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In this study, an online adaptive optimal control scheme is developed for solving the infinite-horizon optimal control problem of uncertain non-linear continuous-time systems with the control policy having saturation constraints. A novel identifier-critic architecture is presented to approximate the Hamilton–Jacobi–Bellman equation using two neural networks (NNs): an identifier NN is used to estimate the uncertain system dynamics and a critic NN is utilised to derive the optimal control instead of typical action–critic dual networks employed in reinforcement learning. Based on the developed architecture, the identifier NN and the critic NN are tuned simultaneously. Meanwhile, unlike initial stabilising control indispensable in policy iteration, there is no special requirement imposed on the initial control. Moreover, by using Lyapunov's direct method, the weights of the identifier NN and the critic NN are guaranteed to be uniformly ultimately bounded, while keeping the closed-loop system stable. Finally, an example is provided to demonstrate the effectiveness of the present approach.

This study investigates the problem of robust fault-tolerant control for uncertain fractional-order (FO) systems against actuator faults, whose commensurate order α is assumed to be 1 ≤ α < 2. By using reciprocal projection lemma and some properties of Kronecker product, the authors present a sufficient condition for the existence of fault-tolerant FO dynamic output feedback controllers for the FO systems with polytope-type uncertainty. The controller designed here takes the possible actuator faults into consideration and ensures the resulting closed-loop system is robustly stable. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed design method.

This study focuses on the asymptotic stability and stabilisation of uncertain linear systems with time-varying delays via delta operator approach. By employing a new model formulation, the time-delayed delta operator system is transformed into an interconnected system for which the uncertainties can become easy to deal with. Based on a two-term approximation of delayed state and scaled small gain theorem, new delay-dependent sufficient conditions of robust asymptotic stability and state-feedback stabilisation of an uncertain delta operator time-delayed system are established by using a novel Lyapunov–Krasovskii functional. The criteria obtained unify some previously suggested relevant methods seen in literature for achieving asymptotic stability and stabilisation of both continuous and discrete systems into the delta operator framework. Numerical examples presented explicitly demonstrate the advantages and effectiveness of the proposed methods.

This study deals with the problem of controlling a class of uncertain non-linear systems in the presence of external disturbances. To achieve this goal, a novel optimal Type-2 fuzzy proportional integral derivative (OT2FPID) controller is introduced. In the proposed controller, a novel heuristic algorithm namely particle swarm optimisation with random inertia weight (RNW–PSO) is employed. To achieve an optimal performance, the parameters of the proposed controller as well as the input and output membership functions are optimised simultaneously by RNW–PSO. To evaluate the performance of the proposed controller, the results are compared with those obtained by optimal H∞ adaptive proportional integral derivative controller, which is the latest research in the problem in hand. Simulation results show the effectiveness of the OT2FPID controller.

The estimation of friction coefficient for a vehicle when it traverses on different surfaces has been an important issue. In this work, the longitudinal vehicle dynamics, the torsional tyre dynamics and the non-linear LuGre friction dynamics are integrated to model the quarter vehicle dynamics. The road adhesion coefficient in the vehicle dynamics is unknown and varies with the contact surface. To address this issue, the authors consider a class of non-linear uncertain systems that covers the vehicle dynamics and develop a higher-order sliding mode observer based on supertwisting algorithm for state and unknown input estimations. Under Lipschitz conditions for the non-linear functions, the convergence of the estimation error is established. By estimating the road adhesion coefficient, the coefficient of friction can be estimated. Simulation results demonstrate the effectiveness of the proposed observer for state and unknown input estimation.

This study is concerned with the quantised feedback stabilisation problem for a class of uncertain linear systems by utilising sliding mode control schemes. It is an extension of our previous work from single-input linear systems with matched uncertainties to multi-input linear systems with matched/mismatched uncertainties. By applying an designed adjustment policy of the quantisation parameter, the proposed quantised feedback sliding mode control law can effectively eliminate the influence of the matched/mismatched uncertainties and guarantee the arrival of the sliding motion. Finally, an example is provided to illustrate the effectiveness of the proposed approach.

In this paper, we study how to design filters for nonlinear uncertain systems over sensor networks. We introduce two Kalman-type nonlinear filters in centralized and distributed frameworks. Moreover, the tuning method for the parameters of the filters is established to ensure the consistency, i.e., the mean square error is upper bounded by a known parameter matrix at each time. We apply the consistent filters to the track-to-track association analysis of multi-targets with uncertain dynamics. A novel track-to-track association algorithm is proposed to identify whether two tracks are from the same target. It is proven that the resulting probability of mis-association is lower than the desired threshold. Numerical simulations on track-to-track association are given to show the effectiveness of the methods.

In this study, a distributed model predictive control algorithm is presented for the polytopic uncertain system subject to randomly occurring actuator saturation and packet loss. The global system is decomposed into several subsystems, and a novel distributed controller model is established to account for both the actuator saturation and packet loss in a unified representation by using two sets of Bernoulli distributed white sequences with known conditional probabilities. By transforming the non-linear feedback law into a convex hull of linear feedback laws, the distributed controllers for subsystems are obtained by solving a linear matrix inequality (LMI) optimisation problem. Finally, two simulation examples are employed to show the effectiveness of the techniques proposed in this study.

This study considers the problem of fault-tolerant control (FTC) by trajectory tracking for uncertain non-linear system described by Takagi–Sugeno models. The considered faults are constant, exponential or polynomial. The provided results are easily formulated in terms of linear matrix inequalities by employing the descriptor redundancy property. This latter introduces ‘virtual’ dynamics both in the active FTC control law scheme and in the output error allowing to decouple the gains of the active FTC controller, the observer gain matrices and the system ones. Numerical examples are given to illustrate the efficiency of the proposed approach.

This study considers impulsive observer-based control of uncertain linear systems. A novel time-varying Lyapunov function is introduced to explore the hybrid characteristic of the impulsive observed-based control systems. By applying the time-varying Lyapunov function method combined with convex combination technique, sufficient conditions for the existence of the impulsive observer-based controller is derived in terms of linear matrix inequalities (LMIs). The control and observer gains can be obtained from the feasible solutions of the newly-obtained LMI-based conditions. Two numerical examples are presented to show the efficiency of the proposed design method.