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In this paper, we present a receding horizon observer for linear time-varying systems. Our main contribution is that known deterministic input has been fully dealt with. This poses considerable challenges for recursive formulation of the filter. The suggested observer can be used in closed-loop feedback control systems. The existing finite memory filters lack this ability. First- and second-order statistical convergence analysis carried out in this paper provide an insight into the stochastic behaviour of the observer. Some examples demonstrate the utility of the proposed filter.

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The paper presents a control scheme for the real-time tracking problem of nonlinear systems subjected to hard nonlinearities. The proposed tracking controller introduces a refining component in the control input designed for the nominal plant model. The refining component compensates for tracking performance degradation caused by modelling uncertainties and external disturbances. The refining component is modelled as a random signal, the probability density function is expressed as a combination of finite weights typical of particle methods. The weights are updated based on sequential tracking error data. The proposed algorithm is simulated for an inverted pendulum affected by Coulomb friction. Comparison with existing techniques exhibits remarkably superior tracking performance. INDEX TERMS Control design, Control refinement, Particle filters, Sampled data systems.