Malicious attacks are often inevitable in cyber-physical systems (CPS). Accuracy in Cyber physical system for position tracking of servos is the major concern now a days. In high precision industrial automation, it is very hard to achieve accuracy in tracking especially under malicious cyber-attacks, control saturations, parametric perturbations and external disturbances. In this paper, we have designed a novel predefined time (PDT) convergence sliding mode adaptive controller (PTCSMAC) for such kind of cyber physical control system. Main key feature of our control is to cope these challenges that are posed by CPS systems such as parameter perturbation, control saturation, and cyber-attacks and the whole system then upgrade to a third-order system to facilitate adaptive control law. Then, we present an adaptive controller based on the novel PDT convergent sliding mode surface (SMS) combined with a modified weight updated Extreme Learning Machine (ELM) which is used to approximate the uncertain part of the system. Another significant advantage of our proposed control approach is that it does not require detailed model information, guaranteeing robust performance even when the system model is uncertain. Additionally, our proposed PTCSMAC controller is nonsingular regardless of initial conditions, and is capable of eradicating the possibility of singularity problems, which are frequently a concern in numerous CPS control systems. Finally, we have verified our designed PTCSMAC control law through rigorous simulations on CPS seeker servo positioning system and compared the robustness and performance of different existing techniques.

This paper proposes a fractional-order time-varying sliding mode control method with predefined-time convergence for a class of arbitrary-order nonlinear control systems with compound disturbances. The method has global robustness and strongly predefined-time stability. All state errors of the system can converge to zero at a desired time, which can be set arbitrarily with a simple parameter. The strongly predefined-time convergence of the system is clearly demonstrated by the analytic expression of state error, which is obtained by solving fractional-order differential equations corresponding to the sliding mode function. The simulation results show that the proposed method still has good control performance in the presence of input saturation and external interference.

In this paper, we address the swing-down control of the Acrobot, a two-link planar robot operating in a vertical plane with only the second joint being actuated. The control objective is to rapidly stabilize the Acrobot around the downward equilibrium point, with both links in the downward position, from almost all initial states. Under the conditions of no friction and measurability of only the angle and angular velocity of the actuated joint, we present a sinusoidal-derivative (SD) controller. This controller consists of a linear feedback of the sinusoidal function of the angle of the actuated joint and a linear feedback of its angular velocity. We prove that the control objective is achieved if the sinusoidal gain is greater than a negative constant and the derivative gain is positive. We establish crucial relationships between the relative stability of the Acrobot under the SD controller and its physical parameters, presenting analytically all optimal control gains. These gains minimize the real parts of the dominant poles of the linearized model of the resulting closed-loop system around the downward equilibrium point. We demonstrate that the resulting dominant closed-loop poles can be double complex conjugate poles, or a quadruple real pole, or a triple real pole, depending on the Acrobot\'s physical parameters. Simulation studies indicate that the proposed SD controller outperforms the derivative (D) controller in rapidly stabilizing the Acrobot at the downward equilibrium point.

In this paper, the problem of a fully actuated hexarotor performing a physical interaction with the environment through a rigidly attached tool is considered. A nonlinear model predictive impedance control (NMPIC) method is proposed to achieve the goal in which the controller is able to simultaneously handle the constraints and maintain the compliant behavior. The design of NMPIC is the combination of a nonlinear model predictive control and impedance control based on the dynamics of the system. A disturbance observer is exploited to estimate the external wrench and then provide compensation for the model which was employed in the controller. Moreover, a weight adaptive strategy is proposed to perform the online tuning of the weighting matrix of the cost function within the optimal problem of NMPIC to improve the performance and stability. The effectiveness and advantages of the proposed method are validated by several simulations in different scenarios compared with the general impedance controller. The results also indicate that the proposed method opens a novel way for interaction force regulation.

