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The problem of output tracking control is addressed for a class of non-linear strict-feedback form systems in the presence of non-linear uncertainties, external disturbances, unmodelled dynamics and unknown time-varying virtual control coefficients. A new design approach of robust controller is proposed by combining standard backstepping with signal compensation method. It is shown that semi-global robust stability and semi-global robust practical tracking property of the closed-loop system can be ensured and the tracking error can be made as small as desired. The designed controller is linear and time invariant, and so can be implemented easily. [ABSTRACT FROM AUTHOR]

The problem of decentralised adaptive robust stabilisation is considered for a class of uncertain large-scale interconnected non-linear systems with time-varying delays. It is assumed that the upper bounds of the uncertainties and interconnection terms are unknown, and that the time-varying delays are any non-negative continuous and bounded functions, and do not require their derivatives to be less than one. In particular, it is only required that the non-linear interconnection terms, which can also include time-varying delays, are bounded in any non-negative non-linear functions, which are not required to be known for the system designer. For such a class of uncertain large-scale time-delay interconnected non-linear systems, a new method is presented whereby a class of continuous memoryless decentralised local adaptive robust state feedback controllers with a rather simpler structure is proposed. It is also shown that the solutions of uncertain large-scale time-delay interconnected systems can be guaranteed as uniformly exponentially convergent towards a ball that can be as small as desired. Finally, a numerical example is given to demonstrate the validity of the results. [ABSTRACT FROM AUTHOR]

In this study, the authors address the problem of the mixed H2/H∞ robust model predictive control (RMPC) for a class of discrete-time systems with structured uncertainty and disturbances. The conditions of RMPC are given to satisfy both the H2 and H∞ performance requirements. In order to reduce the conservativeness caused by an unique feedback control law, a multi-step control strategy is introduced to improve the control performance and enlarge the feasible region of RMPC. Furthermore, an efficient version of the proposed RMPC is also given to reduce the online computational burden, which makes the design more practical. The proposed RMPCs are proven to be input-to-state practically stable (ISpS). A numerical example illustrates the effectiveness of the proposed designs. [ABSTRACT FROM AUTHOR]

A robust adaptive second-order sliding-mode control scheme with finite reaching time is proposed for a class of uncertain non-linear systems. It is shown that the problem is equivalent to the finite-time stabilisation of a second-order input-output dynamics with bounded uncertainties. The controller is designed by using geometric homogeneity and adaptive sliding-mode concept. It contains two parts: one part achieves finite-time stabilisation of the second-order input-output dynamics without uncertainties; the other part rejects bounded uncertainties, and the upper bounds of uncertainties are not required to be known in advance. As a result, a finite-time convergent second-order sliding mode is established. The convergence rate of the second-order sliding mode can be hastened through tuning the controller parameters, and the robustness is ensured. The method is evaluated in simulations on an academic example. [ABSTRACT FROM AUTHOR]

This study investigates the robust quantised H∞ control problem for active suspension systems. First, based on the half-vehicle suspension model, the dynamical system with polytopic parameter uncertainties, which are caused by vehicle load variation, is established. In the meanwhile, the active suspension system performance, namely ride comfort, road holding and suspension deflection, are taken into account for the control design aim. Secondly, an input delay approach is utilised to transform the resulting active vehicle suspension system with sampling and quantisation measurements into a continuous-time system with a delay in the input sector bound uncertainty. Thirdly, robust quantised H∞ performance analysis and controller synthesis criteria are presented in the form of convex optimisation problem by exploiting the Lyapunov functional approach. The existing robust quantised H∞ controller condition not only guarantees the robust asymptotical stability of the closed-loop system, but also satisfies the output constrained performance. Finally, the effectiveness and application of the proposed method can be demonstrated by providing a design example. [ABSTRACT FROM AUTHOR]

