On Continuous Full-Order Integral-Terminal Sliding Mode Control with Unknown Apriori Bound on Uncertainty

This study aims at providing a solution to the problem of designing a continuous and finite-time control for a class of nonlinear systems in the presence of matched uncertainty with an unknown apriori bound. First, we propose a Full-Order Integral-Terminal Sliding Manifold (FOITSM) with a conventional (discontinuous) sliding mode to show that it provides the combined attributes of the nonsingular terminal and integral sliding mode algorithms. Secondly, an Adaptive Disturbance Observer (ADO) has been designed to alleviate the effect of the uncertainty acting on the system. On application of the ADO-based Full-Order Integral-Terminal Sliding Mode Control (FOITSMC), the chattering phenomenon in control input has been reduced substantially in the presence of conditionally known matched disturbances. Moreover, the adaptive gains of ADO are updated non-monotonically without over-bounding the acting disturbance, yet sustain the global boundedness of state trajectories within a specific bound. %Finally, an application of the proposed algorithm for attitude stabilization of a rigid spacecraft has been successively shown.Comment: 14 pages, 9 figure

Control and synchronization of the generalized Lorenz system with mismatched uncertainties using backstepping technique and time‐delay estimation

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140007/1/cta2353.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/140007/2/cta2353_am.pd

Generalised regular form based SMC for nonlinear systems with application to a WMR

In this paper, a generalised regular form is proposed to facilitate sliding mode control (SMC) design for a class of nonlinear systems. A novel nonlinear sliding surface is designed using implicit function theory such that the resulting sliding motion is globally asymptotically stable. Sliding mode controllers are proposed to drive the system to the sliding surface and maintain a sliding mo-tion thereafter. Tracking control of a two-wheeled mobile robot is considered to underpin the developed theoretical results. Model-based tracking control of a wheeled mobile robot (WMR) is first transferred to a stabilisation problem for the corresponding tracking error system, and then the developed theoretical results are applied to show that the tracking error system is globally asymptotically stable even in the presence of matched and mismatched uncertainties. Both experimental and simulation results demonstrate that the developed results are practicable and effective

Decentralised sliding mode control for nonlinear interconnected systems with uncertainties

With the advances in science and technology, nonlinear large-scale interconnected systems have widely appeared in the real life. Traditional centralised control methods have inevitable disadvantages when they are used to deal with complex nonlinear interconnected systems with uncertainties. In connection with this, people desire to develop the novel control strategy which can be applied to complex interconnected systems. Therefore, decentralised sliding mode control (SMC) for interconnected systems has attracted great attention in related fields due to its advantages, for instance, simple structure, low cost of calculation, fast response, reduced-order sliding mode dynamics and insensitivity to matched variation of parameters and disturbances in systems. This thesis focuses on the development of decentralised SMC for nonlinear interconnected systems with uncertainties under certain assumptions. Several methods and different techniques have been considered in design of the controller to improve the robustness. The main contributions of this thesis include: • The state feedback decentralised SMC is developed for nonlinear interconnected systems with matched uncertainty and mismatched unknown interconnections. A state feedback decentralised SMC strategy, under the assumption that all system states are accessible, is proposed to attenuate the impact of the uncertainties by using bounds on uncertainties and interconnections. The bounds used in the design are fully nonlinear which provide higher applicability for different complex interconnected systems. Especially, for this fully nonlinear system, the proposed method does not need to use the technique of linearisation, which is widely used in existing work to deal with nonlinear interconnected systems with uncertainties. • The dynamic observer is applied to complex nonlinear interconnected systems with matched and mismatched uncertainties. This dynamic observer can estimate the system states which can not be achieved during the controller design. The proposed method has great identification ability with small estimated errors for the states of nonlinear interconnected systems with matched and mismatched uncertainties. It should be pointed out that the considered uncertainties of nonlinear interconnected systems have general forms, which means that the proposed method can be effectively used in more generalised nonlinear interconnected systems. • A variable structure observer-based decentralised SMC is proposed to control a class of nonlinear interconnected systems with matched and mismatched uncertainties. Based on the designed dynamic observer, a dynamic decentralised output feedback SMC using outputs and estimated states is presented to control the interconnected systems with matched and mismatched uncertainties. The nonlinear interconnections are employed in the control design to reduce the conservatism of the developed results. The bounds of the uncertainties are relaxed which are nonlinear and take more general forms. Moreover, the limitation for the interconnected system is reduced when compared with the existing results in which the proposed strategies adopt the full-order observer. Besides that, the presented method improves the robustness of nonlinear interconnected systems to be against the effects of uncertainties. This thesis also provides several numerical and practical simulations to demonstrate the effectiveness of the proposed decentralised SMC for nonlinear interconnected systems with matched uncertainty, mismatched uncertainty and nonlinear interconnections

