Uniform finite time stabilisation of non-smooth and variable structure systems with resets

This thesis studies uniform finite time stabilisation of uncertain variable structure and non-smooth systems with resets. Control of unilaterally constrained systems is a challenging area that requires an understanding of the underlying mechanics that give rise to reset or jumps while synthesizing stabilizing controllers. Discontinuous systems with resets are studied in various disciplines. Resets in states are hard nonlinearities. This thesis bridges non-smooth Lyapunov analysis, the quasi-homogeneity of differential inclusions and uniform finite time stability for a class of impact mechanical systems. Robust control synthesis based on second order sliding mode is undertaken in the presence of both impacts with finite accumulation time and persisting disturbances. Unlike existing work described in the literature, the Lyapunov analysis does not depend on the jumps in the state while also establishing proofs of uniform finite time stability. Orbital stabilization of fully actuated mechanical systems is established in the case of persisting impacts with an a priori guarantee of finite time convergence between t he periodic impacts. The distinguishing features of second order sliding mode controllers are their simplicity and robustness. Increasing research interest in the area has been complemented by recent advances in Lyapullov based frameworks which highlight the finite time Convergence property. This thesis computes the upper bound on the finite settling time of a second order sliding mode controller. Different to the latest advances in the area, a key contribution of this thesis is the theoretical proof of the fact that finite settling time of a second order sliding mode controller tends to zero when gains tend to infinity. This insight of the limiting behaviour forms the basis for solving the converse problem of finding an explicit a priori tuning formula for the gain parameters of the controller when and arbitrary finite settling time is given. These results play a central role ill the analysis of impact mechanical systems. Another key contribution of the thesis is that it extends the above results on variable structure systems with and without resets to non-smooth systems arising from continuous finite time controllers while proving uniform finite time stability. Finally, two applications are presented. The first application applies the above theoretical developments to the problem of orbital stabilization of a fully actuated seven link biped robot which is a nonlinear system with periodic impacts. The tuning of the controller gains leads to finite time convergence of the tracking errors between impacts while being robust to disturbances. The second application reports the outcome of an experiment with a continuous finite time controller

Continuous second order sliding mode based finite time tracking of a fully actuated biped robot

International audienceA second order sliding mode controller is modified to form a continuous homogeneous controller. Uniform finite time stability is proved by extending the homogeneity principle of discontinuous systems to the continuous case with uniformly decaying piece-wise continuous nonhomogeneous disturbances. The modified controller is then utilised to track reference trajectories for all the joints of a fully actuated biped robot where the joint torque is modeled as the control input. The modified controller ensures the attainment of a finite settling time between two successive impacts. The main contribution of the paper is to provide straightforward and realizable engineering guidelines for reference trajectory generation and for tuning a robust finite time controller in order to achieve stable gait of a biped in the presence of an external force disturbance. Such a disturbance has destabilising effects in both continuous and impact phases. Numerical simulations of a biped robot are shown to support the theoretical results

Continuous Uniform Finite Time Stabilization of Planar Controllable Systems

Continuous homogeneous controllers are utilized in a full state feedback setting for the uniform finite time stabilization of a perturbed double integrator in the presence of uniformly decaying piecewise continuous disturbances. Semiglobal strong $\mathcal{C}^1$ Lyapunov functions are identified to establish uniform asymptotic stability of the closed-loop planar system. Uniform finite time stability is then proved by extending the homogeneity principle of discontinuous systems to the continuous case with uniformly decaying piecewise continuous nonhomogeneous disturbances. A finite upper bound on the settling time is also computed. The results extend the existing literature on homogeneity and finite time stability by both presenting uniform finite time stabilization and dealing with a broader class of nonhomogeneous disturbances for planar controllable systems while also proposing a new class of homogeneous continuous controllers

Cow Urine Mediated Green Synthesis of Nanomaterial and Their Applications: A State-of-the-art Review

Nowadays, green syntheses have received crucial attention as a reliable, developing and eco-benevolent protocol for synthesizing a broad range of nanomaterials (NMs) including metal/metal oxides NMs, bio-inspired materials and hybrid/composite NMs. As such, biogenic synthesis is regarded as a significant tool to mitigate the destructive impacts associated with the conventional approaches of synthesis for NMs generally utilized in industry and laboratory. In this review, we summed up the general protocols and mechanisms of green synthesis routes, especially for silver (Ag), silver oxide (Ag2O), cadmium (Cd), copper (Cu), copper ferrite (CuFe2O4), palladium (Pd), aceprophyline, cellulose and graphene nanomaterials/nanoparticles using cow urine. Importantly, we explored the main role of biological constituents which is existed in cow urine. These essential biomolecules act as reducing/stabilizing agents in solvent systems. The stability, phase formation and surface morphology of NMs using characterization techniques are also discussed. Finally, we covered the eclectic applications of such synthesized NMs in terms of anti-asthma, antimicrobial, antituberculosis, antioxidant, anticancer activity, catalytic activity and removal of pollutants dyes

Modelling and finite time stability analysis of psoriasis pathogenesis

A new systems model of psoriasis is presented and analysed from the perspective of control theory. Cytokines are treated as actuators to the plant model that govern the cell population under the reasonable assumption that cytokine dynamics are faster than the cell population dynamics. The analysis of various equilibria is undertaken based on singular perturbation theory. Finite time stability and stabilisation has been studied in various engineering applications where the principal paradigm uses non-Lipschitz functions of the states. A comprehensive study of the finite time stability properties of the proposed psoriasis dynamics is carried out. It is demonstrated that the dynamics are finite time convergent to certain equilibrium points rather than asymptotically or exponentially convergent. This feature of finite time convergence motivates the development of a modi?ed version of the Michaelis-Menten function, frequently used in biology. This framework is used to model cytokines as fast finite time actuators

A Finite-Time Partial IGC Approach for Formation Flying with Collision Avoidance

A finite-time stable non-linear partial integrated guidance and control algorithm is proposed for formation flying. A Lyapunov based proof for the outer loop of the integrated guidance and control philosophy is furnished to provide an a priori guarantee of a collision-free guidance trajectory. The guidance and control structure retains the advantages of the time scale separation between the translational and rotational dynamics explicitly while also preserving the integrated two loop structure. Numerical simulation is presented to show the suitability of the proposed algorithm that takes advantage of the latest results in the area of non-linear finite time control