New results in 2D optimal control theory

The infinite horizon optimal control problem is solved for 2D systems described by the Fornasini-Marchesini model. An ₂-approach permits us to reduce the optimal control problem to a norm minimization one in Hilbert spaces. Both necessary and sufficient conditions for solvability and the structure of the solution are established. Moreover, a comparison with known results is presented, and the singularities of the 2D Riccati equation are examined in order to characterize suboptimal control laws that apply whenever the solvability conditions are not satisfied.     

Rational wavelet decompositions of transfer functions in hardy-sobolev classes

The model approximation of transfer functions using rational wavelets (or molecular decompositions) is considered. By using techniques from Hardy-Sobolev spaces it is shown that Hilbert space methods such as a modified matching-pursuit algorithm and least-squares technique can be employed to obtain good approximations in bothH ² andH norms. Several theoretical results are given on rates of convergence when the methods are applied to delay systems and fractional filters.The research of the first author was supported by E.P.S.R.C.     

结合l1/2范数与显著性约束的背景减除

传统背景减除模型在背景静止和前景对象移动较快时提取到的前景效果较好,但当背景变化或前景对象移动缓慢时容易将动态背景误判为前景或检测出的前景有较多空洞。针对传统背景减除模型在动态背景和前景对象移动缓慢条件下存在前景检测精度下降的问题,提出一种基于l_1/2范数与显著性约束的背景减除模型。将观测数据分为低秩背景、运动前景和动态干扰3类,利用l_1/2范数约束运动前景加强前景稀疏性,有效抑制动态背景对前景提取造成的干扰,提高运动前景在动态背景中的检测精度。引入视频每一帧的显著性约束,通过对每一帧图像进行低秩稀疏分解来检测移动缓慢的目标。实验结果表明,该模型对于复杂场景具有较强的适应能力,可有效去除动态背景对前景的干扰,快速检测出移动缓慢的前景对象,相比于l_1/1/2-RPCA背景减除模型的平均查全率、查准率和调和平均值分别提升了9、14和10个百分点。     

Robust Stabilization of Nonlinear Systems via Normalized Coprime Factor Representations

A reasonably complete theory for the synthesis of robust controllers for a broad class of nonlinear systems is now available. We use this theory to generalize the linear theory of normalized coprime factor robustness optimization to the case of affine input nonlinear systems. In particular, we show that the equilibrium controller may be characterized in terms of the stabilizing and destabilizing solutions of the Hamilton–Jacobi equation used to calculate the normalized (right) coprime factors of the plant. We also show that the optimal robustness margin of

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t-Norm based cuts of intuitionistic fuzzy sets

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Reliable control for a class of uncertain singular systems with interval time‐varying delay

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Energy optimal spacecraft attitude control subject to convergence rate constraints

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