In this study, we present a novel sliding mode safety-critical controller designed to address both stability and safety concerns in a class of nonlinear uncertain systems. The controller features two feedback loops: an inner loop designed by conventional sliding mode techniques and an outer safeguarding loop aimed at enhancing system safety. The inner loop, while ensuring asymptotic stability of the closed-loop system, may not guarantee compliance with safety constraints. To overcome this limitation and ensure both stability and safety, the outer loop introduces a correction term known as the safeguarding control signal. This signal is added to the unsafe control signal generated by the inner loop, effectively modifying it to meet the required safety constraints. To design the safeguarding control law, we integrate the system dynamics with an additional state variable. The dynamics of this augmented state are derived based on a stability constraint obtained from Lyapunov theory. By utilizing a control barrier function for the augmented system, we determine the safeguarding control signal, which ensures the system operates within the defined safety constraint. The proposed safety-critical controller exhibits finite-time convergence to the sliding manifold. To mitigate interference between the inner and outer loops, strategies such as defining risky sets are employed, limiting the impact of the safeguarding loop on the functionality of the inner loop. A closed-form solution for designing safeguarding control laws is derived to eliminate the necessity for solving any quadratic problems in real-time. Simulation case studies validate the effectiveness of the proposed controller in maintaining stability and safety.
Within the framework of Sliding Mode Control, safety critical control looks at two problems of theoretical significance: construct a sliding manifold that does not intersect a given unsafe set of the state space, and design a robust controller that safely takes the system trajectory to the manifold during the reaching phase and enforces the sliding motion. In this technical note, we address both problems. We introduce the notion of Safe Sliding Manifold (SSM) of relative degree one, and show that it is possible to construct it from the gradient of a class of Lyapunov-like energy functions, pre…
This work proposes a sliding mode control barrier function to robustly deal with high relative-degree safety constraints in safety-critical control systems. Stability/tracking objectives, expressed as a nominal control law, and safety constraints, expressed as control barrier functions are unified through quadratic programming. The proposed control framework is numerically validated considering a Furuta pendulum and a magnetic levitation system. For the first system, a linear quadratic regulator is considered as a nominal control law, and a safety constraint is considered to guarantee that the…
This paper studies the stabilization and safety problems of nonlinear time-delay systems. Following both Razumikhin and Krasovskii approaches, we propose novel control Lyapunov functions/functionals for the stabilization problem and novel control barrier functions/functionals for the safety problem. The proposed control Lyapunov and barrier functions/functionals extend the existing ones from the delay-free case to the time-delay case, and allow for designing the stabilizing and safety controllers in closed-form. Since analytical solutions to time-delay optimal control problems are hard to be a…
Adaptive type-2 fuzzy second order sliding mode control for nonlinear uncertain chaotic system
QUERE Laboratory, Engineering Faculty, University of Setif 1（塞提夫第一大学工程学院QUERE实验室）；CReSTIC of Reims Champagne-Ardenne University,IUT de Troyes（兰斯香槟-阿登大学CReSTIC中心特鲁瓦高等师范学院）
Robust Adaptive Sliding Mode Control of Markovian Jump Systems with Uncertain Mode-dependent Time-varying Delays and Partly Unknown Transition Probabilities
Mississippi State University（密西西比州立大学）；University of Notre Dame（圣母大学）；Arak University（阿拉克大学）；Tarbiat Modares University（塔里亚特莫达雷斯大学）
This paper presents a novel Sliding Mode Control (SMC) algorithm to handle mismatched uncertainties in systems via a novel Self-Learning Disturbance Observer (SLDO). A computationally efficient SLDO is developed within a framework of feedback-error learning scheme in which a conventional estimation law and a Neuro-Fuzzy Structure (NFS) work in parallel. In this framework, the NFS estimates the mismatched disturbances and becomes the leading disturbance estimator while the former feeds the learning error to the NFS to learn system behavior. The simulation results demonstrate that the proposed S…
This paper addresses to Sliding Mode Learning Control (SMLC) of uncertain nonlinear systems with Lyapunov stability analysis. In the control scheme, a conventional control term is used to provide the system stability in compact space while a Type-2 Neuro-Fuzzy Controller (T2NFC) learns system behavior so that the T2NFC takes the overall control of the system completely in a very short time period. The stability of the sliding mode learning algorithm was proven in literature; however, it is so restrictive for systems without the overall system stability. To address this shortcoming, a novel con…
Dynamic Sliding Mode Control based on Fractional calculus subject to uncertain delay based chaotic pneumatic robot
Farabina Noshirvani’s smart Co.（法拉比亚·诺希拉维智能公司）；Robotic Research Lab.（机器人研究实验室）；Faculty of Electrical and Robotic Engineering, Shahrood University of Technology（沙霍尔德大学电气与机器人工程学院）
