Event-triggered-based adaptive sliding mode control for networked linear control systems

This paper investigates the robust stabilization of the adaptive sliding mode control for a class of linear systems subjected to external disturbance via event-triggered communication (ETC) scheme. First, in order to reduce the bandwidth utilization, a discrete ETC scheme is proposed and the networked sliding mode function is derived using the ETC scheme. Based on the derived sliding mode function, a reduced-order networked sliding mode dynamics with communication delay is established. Second, by constructing a Lyapunov–Krasovskii functional (LKF), asymptotic stability and stabilization criteria of the reduced-order sliding mode dynamics are given in the form of linear matrix inequalities. According to the stabilization result, a novel event-triggered-based adaptive sliding mode controller is designed while guaranteeing the reachability of the sliding surface. Finally, simulation results illustrate the effectiveness and merit of the developed method.

Manifold Calculus in System Theory and Control—Fundamentals and First-Order Systems

The aim of the present tutorial paper is to recall notions from manifold calculus and to illustrate how these tools prove useful in describing system-theoretic properties. Special emphasis is put on embedded manifold calculus (which is coordinate-free and relies on the embedding of a manifold into a larger ambient space). In addition, we also consider the control of non-linear systems whose states belong to curved manifolds. As a case study, synchronization of non-linear systems by feedback control on smooth manifolds (including Lie groups) is surveyed. Special emphasis is also put on numerical methods to simulate non-linear control systems on curved manifolds. The present tutorial is meant to cover a portion of the mentioned topics, such as first-order systems, but it does not cover topics such as covariant derivation and second-order dynamical systems, which will be covered in a subsequent tutorial paper.

Control of an Anthropomorphic Manipulator using LuGre Friction Model - Design and Experimental Validation

Automation technology has been extensively recognized as an emerging field in various industrial applications. Recent breakthrough in flexible automation is primarily due to deployment of robotic arms or manipulators. Autonomy in these manipulators is essentially linked with the advancements in non-linear control systems. The objective of this research is to propose a robust control algorithm for a five degree of freedom (DOF) robotic arm to achieve superior performance and reliability in the presence of friction. A friction compensation-based non-linear control has been proposed and realized for the robotic manipulator. The dynamic model of the robot has been derived by considering the dynamic friction model. The proposed three-state model is validated for all the joints of the manipulator. The integral sliding mode control (ISMC) methodology has been designed; the trajectories of system every time begin from the sliding surface and it eliminates the reaching phase with assistance of integral term in the sliding surface manifold. The designed control law has been first simulated in Matlab/Simulink environment to characterize the control performance in terms of tracking of various trajectories. The results confirm the effectiveness of the proposed control law with model-based friction compensation. The transient parameters like settling and peak time have improvement as well have better results with friction than without considering the friction. The proposed control law is then realized on an in-house developed autonomous articulated robotic rducational platform (AUTAREP) and NI myRIO hardware interfaced with LabVIEW. Experimental results also witnessed the trajectory tracking by the robotic platform.

Outer invariance entropy for discrete-time linear systems on Lie groups

We introduce discrete-time linear control systems on connected Lie groups and present an upper bound for the outer invariance entropy of admissible pairs (K,Q). If the stable subgroup of the uncontrolled system is closed and K has positive measure for a left invariant Haar measure, the upper bound coincides with the outer invariance entropy.

Controllability Properties and Invariance Pressure for Linear Discrete-Time Systems

For linear control systems in discrete time controllability properties are characterized. In particular, a unique control set with nonvoid interior exists and it is bounded in the hyperbolic case. Then a formula for the invariance pressure of this control set is proved.