Nonlinear disturbance observer-based control for multi-input multi-output nonlinear systems subject to mismatching condition

For a multi-input multi-output (MIMO) nonlinear system, the existing disturbance observer-based control (DOBC) only provides solutions to those whose disturbance relative degree (DRD) is higher than or equal to its input relative degree. By designing a novel disturbance compensation gain matrix, a generalised nonlinear DOBC method is proposed in this article to solve the disturbance attenuation problem of the MIMO nonlinear system with arbitrary DRD. It is shown that the disturbances are able to be removed from the output channels by the proposed method with appropriately chosen control parameters. The property of nominal performance recovery, which is the major merit of the DOBCs, is retained with the proposed method. The feasibility and effectiveness of the proposed method are demonstrated by simulation studies of both the numerical and application examples

Disturbance Observer-Based Continuous Finite-Time Sliding Mode Control against Matched and Mismatched Disturbances

In this paper, we propose the disturbance observer-based continuous finite-time sliding mode controller (DOBCSMC) for input-affine nonlinear systems in which additive matched and mismatched disturbances exist. The objective is to show the robustness and disturbance attenuation performance of the closed-loop system with the proposed DOBCSMC subjected to general classes of matched and mismatched disturbances. The proposed DOBCSMC consists of three main features: (i) the nonlinear finite-time disturbance observer to obtain a fast and accurate estimation of matched and mismatched disturbances, (ii) the nonlinear sliding surface to ensure high precision in the steady-state phase of the controlled output, and (iii) the continuous supertwisting algorithm to guarantee finite-time convergence of the controlled output and reduce the chattering under the effect of matched and mismatched disturbances. It should be noted that the existing approaches cannot handle time-varying mismatched disturbances and/or cannot guarantee faster finite-time stability of the controlled output. We prove that the closed-loop system with the DOBCSMC guarantees both finite-time reachability to the sliding surface and finite-time stability of the controlled output to the origin. Various simulations are performed to demonstrate the effectiveness of the proposed DOBCSMC. In particular, the simulation results show that the DOBCSMC guarantees faster convergence of the closed-loop system to the origin, higher precision of the controlled output, and better robustness performance against various classes of (time-varying) matched and mismatched disturbances, compared with the existing approaches

Finite-Time Output Feedback Controller Based on Observer for the Time-Varying Delayed Systems: A Moore-Penrose Inverse Approach

This study proposes a novel variable structure control (VSC) for the mismatched uncertain systems with unknown time-varying delay. The novel VSC includes the finite-time convergence sliding mode, invariance property, asymptotic stability, and measured output only. A necessary and sufficient condition guaranteeing the existence of sliding surface is given. A novel lemma is established to deal with the control design problem for a wider class of time-delay systems. A suitable reduced-order observer (ROO) is constructed to estimate unmeasured state variables of the systems. A novel finite-time output feedback controller (FTOFC) is investigated, which is based on the ROO tool and the Moore-Penrose inverse technique. Moreover, with the help of this lemma and the proposed FTOFC, restrictions on most existing works are also eliminated. In addition, an asymptotic stability analysis is implemented by means of the feasibility of the linear matrix inequalities (LMIs) and given desirable sliding mode dynamics. Finally, a MATLAB simulation result on a numerical example is performed to show the effectiveness and advantage of the proposed method

Learning and Near-Optimal Control of Underactuated Surface Vessels With Periodic Disturbances

In this article, we propose a novel learning and near-optimal control approach for underactuated surface (USV) vessels with unknown mismatched periodic external disturbances and unknown hydrodynamic parameters. Given a prior knowledge of the periods of the disturbances, an analytical near-optimal control law is derived through the approximation of the integral-type quadratic performance index with respect to the tracking error, where the equivalent unknown parameters are generated online by an auxiliary system that can learn the dynamics of the controlled system. It is proved that the state differences between the auxiliary system and the corresponding controlled USV vessel are globally asymptotically convergent to zero. Besides, the approach theoretically guarantees asymptotic optimality of the performance index. The efficacy of the method is demonstrated via simulations based on the real parameters of an USV vessel