The aim of this paper is to propose a high performance control approach for trajectory tracking of Autonomous Underwater Vehicles (AUVs). However, the controller performance can be affected by the unknown perturbations including model uncertainties and external time-varying disturbances in an undersea environment. To address this problem, a Backstepping-based Integral Sliding Mode Control with Time Delay Estimation (BS-ISMC-TDE) is designed. To improve the performance of a conventional backstepping control algorithm, an Integral Sliding Mode Control (ISMC) approach is adopted in the backsteppi…
School of Engineering and Information Technology, University of New South Wales at the Australian Defence Force Academy（新南威尔士大学澳大利亚国防军学院工程与信息科技学院）；Institute of Cyber Systems and Control, State Key Laboratory of Industrial Control Technology, Zhejiang University（浙江大学工业控制技术国家重点实验室 cyber systems and control 研究所）
Queen’s University of Belfast（贝尔法斯特女王大学）；University of Warwick（华威大学）
This paper proposes a novel fixed-time integral sliding mode controller for admittance control to enhance physical human-robot collaboration. The proposed method combines the benefits of compliance to external forces of admittance control and high robustness to uncertainties of integral sliding mode control (ISMC), such that the system can collaborate with a human partner in an uncertain environment effectively. Firstly, a fixed-time sliding surface is applied in the ISMC to make the tracking error of the system converge within a fixed-time regardless of the initial condition. Then, a fixed-ti…
Shimmy is a dangerous phenomenon that occurs when aircraft's nose landing gears oscillate in a rapid and uncontrollable fashion. In this paper, we propose the use of two nonlinear control approaches (zero average control and model reference adaptive control based on minimal control synthesis) as simple yet effective strategies to suppress undesired oscillations, even in the presence of uncertainties and partial state measurements. Numerical results are presented to validate the proposed control approaches.
The fundamental problem of stabilizing a general nonaffine continuous-time nonlinear system is investigated via piecewise affine linear models (PALMs) in this article. A novel integral sliding-mode parallel control (ISMPC) approach is developed, where an uncertain piecewise affine system (PWA) is constructed to model a nonaffine continuous-time nonlinear system equivalently on a compact region containing the origin. A piecewise sliding-mode parallel controller is designed to globally stabilize the PALM and, consequently, to semiglobally stabilize the original nonlinear system. The proposed sch…
This paper proposes a global iterative sliding mode control approach for high-precision contouring tasks of a flexure-linked biaxial gantry system. For such high-precision contouring tasks, it is the typical situation that the involved multi-axis cooperation is one of the most challenging problems. As also would be inevitably encountered, various factors render the multi-axis cooperation rather difficult; such as the strong coupling (which naturally brings nonlinearity) between different axes due to its mechanical structure, the backlash and deadzone caused by the friction, and the difficultie…
Harbin Institute of Technology（哈尔滨工业大学）；University of California, Berkeley（加州大学伯克利分校）
The precise motion control of a multi-degree of freedom~(DOF) robot manipulator is always challenging due to its nonlinear dynamics, disturbances, and uncertainties. Because most manipulators are controlled by digital signals, a novel higher-order sliding mode controller in the discrete-time form with time delay estimation is proposed in this paper. The dynamic model of the manipulator used in the design allows proper handling of nonlinearities, uncertainties and disturbances involved in the problem. Specifically, parametric uncertainties and disturbances are handled by the time delay estimati…
In this paper, a new model based nonlinear control technique, called PID (Proportional-Integral-Derivative) type sliding surface based sliding mode control is designed using improved reaching law. To improve the performance of the second order nonlinear differential equations with unknown parameters modified particle swarm intelligent optimization (MPSO) is used for the optimized parameters. This paper throws light on the sliding surface design, on the proposed power rate exponential reaching law, parameters optimization using modified particle swarm optimization and highlights the important f…
In adaptive sliding mode control methods, an updating gain strategy associated with finite-time convergence to the sliding set is essential to deal with matched bounded perturbations with unknown upper-bound. However, the estimation of the finite time of any adaptive design is a complicated task since it depends not only on the upper-bound of unknown perturbation but also on the size of initial conditions. This brief proposes a uniform adaptive reaching phase strategy (ARPS) within a predefined reaching-time. Moreover, as a case of study, the barrier function approach is extended for perturbed…
This work proposes a quaternion-based sliding variable that describes exponentially convergent error dynamics for any forward complete desired attitude trajectory. The proposed sliding variable directly operates on the non-Euclidean space formed by quaternions and explicitly handles the double covering property to enable global attitude tracking when used in feedback. In-depth analysis of the sliding variable is provided and compared to others in the literature. Several feedback controllers including nonlinear PD, robust, and adaptive sliding control are then derived. Simulation results of a r…
