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.

The problem of adaptive neural networks (NNs) control for a class of uncertain non-linear systems with input delay and disturbances is studied. By using Pade approximation method, an auxiliary system is constructed to compensate the input delay based on the introduced variable. NNs are used to approximate the unknown non-linear functions. With the aid of backstepping technique, adaptive NNs controllers are designed which can guarantee all the signals in the closed-loop systems are semi-globally uniformly ultimately bounded and the tracking error can be adjusted around the origin with a small neighbourhood. The stability of the closed-loop systems is proved by using the Lyapunov stability theorem and two simulation examples are given to illustrate the effectiveness of the proposed methods.

This study is concerned with the problem of designing a robust model predictive control (MPC) for a class of uncertain discrete-time Markov jump linear systems. The main contribution is a set of linear matrix inequality (LMI) conditions obtained under new control policies for the unconstrained as well as the constrained MPC when uncertainties are present both in the system's matrices and in the transition probabilities of the modes. For the constrained MPC, hard constraints are considered over the input control and the states and results are extended to the so-called multi-step mode-dependent state-feedback control design. To illustrate the improvements obtained with the new set of LMI conditions, numerical simulations are carried out and compared with a recent reference in the literature.

This study considers the tracking control problem of an uncertain quadrotor unmanned aerial vehicle with model uncertainties and wind gust disturbances, and a novel robust dynamic surface control based multiple state variables constrained control scheme is proposed. Under the presented control framework, the overall quadrotor system is decoupled into a translational subsystem and a rotational subsystem. These two subsystems are connected to each other through common attitude extraction algorithms. For the translational subsystem, the novel robust multiple state variables constrained control inputs are designed to ensure the state variables within the prescribed constraints. For the rotational subsystem, the dynamic surface control based tracking controllers are proposed to track the desired attitudes. In the end, the resulting closed-loop system is proved to be stable in the sense of uniform ultimate boundness, and numerical simulations and experiments are conducted to validate the feasibility and effectiveness of the designed control scheme.

In this study, the authors investigate the problem of the stochastically finite-time stability analysis and control design of an adaptive single-input and single-output (SISO) uncertain stochastic non-linear system via establishing a new stability criterion. Owing to the unknown dynamics and unmeasured system variables, fuzzy logic systems and a fuzzy state observer are constructed and applied to identify the stochastic system, respectively. Combining the finite-time definition, stochastic differential equation and formula, a novel stochastically finite-time stability theorem is raised in this study. By utilising the novel criterion and adaptive backstepping intelligent control, a stochastically finite-time control method is proposed. It is illustrated that the controlled stochastic system is semi-global finite-time stable in probability and behaves excellent convergence. The simulation results of a two-stage continuous stirred tank reactor process reveal the validity and efficiency.

This study is concerned with the distributed fault tolerant tracking control for large-scale multi-motor web-winding systems. Firstly, the web-winding system is considered a synthetic system with several dynamic subsystems subject to multiple disturbances and actuator faults. Then, a disturbance compensation-based distributed fault diagnosis scheme is developed to estimate the system actuator faults. By setting the reference outputs, a method of obtaining equilibrium control inputs and equilibrium states is formulated to achieve the distributed variation dynamic model at equilibrium points by Taylor expansion. Based on the estimated actuator faults, an effective distributed fault tolerant control strategy is proposed by the techniques of interval matrix and disturbance local compensation. Sufficient conditions of asymptotic stability of the estimation error systems and the closed-loop systems are derived based on the Lyapunov theory. A fault diagnosis observer and a fault tolerant controller gain matrices are obtained by solving the linear matrix inequalities. Finally, simulations and analysis are performed on the three-motor web-winding system to verify the effectiveness of the proposed distributed fault tolerant control strategy.

Fault recoverability (FR) property reflects the capability of the system to accommodate faults through control reconfiguration under admissible input energy constraints. This study analyses the FR of interconnected non-linear and linear systems. Several explicit bounds of the amount of control energy required to drive the initial states of the interconnected system to the origin are computed. This helps to evaluate the FR under both centralised and distributed control schemes. The new results are further applied to meta aircraft configuration to verify the effectiveness.

This study is concerned with the problem of the functional observer-based sliding mode control (SMC) design for parametric uncertain discrete-time delayed stochastic systems includes mismatched parameter uncertainty in the state matrix and in the delayed state matrix. Stability analysis of sliding function is presented in the time delayed stochastic system with a linear matrix inequality approach. Moreover, it is shown that the state trajectories can be driven onto the specified sliding surface despite the presence of state delay, unmatched parameter uncertainty and stochastic noise in the system. The research is motivated by the fact that the system states are not always accessible for the state feedback. Therefore, SMC is estimated using the functional observer technique. To mitigate the side effect of the parameter uncertainty on the estimation error, a sufficient condition of stability is proposed based on Gershgorin disc theorem. The claims made are validated through numerical simulations.

This study presents a new controller that is integrating sliding mode control method, a backstepping technique with disturbance observer (DO) for the flexible air-breathing hypersonic vehicle (FAHV). A control-oriented model (COM) is firstly established based on the engineering background of FAHV, and the COM is decomposed into a velocity subsystem and an altitude subsystem, then controllers and the DO are designed for them. The developed sliding mode surface with exponential form can accelerate the convergence speed of the sliding mode state. Furthermore, the time derivative of the virtual control inputs is seen as uncertainty, and the DO is used to estimate it, so the problem of ‘explosion of terms’ is avoided. Then the stability of the closed-loop system is proved by Lyapunov theory, the tracking error of velocity converges to the random neighbourhood around zero, and the tracking error of altitude is asymptotic stable. Lastly, the compared simulation result is shown to verify that the proposed control method has better tracking performance than that of an adaptive backstepping controller.

In this study, novel iterative algorithms based on optimisation are developed to solve the continuous-time and discrete-time Sylvester matrix equations. The great difference of the proposed algorithms is that solutions of the equations are updated by two different sequences generated by the proposed algorithms. Convergence rates of the proposed algorithms can be markedly improved by choosing appropriate tuning parameters. Convergence conditions of the proposed algorithms are provided for different cases. Moreover, efficient numerical methods are presented to find the appropriate tuning parameters. Finally, three examples are given to illustrate the effectiveness of the proposed algorithms, and to compare the convergence performance of different algorithms.

The stochastic stabilisation of networked control systems is investigated with a special focus on the lossy multi-packet transmission in the wireless communication context. The resulting partially available system states due to multi-packet transmission are firstly reconstructed at the controller, and the sufficient conditions for stochastic stability are then given for the closed-loop system, which finally leads to a controller design method with explicit consideration of multi-packet transmission. The proposed theoretical results are verified by both numerical and TrueTime-based examples.

In this study, the authors derive a new type of maximum principle for both stochastic evolution and parabolic type stochastic partial differential systems. The systems only require the Hamiltonian functional to be concave in the state variable rather than in both state and control variables. They also show a connection between these two types of systems. Finally, examples are given to illustrate the authors' theoretical results.