Rank-constrained Linear Matrix Inequality Research Articles

A unifying framework for form-finding and topology-finding of tensegrity structures

This paper presents a unifying framework for the form-finding and topology-finding of tensegrity structures. The novel computational framework is based on rank-constrained linear matrix inequalities. For form-finding, given the topology (i.e., member connectivities), the determination of the member force densities is formulated into a linear matrix inequality (LMI) problem with a constraint on the rank of the force density matrix. The positive semi-definiteness and rank deficiency condition of the force density matrix are well managed by the rank-constrained LMI-based formulation. A Newton-like algorithm is employed to solve the rank-constrained LMI problem. Two methods, named direct method and indirect method, are proposed to determine the nodal coordinates once the force densities have been obtained. For topology-finding, given the geometry (i.e., nodal coordinates), the determination of the topology is also formulated into an LMI problem with a constraint on the rank of the tangent stiffness matrix. Numerical examples demonstrate that different types of form-finding problems (such as tensegrity structures with single and with multiple self-stress states, symmetric and irregular tensegrity structures) can be uniformly and efficiently solved by the proposed approach. Furthermore, three well-known tensegrity structures are reproduced to verify the effectiveness of the proposed formulation on the topology-finding of tensegrity structures.

Mixed LQG and H∞ coherent feedback control for linear quantum systems

ABSTRACTThe purpose of this paper is to study the mixed linear quadratic Gaussian (LQG) and H∞ optimal control problem for linear quantum stochastic systems, where the controller itself is also a quantum system, often referred to as ‘coherent feedback controller’. A lower bound of the LQG control is proved. Then two different methods, rank-constrained linear matrix inequality method and genetic algorithm are for controller design. A passive system (cavity) and a non-passive one (degenerate parametric amplifier) demonstrate the effectiveness of these two proposed algorithms.

Decentralised - filtering of networked control systems: a jump system approach

We consider the problem of decentralised estimation of discrete-time interconnected systems with local estimators communicating with their subsystems over lossy communication channels. Assuming that the packet losses follow the Gilbert–Elliot model, the networked estimation problem can be formulated into a Markovian jump linear system framework. Modelling subsystem interactions as sum quadratic constrained uncertainties, we design mode-dependent decentralised -estimators that robustly stabilise the estimator system and guarantee a given disturbance attenuation level. The estimation gains are derived with necessary and sufficient rank-constrained linear matrix inequality conditions. Results are also provided for local mode-dependent estimators. Estimator synthesis is done using a cone-complementarity linearisation algorithm for the rank-constraints. The results are illustrated via an example.

Improved low-voltage-ride-through capability of fixed-speed wind turbines using decentralised control of STATCOM with energy storage system

The design and implementation of a new control scheme for reactive power compensation, voltage regulation and transient stability enhancement for wind turbines equipped with fixed-speed induction generators (IGs) in large interconnected power systems is presented in this study. The low-voltage-ride-through (LVRT) capability is provided by extending the range of the operation of the controlled system to include typical post-fault conditions. A systematic procedure is proposed to design decentralised multi-variable controllers for large interconnected power systems using the linear quadratic (LQ) output-feedback control design method and the controller design procedure is formulated as an optimisation problem involving rank-constrained linear matrix inequality (LMI). In this study, it is shown that a static synchronous compensator (STATCOM) with energy storage system (ESS), controlled via robust control technique, is an effective device for improving the LVRT capability of fixed-speed wind turbines.

Low-order robust power system stabilizer for single-machine systems: An LMI approach

This paper describes a linear matrix inequality (LMI) approach to the design of robust loworder power system stabilizers (PSSs), which are used to damp out local-mode oscillations of synchronous generators. The performance of a PSS is expressed as the location of the closed-loop poles, and a single fixed-gain pole-placement controller is synthesized for a wide range of operating conditions. The synthesis results in simultaneous regional pole-placement stabilization through static output feedback, and is formulated as a novel LMI feasibility problem with a rank condition. A penalty method is applied to solve the rank-constrained LMI problem. Numerical experiments with a single machine connected to an infinite bus system were performed to demonstrate the proposed LMI method, and the results were compared with those of previous work.

계수조건부 LMI를 이용한 다목적 제어기 설계

This paper presents a rank-constrained linear matrix inequality (LMI) approach to the design of a multi-objective controller such as control. Multi-objective control is formulated as an LMI optimization problem with a nonconvex rank condition, which is imposed on the controller gain matirx not Lyapunov matrices. With this rank-constrained formulation, we can expect to reduce conservatism because we can use separate Lyapunov matrices for different control objectives. An iterative penalty method is applied to solve this rank-constrained LMI optimization problem. Numerical experiments are performed to illustrate the proposed method.

계수조건부 LMI를 이용한 동시안정화 LQ 최적제어기 설계

This paper presents a rank-constrained linear matrix inequality(LMI) approach to simultaneous linear-quadratic(LQ) optimal control by static output feedback. Simultaneous LQ optimal control is formulated as an LMI optimization problem with a nonconvex rank condition. An iterative penalty method recently developed is applied to solve this rank-constrained LMI optimization problem. Numerical experiments are performed to illustrate the proposed method, and the results are compared with those of previous work.

Solving Rank-Constrained LMI Problems With Application to Reduced-Order Output Feedback Stabilization

This paper presents an iterative penalty function method for solving rank-constrained linear matrix inequality (LMI) problems and illustrates its application to reduced-order output feedback stabilization. We propose a penalized objective function to replace the rank condition, so that a solution to the original nonconvex LMI feasibility problem can be obtained by solving a series of convex LMI optimization subproblems. Numerical experiments were performed to demonstrate the proposed method.

Structurally constrained [formula omitted] and [formula omitted] control: A rank-constrained LMI approach

This paper describes an iterative linear matrix inequality (LMI) approach to the design of a structurally constrained output feedback controller. The structured synthesis is formulated as a novel rank-constrained LMI optimization problem, where the controller parameters are explicitly described so as to impose structural constraints on the parameter matrices. An iterative penalty-function method based on heuristics is used to solve the rank-constrained LMI problem. A numerical experiment illustrates the practicality of the proposed method.

페널티화된 LMI를 이용한 구조적 제약이 있는 제어기 설계

This paper is concerned with an iterative linear matrix inequality (LMI) approach to the design of a structurally constrained output feedback controller such as decentralized control. The structured synthesis is formulated as a novel rank-constrained LMI optimization problem, where the controller parameters are explicitly described so as to impose structural constraints on the parameter matrices. An iterative penalty method is applied to solve the rank-constrained LMI problem. Numerical experiments are performed to illustrate the effectiveness of the proposed method.

반복 선형행렬부등식을 이용한 저차원 H∞제어기 설계

This paper deals with the design of a low-order H/sub ∞/ controller by using an iterative linear matrix inequality (LMI) method. The low-order H/sub ∞/ controller is represented in terms of LMIs with a rank condition. To solve the non-convex rank-constrained LMI problem, the recently developed penalty function method is applied. With an increasing sequence of the penalty parameter, the solution of the penalized optimization problem moves towards the feasible region of the original non-convex problem. Numerical experiments showed the effectiveness of the proposed algorithm.