This study deals with the design of fractional-order proportional-integral-differential (PID) controllers. Two design techniques are presented for tuning the parameters of the controller. The first method uses the idea of the Ziegler-Nichols and the Åström-Hägglund methods. In order to achieve required performances, two non-linear equations are derived and solved to obtain the fractional orders of the integral term and the derivative term of the fractional-order PID controller. Then, an optimisation strategy is applied to obtain new values of the controller parameters, which give improved step response. The second method is related with the robust fractional-order PID controllers. A design procedure is given using the Bode envelopes of the control systems with parametric uncertainty. Five non-linear equations are derived using the worst-case values obtained from the Bode envelopes. Robust fractional-order PID controller is designed from the solution of these equations. Simulation examples are provided to show the benefits of the methods presented. [ABSTRACT FROM AUTHOR]

The adaptive robust control (ARC) for DC motors subjected to parametric uncertainties, disturbances and input saturation is considered in this study. To achieve high performance while keeping the control authority within saturation limit, a saturated ARC scheme is proposed. In this scheme, a variable-gain saturation function is introduced for the virtual control law, so that the amplitude of the virtual control and its derivative decrease when the control input approaches to the prescribed bound. Consequently, the virtual control and its derivative will not be excessively large, which is crucial for stabilising the system with a bounded input. We prove that the proposed controller cannot only assure global stability, but also provide desirable control performance, that is, the tracking error can be steered to the neighbourhood of the origin in finite time. Moreover, asymptotic tracking can be achieved in the presence of parametric uncertainties only. Finally, simulation results illustrate the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

A robust adaptive neural network controller is proposed for a class of uncertain non-linear time-delay systems in strict feedback form with both completely unknown control gains and unknown non-symmetric dead-zone non-linearity based on backstepping design. The proposed design approach does not require a priori knowledge of the signs of the unknown control gains. The unknown time delays are compensated for constructing appropriate Lyapunov-Krasovskii functionals. By utilising integral Lyapunov design and sliding-mode control strategy, the controller singularity problem and the effect of dead-zone input non-linearity are avoided perfectly. From Lyapunov stability theorem, it is proved that the proposed design approach is able to guarantee semi-globally uniformly ultimately boundedness of all the signals in the closed-loop system, and the tracking error of the system is proven to be converged to a small neighbourhood of the origin. The simulation results demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This study investigates the problem of state feedback robust stabilisation for discrete-time fuzzy singularly perturbed systems (SPSs) with parameter uncertainty. The considered system is approximated by Takagi-Sugeno fuzzy model. Based on a matrix spectral norm approach, new sufficient conditions, which ensure the existence of state feedback controller such that the resulting closed-loop system is asymptotically stable, are given. The gains of controllers are obtained by solving a set of ℇ-independent linear matrix inequalities (LMIs) such that, the ill-conditioned problems caused by ℇ can be easily avoided. In contrast to the existing results, the proposed method can be applied to both certain and uncertain SPSs with greater singular perturbation parameter ℇ. A numerical example is provided to illustrate the reduced conservatism of the authors' results. [ABSTRACT FROM AUTHOR]

This article deals with the design of robust ℋ∞ filter for singular systems in general form, subject to bounded time-varying uncertainties. The aim is to design linear admissible descriptor filters that ensure a guaranteed bound on the L2 gain of the operator from the noise signals to the estimation error signal, irrespective of the time-varying uncertain parameters. A strict linear matrix inequality based method is proposed to the robust ℋ∞ filter design employing affine Lyapunov functions. A numerical example is presented to show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Real parametric uncertainty is common in many applications. In this study, the authors analyse the robust stability of feedback loops of single-input single-output systems with negative imaginary frequency response subject to real parametric uncertainty. A recent result on the stability of such feedback loops is specialised to this case, resulting in a very simple stability condition dependent only on the steady-state parameters of the systems. The structured singular value for this system type is also obtained, and it is shown that it yields related but more constrained, easily computable stability guarantees. In a numerical example, the robust stability of a control loop for a DC machine subject to real parametric uncertainty is analysed. [ABSTRACT FROM AUTHOR]

