributed, and interconnected. The scale of these systems poses fundamental challenges for controller design: the traditional optimal control methods are globally centralized, which require solving a large-scale optimization problem with the knowledge of the global plant model, and collecting global measurement instantaneously during implementation. The ultimate goal of distributed control design is to provide a local, distributed, scalable, and coordinated control scheme to achieve centralized control objectives with nearly global transient optimality. This dissertation provides a novel theoretical and computational contribution to the area of constrained linear optimal control, with a particular emphasis on addressing the scalability of controller design and implementation for large-scale distributed systems. Our approach provides a fundamental rethinking of controller design: we extend a control design problem to a system level design problem, where we directly optimize the desired closed loop behavior of the feedback system. We show that many traditional topics in the optimal control literature, including the parameterization of stabilizing controller and the synthesis of centralized and distributed controller, can all be cast as a special case of a system level design problem. The system level approach therefore unifies many existing results in the field of distributed optimal control, and solves many previously open problems. Our system level approach has at least the following four technical merits. First, we characterize the broadest known class of constrained linear optimal control problem that admits a convex formulation. Specifically, we show that the set of convex system level design problems is a strict superset of those that can be parameterized using quadratic invariance. Second, we identify a class of system level design problems, which we called the localized optimal control problems, that are scalable to arbitrary large-scale systems. In particular, the parallel synthesis and implementation complexity of the localized optimal controller are O(1) compared to the size of the networked system. Third, we provide a unified framework to simultaneously incorporate user-specified design specification on the closed loop and the hardware implementation constraints on the controller into the optimal controller design process. Lastly, we provide a system level approach that supports the co-design of optimal controller and its sensing and actuating architecture. We demonstrate the effectiveness of our method on a 51200-state randomized heterogeneous power network model, and show that the system level approach provides superior scalability over the centralized and distributed method. For such a large-scale example, the theoretical computation time for the centralized scheme is more than 200 days, and the distributed optimal control scheme is intractable. In contrast, it only takes 38 minutes to synthesize a localized optimal controller that achieves at least 99% global optimality guarantee.</p