Robust, stable financial systems significantly improve the growth of an economic system. The stabilization of financial systems poses the following challenges. The state variables\' trajectories (i) lie outside the basin of attraction, (ii) have high oscillations, and (iii) converge to the equilibrium state slowly.
This paper aims to design a controller that develops a robust, stable financial closed-loop system to address the challenges above by (i) attracting all state variables to the origin, (ii) reducing the oscillations, and (iii) increasing the gradient of the convergence.
This paper proposes a detailed mathematical analysis of the steady-state stability, dissipative characteristics, the Lyapunov exponents, bifurcation phenomena, and Poincare maps of chaotic financial dynamic systems. The proposed controller does not cancel the nonlinear terms appearing in the closed-loop. This structure is robust to the smoothly varying system parameters and improves closed-loop efficiency. Further, the controller eradicates the effects of inevitable exogenous disturbances and accomplishes a faster, oscillation-free convergence of the perturbed state variables to the desired steady-state within a finite time. The Lyapunov stability analysis proves the closed-loop global stability. The paper also discusses finite-time stability analysis and describes the controller parameters\' effects on the convergence rates. Computer-based simulations endorse the theoretical findings, and the comparative study highlights the benefits.
Theoretical analysis proofs and computer simulation results verify that the proposed controller compels the state trajectories, including trajectories outside the basin of attraction, to the origin within finite time without oscillations while being faster than the other controllers discussed in the comparative study section.
This article proposes a novel robust, nonlinear finite-time controller for the robust stabilization of the chaotic finance model. It provides an in-depth analysis based on the Lyapunov stability theory and computer simulation results to verify the robust convergence of the state variables to the origin.

This paper develops a novel Lyapunov function candidate for control of the three-dimensional (3-D) overhead crane, which yields a nonlinear controller to inject active damping. Different from the existing passivity-based controls that employ either the angular displacement or its integral as passive elements, the proposed controller incorporates both of them in a new coupled-dissipation signal, thus significantly enhancing the closed-loop passivity. Owing to the improved passivity, the proposed controller ensures the effective suppression of payload oscillations and robustness. Moreover, the control design is extended with the hyperbolic tangent function to prevent overdriving the trolley. The asymptotic stability is guaranteed by LaSalle\'s invariance principle. The transit performance of the closed-loop system, including robustness, is validated by numerical simulations.

This paper proposes a saturated smooth adaptive controller for regulating a certain type of underactuated Euler-Lagrange systems (UELSs) with modeling uncertainties and control saturations based on a singular perturbation approach. Compared with relevent literature, the advantages of the proposed controller include: (1) it renders the UELS semiglobally asymptotically track the desired position without the violation of control input constraints; (2) high-order derivatives of positions are not required in its implementation. The Hoppensteadt\'s Theorem is employed to show that the proposed saturated controller renders the UELS semiglobally asymptotically stable about the desired set point with the satisfaction of control input constraints. The control effectiveness is validated by simulations on a two-link compliant robot arm.

Back-stepping design method is widely used in high-performance tracking control tasks As is known to all, the controller based on back-stepping design will become complex as the model order increases, which is the so called \"explosion of terms\" problem. In this paper, a tracking differentiator (TD) based back-stepping controller is proposed to handle the \"explosion of terms\" problem. Instead of calculating the derivatives of intermediate control variables through tedious analytical expressions, for the proposed method, the tracking differentiator is embedded into each recursive procedure to generate the substitute derivative signal for every intermediate control variable. As a result, the complexity of implementation procedure of back-stepping controller is significantly reduced. The discrepancies between the derivative substitutes and the real derivatives are considered. And the effects on control performances caused by the discrepancies are analyzed. In addition to giving the theoretical results and the stability proofs with Lyapunov methods, the developed controller design method is evaluated through a series of experiments with a hydraulic robot arm position serve system. The control performance of the proposed controller is verified by the experiments results.

In this paper, we present a coupling-based anti-swing control for 2-dimensional (2-D) under-actuated cranes with load hoisting/lowering, which achieves precise trolley positioning, accurate load hoisting/lowering and efficient load swing suppression. Compared to the existing methods for cranes with load hoisting/lowering, this paper introduces a novel composite signal which enhances the coupling behavior between the actuated and under-actuated variables. Then, based on this signal and its derivatives, we constructed our controller without linearization or approximation operations to the original nonlinear crane model. In addition, some common assumptions related to the rope length and original model among existing works are further relaxed in this paper. Last, we provide numerical simulation results to validate the feasibility and effectiveness of the proposed controller.

In this paper, we propose an anti-disturbance backstepping control approach with extended state observer (ESO) for tracking control of air-breathing hypersonic vehicles. Considering the large uncertainties, the external disturbances, and especially the lack of aerodynamic knowledge, several ESOs are introduced in the backstepping controller. With the total disturbance estimation ability of ESOs, almost no aerodynamic knowledge is needed for the controller design. Meanwhile, ESOs are also used to estimate the derivatives of the virtual control signals. The problem of \"explosion of terms\" is avoided. A key strategy of the controller is that each step of backstepping is activated successively. Consequently, the closed-loop system has time-scale structure. Rigorous stability proof can be obtained. At last, compared simulation results verify the superior tracking performance of the proposed controller.