The paper considers autonomous rendezvous maneuver and proximity operations of two spacecraft in presence of obstacles. A strategy that combines guidance and control algorithms is analyzed. The proposed closed-loop system is able to guarantee a safe path in a real environment, as well as robustness with respect to external disturbances and dynamic obstacles. The guidance strategy exploits a suitably designed Artificial Potential Field (APF), while the controller relies on Sliding Mode Control (SMC), for both position and attitude tracking of the spacecraft. As for the position control, two dif…
This work investigates the real-time estimation of the state-of-charge (SoC) of Lithium-ion (Li-ion) cells for reliable, safe and efficient utilization. A novel attractive ellipsoid based sliding-mode observer (AESMO) algorithm is designed to estimate the SoC in real-time. The algorithm utilizes standard equivalent circuit model of a Li-ion cell and provides reliable and efficient SoC estimate in the presence of bounded uncertainties in the battery parameters as well as exogenous disturbances. The theoretical framework of the observer design is not limited to the SoC estimation problem of Li-i…
This paper deals with the design of robust tracking and model following (RTMF) controller for linear time-invariant (LTI) systems with uncertainties. The controller is based on the second order sliding mode (SOSM) algorithm (super twisting) which is the most effective and popular in the family of higher order sliding modes (HOSM). The use of super twisting algorithm (STA) eliminates the chattering problem encountered in traditional sliding mode control while retaining its robustness properties. The proposed robust tracking controller can guarantee the asymptotic stability of tracking error in …
Presence of model uncertainties creates challenges for model-based control design, and complexity of the control design is further exacerbated when coping with nonlinear systems. This paper presents a sliding mode control (SMC) design approach for nonlinear systems with partially known dynamics by blending data-driven and model-based approaches. First, an SMC is designed for the available (nominal) model of the nonlinear system. The closed-loop state trajectory of the available model is used to build the desired trajectory for the partially known nonlinear system states. Next, a deep policy gr…
In this paper, we present a new terminal sliding mode control to achieve predefined-time stability of robot manipulators. The proposed control is developed based on a novel predefined-time terminal sliding mode (PTSM) surface, on which the states are forced to reach the origin in a predefined time, i.e., the settling time is independent to the initial condition and can be explicitly user-defined via adjusting some specific parameters called the predefined-time parameters. It is also demonstrated that the proposed control can provide satisfactory steady-state performance in the case of both ext…
This paper presents three types of sliding mode controllers for a magnetic levitation system. First, a proportional-integral sliding mode controller (PI-SMC) is designed using a new switching surface and a proportional plus power rate reaching law. The PI-SMC is more robust than a feedback linearization controller in the presence of mismatched uncertainties and outperforms the SMC schemes reported recently in the literature in terms of the convergence rate and settling time. Next, to reduce the chattering phenomenon in the PI-SMC, a state feedback-based discrete-time SMC algorithm is developed…
This paper proposes a distributed secondary voltage control method based on extended state Kalman-Bucy filter (ESKBF) and fast terminal sliding mode (FTSM) control for the resilient operation of an islanded microgrid (MG) with inverter-based distributed generations (DGs). To tackle the co-existence of multiple uncertainties, a unified modelling framework is proposed to represent the set of different types of disturbances, including parameter perturbation, measurement noise, and immeasurably external variables, by an extended state method. Kalman-Bucy filter is then applied to accurately estima…
Deploying safety-critical controllers in practice necessitates the ability to modulate uncertainties in control systems. In this context, robust control barrier functions -- in a variety of forms -- have been used to obtain safety guarantees for uncertain systems. Yet the differing types of uncertainty experienced in practice have resulted in a fractured landscape of robustification -- with a variety of instantiations depending on the structure of the uncertainty. This paper proposes a framework for generalizing these variations into a single form: parameterized barrier functions (PBFs), which…
The design of robust orbitally stabilizing feedback is considered. From a known orbitally stabilizing controller for a nominal, disturbance-free system, a robustifying feedback extension is designed utilizing the sliding-mode control (SMC) methodology. The main contribution of the paper is to provide a constructive procedure for designing the time-invariant switching function used in the SMC synthesis. More specifically, its zero-level set (the sliding manifold) is designed using a real Floquet-Lyapunov transformation to locally correspond to an invariant subspace of the Monodromy matrix of a …