The problems of delay-dependent robust stability and stabilisation for a class of uncertain two-dimensional (2-D) discrete systems with time-varying delays described by the second Fornasini-Marchesini local state space (FM LSS) model are investigated in this study. By employing improved free-weighting matrix approach, delay-dependent stability criterion for the nominal 2-D state-delayed system is first obtained and formulated in terms of linear matrix inequalities (LMIs); and then, a stabilisation design criterion using static state feedback controller is derived based on the stability result. Since the design criterion is not expressed strictly in terms of LMI, an improved cone complementary linearisation algorithm is employed to solve the non-convex feasibility problem. Furthermore, the stability and stabilisation results are extended to robust stability and stabilisation of the uncertain 2-D state-delayed system. Numerical examples are provided to demonstrate the effectiveness and advantage of the proposed method. [ABSTRACT FROM AUTHOR]

In this study, experimental tests for an observer-based controller scheme are given to drive a sensorless Induction Motor (IM) even for the low frequencies case. Combining the advantages of a field oriented controller with the backstepping control method, a new robust controller is designed to track low frequencies trajectories. The static errors are eliminated using an integral backstepping technique, improving the robustness properties of the controller in spite of the uncertainties and the perturbations. An adaptive interconnected observer is designed for estimating fluxes, speed, load torque and the stator resistance in order to implement the controller. The knowledge of the stator parameter is crucial for sensorless control in particular to track low-speed trajectories when the observability property is lost. Practical stability based on Lyapunov theory has been proved to guarantee the strongly uniformly practical stability of the closed-loop system using the proposed observer-controller scheme. The tests are completed thanks to the reference trajectories of a specific sensorless IM benchmark where the robustness properties are validated under parameter variations and in presence of disturbances even for the low frequencies case. [ABSTRACT FROM AUTHOR]

This study firstly addresses an integral sliding mode control method for discrete time systems. The underlying continuous system is affected by both matched and unmatched uncertainties. The past value of the disturbance signal is taken as the estimate of its present value. The sliding mode controller is designed to ensure the existence of sliding mode in the presence of uncertainties. The proportional part is designed based on the analysis of closed-loop stability conditions. The controller design theory above is applied to an overhead crane system in later sections. The overhead crane system, which is a familiar control problem is described by a linear model, the parameters of which are estimated. It is affected by uncertainties such as friction, swing of the load and non-linearities because of changing rope length. Both simulation and experimental results are reported. The efficacy and robustness of the proposed controller are demonstrated. [ABSTRACT FROM AUTHOR]

This study presents a new non-linear sliding surface to control a class of non-minimum phase underactuated mechanical systems, taking into account uncertainties in their physical parameters. The non-linear surface is designed through a fictitious output, which provides the minimum-phase property and allows to prove stability using Lyapunov theory. The non-linear surface is based on the fictitious output and augmented with a non-linear external controller designed using the Lyapunov theory. The present approach assures exponential stability of the equilibrium point and robust stability to parametric uncertainties, avoiding the appearance of non-desired phenomena, as limit cycles. Two pendulum-like examples inside the class are thoroughly analysed and solved, that is, the pendulum on a cart and the inertia wheel pendulum. Performance, time response and parametric robustness are shown through simulations. [ABSTRACT FROM AUTHOR]

The robust asymptotic stabilisation of a class of nonlinear uncertain singularly perturbed systems by using nonlinear PI control techniques is presented. The original system is decomposed into two reduced-order systems, to which the nonlinear uncertain term belongs. In order to alleviate the deterioration of these nonlinear uncertainties, the nonlinear PI controllers are applied to each subsystem and the results are combined to construct the composite controller of the full-order system. An example is given to illustrate the design procedures and good performance of the proposed control scheme. [ABSTRACT FROM AUTHOR]