Gravity-magnetic cross-gradient joint inversion by the cyclic gradient method

In this paper, we consider a joint-inversion problem using different types of geophysical data: gravity and magnetism. We first formulate two kinds of inverse problems in the famework of the first kind Fredholm integral equations, and then build up a sparse inversion model combining the two inverse problems as well as the cross-gradient term. The cyclic gradient method for quadratic function minimization is extended for solving the corresponding optimization problem. We update the stepsizes in a cyclic way, by combining the approximated Cauchy steps and the fixed steplengths. Theoretical analysis shows that the algorithm converges R-linearly. Experimental tests show that the proposed joint inversion sparse model as well as the proposed cyclic gradient method improve the numerical performances effectively, compared to the state of the art.     

A note on attraction and stability of neutral stochastic delay differential equations with Markovian switching

This paper is concerned with neutral stochastic delay differential equations with Markovian switching (NSDDEs-MS). A kind of ψ ??function is introduced and some criteria on the attractor for the product of the ψ ??function are obtained. By the new criteria, the almost sure stability with the general decay rate of NSDDEs-MS could be examined, including the exponential stability and the polynomial stability. Finally, an example is provided to illustrate the applications of our results clearly.     

Output feedback control of linear fractional transformation systems subject to actuator saturation

In this paper, the control problem for a class of linear parameter varying (LPV) plant subject to actuator saturation is investigated. For the saturated LPV plant depending on the scheduling parameters in linear fractional transformation (LFT) fashion, a gain-scheduled output feedback controller in the LFT form is designed to guarantee the stability of the closed-loop LPV system and provide optimised disturbance/error attenuation performance. By using the congruent transformation, the synthesis condition is formulated as a convex optimisation problem in terms of a finite number of LMIs for which efficient optimisation techniques are available. The nonlinear inverted pendulum problem is employed to demonstrate the effectiveness of the proposed approach. Moreover, the comparison between our LPV saturated approach with an existing linear saturated method reveals the advantage of the LPV controller when handling nonlinear plants.     

Robust limit cycle control in a class of nonlinear discrete-time systems

This paper studies generation of robust periodic solutions in a class of nonlinear discrete-time system. The sustained oscillations, with the desired frequency and amplitude, are achieved through the creation of the appropriate elliptic limit cycle in the phase plane of the uncertain closed-loop discrete-time system. In the first step, the nominal control law is designed to enforce the trajectories of the nominal closed-loop system to converge to the desired limit cycle. Next, considering uncertain terms, an additional robustifying term is designed. This term is added to the nominal controller to sustain the desirable stable oscillations in the presence of uncertain terms. The resulted robust controller brings the trajectories of the uncertain closed-loop discrete-time system to a boundary layer (with adjustable width) around the desired limit cycle. Moreover, the domain of attraction of the limit cycle and also the ultimate boundary layer around it are calculated via the Lyapunov analysis. Additionally, in order to verify the applicability of the proposed method, it is implemented on the discretised model of a spring–damper system. Computer simulations confirm the theoretical results in generating robust stable oscillations.     

Orthonormal basis functions applied to optimal control design with closed-loop pole location constraints

This article proposes an optimal control design technique to ensure that the closed-loop poles are assigned to prescribed locations in the complex plane. A key element in this approach is the usage of orthonormal basis functions to parametrise the main design parameter. This goal is achieved by using a quadratic cost based optimisation approach, considering control effort penalisation as well as cheap control. Youla parametrisation is used, subject to a set of constraints which guarantee stability, zero steady error to constant references and disturbances, and yielding the prescribed set of closed-loop poles.