The Kalman filter is a powerful recursive state estimator and has been widely used in many applications. To guarantee its optimality, the noise covariances should to be exactly known. In reality, however, for most practical applications, it is difficult or unrealistic to obtain the noise covariances. A typical practice is to use some pre-determined alternatives for unknown noise covariances. The main issue concerning this is how the pre-determined alternatives will affect the performance of the Kalman filter. In this study, the authors study recursive performance ranking of Kalman filter with mismatched noise covariances. For this purpose, three types of mean squared errors (MSEs) have been used, i.e., the ideal MSE (IMSE), the filter calculated MSE (FMSE), and the true MSE (TMSE). This study considers the recursive ranking of these three types of MSEs at each time step. It is found that for the case with positive semi-definite deviation from the truth, they have FMSE TMSE IMSE at each time step recursively. On the contrary, for the case with negative semi-definite deviation, they have TMSE IMSE FMSE at each time step recursively. Target tracking examples further verify these results.

In this study, the anti-swing control is investigated for a suspension cable system of a helicopter subject to external disturbance. First, a disturbance observer is designed to compensate for the effect of the external disturbance in finite time. Next, based on the proposed disturbance observer and the given desired trajectory, a unilateral boundary control law is proposed to eliminate the vibration by using Lyapunov's direct method. Under the designed control scheme, the ultimately boundedness of closed-loop is guaranteed. Moreover, the vibration range and trajectory tracking error will converge to a small neighbourhood of zero by selecting suitable parameters. Simulation results verify the rationality and validity of proposed control scheme.

Hammerstein system identification is difficult because there exist the product items of the parameters between the non-linear block and the linear block. This study presents a novel parameter separation based recursive least squares (PS-RLS) identification algorithm for resolving this problem. Its basic idea is to use a linear filter to filter the output data and the noise, and then to obtain two new identification submodels in each of which the output is linear in the corresponding parameter vector. Compared with the over-parametrisation based recursive least squares method, the proposed algorithm can avoid estimating the redundant parameters and has a higher computational efficiency. The simulation results show that the proposed PS-RLS algorithm can generate highly accurate parameter estimates with less computational effort.

This study deals with the problem of robust gain-scheduled dynamic output feedback control for uncertain discrete-time linear parameter varying systems. The obtained controller guarantees an upper bound on the induced -gain performance of the closed-loop system. The system matrices are assumed to depend polynomially on both the scheduling and uncertain parameters which are supposed to belong to intervals with a priori known bounds. To formulate the design problem in a linear matrix inequality (LMI) setting, a required auxiliary matrix is initially determined using a necessary condition for finding a gain-scheduled controller by the proposed method. Then, a robust gain-scheduled controller is designed by LMI conditions combined with a scalar search using the obtained auxiliary matrix. The method is applied to an inverted pendulum on a cart to illustrate the benefits and applicability of the proposed method.

In this study, the robust containment control problem of general non-linear multi-agent systems (MASs) subject to structural uncertainties is studied. The leaders are also described by general non-linear dynamics satisfying a locally quasi-Lipschitz condition and a distributed non-linear observer is designed to estimate the leaders' states for the followers. The solvability of the regulator equations associated with the non-linear dynamics of agents is normally essential for solving the containment control problem of heterogeneous MASs, but the closed-form solution of many non-linear regulator equations may not be obtained. Towards this end, the power series approach is adopted to decompose the regulator equations into a series of solvable linear equations. Based on the solution of the linear equations as the feedforward information, the distributed robust containment control scheme based on state feedback and output feedback control is proposed. The p-copy internal model is employed to compensate the parameter uncertainties of the follower agents. A numerical example is studied to demonstrate the effectiveness and efficiency of the proposed control law.