Convex optimization

About: Convex optimization is a research topic. Over the lifetime, 24906 publications have been published within this topic receiving 908795 citations. The topic is also known as: convex optimisation.

State feedback controller design of networked control systems with interval time-varying delay and nonlinearity

Abstract: SUMMARY This paper proposes a method for robust state feedback controller design of networked control systems with interval time-varying delay and nonlinearity. The key steps in the method are to construct an improved interval-delay-dependent Lyapunov functional and to introduce an extended Jessen’s inequality. Neither free weighting nor model transformation are employed in the derivation of the system stability criteria. It is shown that the maximum allowable bound on the nonlinearity could be computed through solving a constrained convex optimization problem; and the maximum allowable delay bound and the feedback gain of a memoryless controller could be derived by solving a set of linear matrix inequalities (LMIs). Numerical examples are given to demonstrate the efiectiveness of the proposed method.

Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture

Abstract: Several convex mappings of linear operators on a Hilbert space into the real numbers are derived, an example being A → — Tr exp(L + In A). Some of these have applications to physics, specifically to the Wigner—Yanase—Dyson conjecture which is proved here and to the strong subadditivity of quantum mechanical entropy which will be proved elsewhere.

Voltage/VAR Control in Distribution Networks via Reactive Power Injection Through Distributed Generators

Abstract: This paper demonstrates how reactive power injection from distributed generators can be used to mitigate the voltage/VAR control problem of a distribution network. Firstly, power flow equations are formulated with arbitrarily located distributed generators in the network. Since reactive power injection is limited by economic viability and power electronics interface, we formulate voltage/VAR control as a constrained optimization problem. The formulation aims to minimize the combined reactive power injection by distributed generators, with constraints on: 1) power flow equations; 2) voltage regulation; 3) phase imbalance correction; and 4) maximum and minimum reactive power injection. The formulation is a nonconvex problem thereby making the search for an optimal solution extremely complex. So, a suboptimal approach is proposed based on methods of sequential convex programming (SCP). Comparing our suboptimal approach with the optimal solution obtained from branch and bound method, we show the trade-off in quality of our solution with runtime. We also validate our approach on the IEEE 123 node test feeder and illustrate the efficacy of using distributed generators as distributed reactive power resource.

Combining Convex–Concave Decompositions and Linearization Approaches for Solving BMIs, With Application to Static Output Feedback

Abstract: A novel optimization method is proposed to minimize a convex function subject to bilinear matrix inequality (BMI) constraints. The key idea is to decompose the bilinear mapping as a difference between two positive semidefinite convex mappings. At each iteration of the algorithm the concave part is linearized, leading to a convex subproblem. Applications to various output feedback controller synthesis problems are presented. In these applications, the subproblem in each iteration step can be turned into a convex optimization problem with linear matrix inequality (LMI) constraints. The performance of the algorithm has been benchmarked on the data from the COMPleib library.

Convex Optimization for the Energy Management of Hybrid Electric Vehicles Considering Engine Start and Gearshift Costs

Abstract: This paper presents a novel method to solve the energy management problem for hybrid electric vehicles (HEVs) with engine start and gearshift costs. The method is based on a combination of deterministic dynamic programming (DP) and convex optimization. As demonstrated in a case study, the method yields globally optimal results while returning the solution in much less time than the conventional DP method. In addition, the proposed method handles state constraints, which allows for the application to scenarios where the battery state of charge (SOC) reaches its boundaries.